HELP!!!

Scott and Mark are rock climbing.



Scott is at the top of a 75‑foot cliff, when he throws a 96‑foot rope straight down to Mark, who is on the ground directly below.



If the rope is stretched tightly from Mark’s feet to Scott’s feet, how far over from the base of the cliff s Mark standing?

The exact values of the trigonometric functions for an angle are:

The direction of an angle (θ), in degrees, with respect to origin is determine by coordinates on the terminal side. For a point in rectangular format we can determine the exact values of two fundamental trigonometric functions (sine, cosine) and four derivate trigonometric functions (tangent, cotangent, secant, cosecant:

For P(x, y) = (x, y)

Sine

sin θ = y / √(x² + y²)

Cosine

cos θ = x / √(x² + y²)

Tangent

tan θ = sin θ / cos θ

Cotangent

cot θ = 1 / tan θ

Secant

sec θ = 1 / cos θ

Cosecant

csc θ = 1 / sin θ

If we know that x = 2 and y = - 7, then exact values of trigonometric functions are, respectively:

Sine

sin θ = - 7 / √[2² + (- 7)²]

sin θ = - 7 / √53

sin θ = - 7√53 / 53

Cosine

cos θ = 2 / [2² + (- 7)²]

cos θ = 2 / √53

cos θ = 2√53 / 53

Tangent

tan θ = [- 7√53 / 53] / [2√53 / 53]

tan θ = - 7 / 2

Cotangent

cot θ = 1 / (- 7 / 2)

cot θ = - 2 / 7

Secant

sec θ = 1 / (2 / √53)

sec θ = √53 / 2

Cosecant

csc θ = 1 / (- 7 / √53)

csc θ = - √53 / 7

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Answer:

Choice B

Step-by-step explanation:

The y increases by 3 every time that the x increases by 1.

Hope this helped! :)

Answer:

first number= -2 and the second number = 2

Step-by-step explanation:

x= one number and y= the other

your two equations are x+y=4x+8 and  x-y=3y-10

by solving the first one for y, y=3x+8 so plug that in for y in the second equation

x-(3x+8)=3(3x+8)-10

x-3x-8=9x+24-10

-2x-8=9x=14

11x=-22 so x=-2

now plug that in and solve for y

-2+y=4(-2)+8

y=2

When the ellipse has co-vertices at (4,0) and foci at (0,+-4), the equation is y2/32+x2/16=1.

The algebraic equation y=mx+b is known as a linear equation. M serves as the y-intercept, and B serves as the slope. The previous clause has two variables, y and x, and is sometimes referred to as a "linear equation with two variables". Bivariate linear equations are those with two independent variables. The following are a few examples of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation takes the form y=mx+b, with m denoting the slope and b denoting the y-intercept, it is referred to as being linear. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

The center is

=(0,0)

The equation is

y2/a2+x2/b2=1

b=4

c=4

a2=b2+c2

=16+16=32

When the ellipse has co-vertices at (4,0) and foci at (0,+-4), the equation is y2/32+x2/16=1.

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Answer: with ?

Step-by-step explanation:

The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line.

The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line

Given here: The inequality y≥ -x/3 +1

Now, To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.

Therefore y=-x/3 +1 is a line in slope-intercept form with slope=-1/3 and y-intercept 1

Thus the line should intersect the y-axis  at y=1 and the x-axis at x=3

∴ The graph of this equation is plotted in attached file.

Hence, The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line.

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Answer:

A

Step-by-step explanation:

i took the test xx

An equivalent expression to 7.5 + s using commutative property is; s + 7.5

The commutative property under addition is an algebra property that states that the change in the order of numbers in an addition operation does not change the sum.

This means that for any real numbers x, y, we have;

x + y = y + x

The commutative property under multiplication states that the change in the order of numbers in multiplication operation does not change the product.

This means that for any real numbers c, d we have;

c × d = d × c

We want to find n equivalent expression to 7.5 + s using commutative property. Thus, we will apply the commutative property of addition as followd; 7.5 + s = s + 7.5

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Answer:

$20 per square foot

Step-by-step explanation:

[tex]8.2x-3.7x=90 \\ \\ 4.5x=90 \\ \\ x=20[/tex]

If the mid point of AB is M (-4,-3). and the coordinates of A are (-1,-2), the coordinates of B is solved to be (-7, -4)

The midpoint of a line segment is the centroid of the segment. It is equally distant from both of the ends and hence cuts the section in half.

The formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

From the formula the second end point is calculated

-4= (-1 + x₁)/2

-8 = -1 +  x₁

x₁ = -7

-3 = (-2 + y₁)/2

-6 = -2 + y₁

y₁ = -4

The coordinates of B are (-7, -4)

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The known quantities are then identified using the visual overview as a guide, and they are q1 q2 q3 x1 and x2. The unknown quantity is then x3

Based on the details provided;

e charge 1 is located at the origin of the x-axis and the positive x-axis points to the right. Let x1, x2, and x3 denote the positions of charge 1, charge 2, and charge 3, respectively

Considering that charge 1 is thought to be at the source;

The known quantities are then identified using the visual overview as a guide, and they are:

q1 q2 q3 x1 and x2

However, given that we are unsure of its precise position x3,

The unknown quantity is then x3

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CV stands for standard deviation divided by sample mean multiplied by 100.

CV = (std. deviation*100)/mean = 41.2 %

for SAT score:

CV = (std. deviation*100)/mean = 17.55%

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Answer: 220

Step-by-step explanation:

Create ratios using fractions, one for the students, and one for the percent

students: [tex]\frac{11}{x}[/tex]  percents: [tex]\frac{5}{100}[/tex]

Then cross multiply 1. [tex]11 *100 = 1100[/tex], 2. [tex]1100 / 5 = 220[/tex]

So [tex]x = 220[/tex], this means there are a total of 220 students in 7th grade

The area of the mirror is 480 square inches

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

A mirror that has the shape of a parallelogram (see attachment)

From the attachment, we have the following dimensions

Base length = 5 units

Height = 6 units

The area is the product of the dimensions

Since the side length of each square tile is 4 in, then we have

Area = 4 * 4 * 5 * 6

Evaluate

Area = 480

Hence, the area is 480 square inches

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The simplified form of (f o g)(x) = 8x²  + 8x + 4.

Differentiation is a process in calculus that is used to find the rate of change of a function at a specific point. It is the process of finding the derivative of a function.

To find (f o g)(x), we need to first find g(x) and then substitute that expression into f(x).

Given:

f(x) = 2x + 4

g(x) = 4x²  + 4x

So:

(f o g)(x) = f(g(x)) = f(4x²  + 4x) = 2(4x²  + 4x) + 4

Now we can substitute the expression for g(x) into f(x) and simplify:

= 2(4x²  + 4x) + 4 = 8x²  + 8x + 4

Hence, (f o g)(x) = 8x² + 8x + 4

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The value of k from the equation is k = 4

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

f ( x ) = ( 2 - k ) / ( 5x + k )   be equation ( 1 )

Now , the equation passes through the point P ( 3 , -2/19 )

On simplifying the equation , we get

Substituting the values of x and y in the equation , we get

y = ( 2 - k ) / ( 5 ( 3 ) + k ) )

-2/19 = ( 2 - k ) / ( 15 + k )

Multiply by ( 15 + k ) on both sides of the equation , we get

-2 ( 15 + k ) / 19 = 2 - k

Multiply by 19 on both sides of the equation , we get

-30 - 2k = 38 - 19k

Adding 2k on both sides of the equation , we get

38 - 17k = -30

Subtracting 38 on both sides of the equation , we get

17k = 68

Divide by 17 on both sides of the equation , we get

k = 4

Hence , the value of k = 4

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The total volume of glass that makes up the globe to the nearest hundredth is equal to 12,771.71 cubic centimeters.

Mathematically, the volume of a sphere can be calculated by using this mathematical expression:

Volume = 4/3 × πr³

Where:

r represents the radius.

Based on the information provided about the globe, the diameter of the hollow sphere is given by;

Diameter of sphere = 30 cm

Radius = diameter/2 = 30/2 = 15 cm.

Actual radius = 15 cm - 0.5 cm = 14.5 cm.

Substituting the given points into the volume of a sphere formula, we have the following;

Volume of sphere = 4/3 × 3.142 × 14.5³

Volume of sphere = 12,771.71 cubic centimeters.

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The proof for the side AB congruent to side ED is given below.

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

Given that

C is the intersecting point of AD and EB.

Side AC is congruent to side EC.

Also ∠A = ∠E

By vertical angles theorem, a pair of intersecting lines form 2 pairs of vertically opposite angles which are equal.

Therefore, ∠ACB = ∠ECD

Also given that sides AC and EC are congruent.

By ASA congruence theorem, if two angles and an included side of a triangle is equal to the corresponding two angles and included side of another triangle, then the triangles are congruent.

So triangles ABC and CDE are congruent.

C is the common point for both the triangles.

So the side opposite to C are AB and ED.

So they are equal and thus congruent.

Hence the sides AB and ED are proved to be congruent.

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The required function g(x) = 4x² and the related graph is a parabola that is opened upwards on the x-axis  

The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. This means that when we replace x - coordinate with a numerical value in the expression, we get the y-value for the given function f(x).

Here we have

f(x) = x²  

Given that g(x) = f(2x)

To find the g(x) take x = 2x

=> f(2x) = (2x)²

=> g(x) = 4x²  

Therefore,

The required function g(x) = 4x² and the related graph is a parabola that is opened upwards on the x-axis  

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An equation of the line in slope-intercept form that passes through the point (1, 17) and has a slope of 1 is equal to y = x + 16.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Given the following parameters:

Substituting the given parameters into the point-slope formula, the equation of the line in is slope-intercept form given by;

y - y₁ = m(x - x₁)

y - 17 = 1(x - 1)

y = x - 1 + 17

y = x + 16

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A grid that correctly graphs the points A (3, 1), B (0, 3), and C (1, 3) include the following: B. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 3 units to the right and 1 unit above the origin. Point B is plotted 3 units above the origin. Point C is plotted 1 unit to the right and 3 units above the origin.

In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs (data points) on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis (x-coordinate) and y-axis (y-coordinate) respectively.

Next, we would use an online graphing calculator to plot the above set of data points with a point of intersection at (2, 3) as shown in the graph attached below.

By critically observing graph B of the given set of data points, we can logically deduce that it correctly graphs the points A(3, 1), B(0, 3), and C (1, 3) as shown in the image attached below.

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Complete Question:

Which of the following grids correctly graphs the points A (3, 1), B (0, 3), and C (1, 3)?

A. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 3 units to the right and 1 unit above the origin. Point B is plotted 3 units to the right of the origin. Point C is plotted 1 unit to the right and 3 units above the origin.

B. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 3 units to the right and 1 unit above the origin. Point B is plotted 3 units above the origin. Point C is plotted 1 unit to the right and 3 units above the origin.

C. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 1 unit to the right and 3 units above the origin. Point B is plotted 3 units above the origin. Point C is plotted 3 units to the right and 1 unit above the origin.

D. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 1 unit to the right and 3 units above the origin. Point B is plotted 3 units to the right of the origin. Point C is plotted 3 units to the right and 1 unit above the origin.

Answer:c

Step-by-step explanation:

c

Answer:b

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given m = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (- 6, 5 ) into the partial equation

5 = [tex]\frac{1}{3}[/tex] (- 6) + c = - 2 + c ( add 2 to both sides )

7 = c

y = [tex]\frac{1}{3}[/tex] x + 7 ← equation of line

The statements which are always true in the triangle with interior angles, ∠2, ∠3, and m∠5, and exterior angles, ∠1, ∠4, and ∠5 are;

m∠5 + m∠6 = 180°

m∠2 + m∠3 = m∠6

m∠2 + m∠3 + m∠5 180°

An exterior angle is an angle that is formed by the extension of a side of the triangle and the side adjacent to the extended side.

The interior angles of the triangle are; angle ∠2, angle ∠3, and angle ∠5

The exterior angles at the interior angles of the triangle ∠2, ∠3, and ∠5 are angles  ∠1, angle ∠4, and angle ∠6 respectively.

Therefore, according to the exterior angle theorem, we get;

m∠1 = m∠3 + m∠5

m∠4 = m∠2 + m∠5

m∠6 = m∠2 + m∠3

The exterior angle and the adjacent internal angle are supplementary angles, therefore;

m∠2 + m∠1 = 180°

m∠3 + m∠4 = 180°

m∠5 + m∠6 = 180°

The angle sum property of a triangle indicates that the sum of the interior angles of a triangle is 180°, therefore;

m∠2 + m∠3 + m∠5 = 180°

The statements that are always true are therefore;

m∠5 + m∠6 = 180°

m∠2 + m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

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Answer:

yes

Step-by-step explanation:

Out of the given statements, statement a. If 4 is a prime number, then 6 is a prime number is the false one. A prime number is a positive integer that has exactly two distinct natural number divisors: 1 and itself.

For example, the number 2 is a prime number because it can only be divided evenly by 1 and 2. 4 is not a prime number because it can be divided evenly by 1, 2, and 4. 6 can be divided evenly by 1, 2, 3, and 6, so it is not a prime number. Therefore, statement a is false because if 4 is a prime number, 6 is not a prime number.

When determining whether a number is a prime number, it is important to remember that 1 is not a prime number. This is because 1 only has one divisor - itself. Any other number that can be divided evenly by more than two distinct natural numbers is not a prime number.

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The point (2,-4) satisfies y < 3x - 6