Fill in the Blank: Solve the following system of linear equations graphically. Then, fill in the blanks below with the solution.

Equation #1: y=14x−2
Equation #2: y=x+1



The solution to the system of equations is the ordered pair (
,
)

Answer:

7.4

Step-by-step explanation:

Use Pythagorean Theorem: [tex]a^2+b^2+c^2[/tex]

In this case we have a and c. So let's plug those into the equation:

[tex](6.7)^2+b^2=10^2[/tex]

[tex]44.9+b^2=100[/tex]

[tex]b=\sqrt{55.1}[/tex]

[tex]b=7.4[/tex]

Answer:

First option: 4.9 in

Step-by-step explanation:

The area of a circle, given radius = r is computed using the formula
A = πr²

Here we are given the area and asked to find the radius r

A = 75.43 in² = πr²

So
πr² = 75.43
r² = 75.43/π
   = 24.01
   = 24 rounded to nearest integer

r = √24
  = 4.9

Answer:

$60

50×3=150

182-150=32

so Sally made 3 $50 so 20+20+20=60

Answer:

15.81 ft

Step-by-step explanation:

Basically it's giving your 2 sides of the right angle triangle & ask you for the long side length.

15²+5²=250

√250 =15.81

Answer:

956 centimeters is equal to 9.56 meters.

How many meters are in 956 centimeters?

Well, first, we must understand the conversion from meters to centimeters and centimeters to meters.

1m=100cm and 1cm=0.01m. So multiply by 100 if converting from m to cm and divide by 100 if converting from cm to m.

In this problem, we're looking at cm to m.

Take 956cm and divide that by 100. You'll get 9.56m. That's your answer.

Hope this helped!

The midpoint is given by the coordinates M ( 6 , 7.5 )

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

Measure the distance between the two end points, and divide by 2.

Let A ( x₁ , y₁ ) be the first point

Let B ( x₂ , y₂ ) be the second point

The midpoint between A and B is M ( a , b ) where

a = ( x₁ + x₂ )/2

b = ( y₁ + y₂ ) / 2

Given data ,

Let the midpoint of gazebo and the ice cream shop in town be M ( a , b )

Now , the equation will be

The coordinates of the point Gazebo = G ( 10 , 12 )

The coordinates of the point Ice Cream = C ( 2 , 3 )

Now , midpoint between A and B is M ( a , b ) where

a = ( x₁ + x₂ )/2

b = ( y₁ + y₂ ) / 2

Substituting the values in the equation , we get

a = ( 10 + 2 ) / 2

a = 12 / 2

a = 6

b = ( 12 + 3 ) / 2

b = 15 / 2

b = 7.5

So , the coordinates of the midpoint is M ( 6 , 7.5 )

Hence , the midpoint is M ( 6 , 7.5 )

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The average rate of change for the given function is -72.

What Is the Average Rate of Change?

To determine the slope of a graphed function, use the average rate of change formula. Divide the change in y-values by the change in x-values to determine the average rate of change. To determine the slope of a graphed function, use the average rate of change formula. Divide the change in y-values by the change in x-values to determine the average rate of change.

The rate of the change for the interval [a,b] is given by

[tex]\frac{f(b)-f(a)}{b-a} \\[/tex]

For the given interval [3,11],

[tex]= \frac{f(11)-f(3)}{11-3} \\\\= \frac{-623+47}{8} \\\\= -72[/tex]

So, the required average rate of change is -72.

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Answer:

3C ÷ 21 = 63 C = 21

great question BTW

The value of proportionality is not same.So the it is not proportional.

Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.

Let

y ∝ x

y = kx , k is constant

Take x = 2, y = 3

3 = k(2)

k = 3/2 = 1.5

At x= 4, y = 7

7 = k(4)

k = 7/4 = 1.75

The value of proportionality is not same.So the it is not proportional.

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Answer:

Step-by-step explanation:

Here are three ways to compare A and B, where A= 51,102 is the number of deaths due to a deadly disease in the United States in 2005 and B= 17,056 is the number of deaths due to the same disease in the United States in 2009:

Magnitude: A is approximately three times larger than B. This means that the number of deaths due to the disease was significantly higher in 2005 than in 2009.

Trend: There was a significant decrease in the number of deaths due to the disease between 2005 and 2009. The number of deaths decreased by approximately 67%, from 51,102 in 2005 to 17,056 in 2009.

Impact: Despite the significant decrease in the number of deaths, the disease still caused a significant number of deaths in both 2005 and 2009. This highlights the ongoing importance of disease prevention and treatment efforts to reduce the impact of the disease on public health.

Answer:

not sure but slope doesn't belong

Step-by-step explanation:

Answer: To find the height of the roof, we need to find the point where the ball reaches the maximum height, i.e., the point where the velocity of the ball is equal to 0.

The velocity of the ball can be found by taking the derivative of the function s. The derivative of the function s = −t^2 + 3t + 4 is given by v = ds/dt = 3 − 2t, and the derivative of the function s = −2t^2 + t + 7 is given by v = ds/dt = 1 − 4t.

Setting v = 0, we get 3 − 2t = 0 and t = 3/2 seconds.

Plugging t = 3/2 seconds into the first equation, s = −t^2 + 3t + 4, we get s = −(3/2)^2 + 3(3/2) + 4 = 9/4 + 9/2 + 4 = 7 metres.

Therefore, the height of the roof from the ground is 7 metres.

Step-by-step explanation:

A rational function does not have any factors in the denominator that can be equal to 0, then it will not have a vertical asymptote.

An even degree  must be an even function is true. This is because a polynomial with an even degree has an even-numbered power, such as f(x)=x^2. This means that the function is symmetrical when its graph is reflected over the y-axis. This means that the graph will look the same if the x-values are reflected over the y-axis. For example, if f(3)=9, then f(-3)=9 as well.

Every polynomial of odd degree has at least one zero is true. This is because a polynomial with an odd degree will always have at least one x-value for which the equation is equal to 0. This is because the highest power of the equation must be odd, and the equation must cross the x-axis at least once. For example, f(x)=x^3 will have at least one x-value, such as x=0, where f(x)=0.

Every rational function that is not a polynomial has a vertical asymptote is false. A rational function that is not a polynomial may have a vertical asymptote, but it is not guaranteed. A vertical asymptote is created when the denominator of a rational equation has a factor that is equal to 0. This means that when this factor is equal to 0, the equation has an undefined value. If a rational function does not have any factors in the denominator that can be equal to 0, then it will not have a vertical asymptote.

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Answer: The annual percentage yield for Rahela's account can be calculated by finding the effective annual interest rate, which takes into account the frequency of compounding. The effective annual interest rate is calculated as follows:

Effective annual interest rate = (1 + (6.5/2))^2 - 1 = 6.6725%

So, the annual percentage yield for Rahela's account is 6.6725%.

Step-by-step explanation:

The factors of the quadratic function  x² - 2x - 4  is equal to

(x + 1 + √5)(x - 1 + √5)

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, The zeros of the quadratic function x² - 2x - 4  are,

(1 + √5) and (1 - √5). (As they occur in conjugate pairs).

Therefore, The factors of (x + (1 + √5))(x + (x - (1 - √5))

x² - 2x - 4 = (x + 1 + √5)(x - 1 + √5)

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Answer:

im pretty sure ia 31,61

Step-by-step explanation:

Answer: 10⁰

Step-by-step explanation:

We know that,

 the summation of 3 angles of a triangle is 180⁰.

now, (6x-5)⁰+(5x-5)⁰+8x⁰=180

 or, 19x-10=180⁰

 or, 19x=190⁰

 or, x= (190/19)⁰

 or, x= 10⁰

Answer:

60%

Step-by-step explanation:

12/20 = 3/5 = 0.6 = 60%

Hey there! To find out how much of her homework Jewel completed, all we need to do is a little math. First, let's divide the number of questions she did by the total number of questions. That's 12 divided by 20 which equals 0.6.

Now, we just need to turn that decimal into a percentage. To do that, we simply multiply 0.6 by 100, which gives us 60. And voila! Jewel completed 60% of her homework.

Solving the quadratic equation, we found that the object is at a height of 269 feet when t is 1.99s and 8.55s and the object reaches the ground when t = 9.78s.

What is a quadratic equation?

Any equation in algebra that can be written in standard form:

          ax² + bx + c =0

where x stands for an unknown value, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.

The given equation of height h = -16t² + 156t +5

a) The time when the height is 269 feet can be found by substituting this value for h in the above equation.

            h = -16t² + 156t +5

         169 = -16t² + 156t +5

         16t² - 156t + 164 = 0

     Solving we get t = 8.55 s, 1.99s

b) The time when the object reaches the ground.

For this, we can take h = 0

   -16t² + 156t +5 = 0

  t = -0.03, 9.78

The negative value can be ignored.

Therefore solving the quadratic equation, we found that the object is at a height of 269 feet when t is 1.99s and 8.55s and the object reaches the ground when t = 9.78s.

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Therefore , the solution of the given problem of function comes out to be Since 4 > 2, function A has a greater rate of change than function B.

The mathematics curriculum covers the study of numbers or rather their variations as well as in our environment, buildings, and both actual and imagined locations. A function presents a graph representation of the relationship between input and output quantities. A function, expression simply, is a collection of sources that, when combined, result in particular outputs by each input. There is a locale, territory, or range assigned to each job.

Here,

The rate of change of a linear function is the slope of the line.

Function A is y = 4x - 3, so the rate of change (slope) is 4.

To find the rate of change of function B, we can calculate the slope of the line passing through the points given in the table. Using the two points (1,4) and (5,12), we get:

slope = (change in y) / (change in x) = (12-4) / (5-1) = 2

So the rate of change of function B is 2.

Since 4 > 2, function A has a greater rate of change than function B.

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Before any taxes, deductions, and other adjustments, she earns $98.40 per week.

Gross pay refers to the total amount of money an employee earns before any deductions or taxes are taken out. It is the total amount of money earned by an employee for the hours worked, including any overtime or bonuses.

here, we have,

To calculate Talia's gross pay for a week, we need to know how many hours she works per day and her pay rate.

You've provided that information:

Talia works 6 hours per day on Fridays and Saturdays each week.

Her pay rate is $8.20 per hour.

First, we need to find out how many hours she works a week. As she works 6 hours on Friday and 6 hours on Saturday, the total hours she works in a week is 6 hours/day x 2 days/week = 12 hours/week.

Next, we need to multiply her hourly rate by the number of hours she works per week to find her gross pay. Her pay rate is $8.20/hour and she works 12 hours/week, so her gross pay is:

$8.20/hour x 12 hours/week = $98.40/week

So, Talia's gross pay for a week is $98.40.

Therefore, before any taxes, deductions, and other adjustments, she earns $98.40 per week.

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Answer:

y = 14x - 1

Step-by-step explanation:

By equation of the line, we mean the slope intercept form equation [tex]y=mx+b[/tex] where m is the slope and b is the y intercept. As a result, we are given the slope and the y intercept in the problem. So we can use this to write our equation

[tex]y=14x-1[/tex]

Hope this helps!

The probabilities of all the events related to drawing two marbles without replacement are discussed below.

What is meant by probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given,

  Number of blue marbles B = 2

 Number of red marbles R = 3

Number of marbles drawn = 2

a) Sample points are different possible combinations.

  { R,R} , {R,B}, {B, R}, {B,B}

b) Probablitiy of  { R,R} = 3/5 * 2/4 = 6/20 = 3/10 = 0.3

    Probablitiy of {R,B} = 3/5 * 2/4 = 0.3

    Probablitiy of {B,R} = 2/5* 3/4 = 0.3

     Probablitiy of {B,B} = 2/5 * 1/4 = 0.1

c) A: { Two blue marbles are drawn. }

    Probability = 2/5 * 1/4 = 0.1

  B:{ A red and a blue marble are drawn. }

 Probability = 0.3 ( from above)

C:{ Two red marbles are drawn. }

 Probability = 0.3 (from above)

Therefore the different sample points are found and probabilities of different events are also found.

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The equations that represent the balance A after m months are given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For this problem, we have that each month, the balance increases by 100, hence the slope m is given as follows:

m = 100.

Hence:

y = 100x + b.

When x = 5, y = 1200, hence the intercept b is given as follows:

1200 = 500 + b

b = 700.

Hence these following two equations are correct:

Taking the fifth month as the initial month, we consider an intercept of 1200, hence the final equation is given as follows:

A = 1200 + 100(m - 5).

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Step-by-step explanation:

Classmate Conjecture

John | All circles are similar if they have the same center and can be dilated or contracted to the same size.

Teresa | All circles are similar if their corresponding radii have a constant ratio.

Evaluate the Conjectures:

2. Yes, it makes intuitive sense that all circles are similar because they all have the same shape and form.

Construct the Circles:

3. [Diagram not provided]

[Diagram not provided]

The hypotenuse of △ABC is the diameter of the smaller circle.

[Diagram not provided]

The hypotenuse of △XYZ is the diameter of the larger circle.

The two triangles, △ABC and △XYZ, are similar because they are both isosceles right triangles with the same angle measures.

The ratio of the lengths of their sides are equal, therefore the ratio of their radii is a constant.

Making a Decision:

10. Both John and Teresa were right as all circles are similar if they have the same center and can be dilated or contracted to the same size (John's method) and also if their corresponding radii have a constant ratio (Teresa's method).

Further Exploration:

11. The circumference of the circle that circumscribes a triangle with side lengths 3, 4, and 5 can be found using the Pythagorean theorem to find the diameter of the circle, which is equal to the sum of the lengths of the three sides. The diameter is equal to 5, so the circumference is equal to 2 * pi * (5 / 2) = 5 * pi

Please provide all information when asking a question

The length of the triangle is given by the equation L = 15.9 yards

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the length of the triangle be represented as L

Now , the equation will be

Let the base of the triangle be represented as W

Now , the value of W = 8 yards

The area of the triangle = 63.6 yards²

Now , Area of the triangle = ( 1/2 ) x Length x Base

Substituting the values in the equation , we get

Area of the triangle A = ( 1/2 ) x 8 x L

4L = 63.6

Divide by 4 on both sides of the equation , we get

L = 15.9 yards

Hence , the length of the triangle is 15.9 yards

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The required domain of the function If g(x) = f(-2x) is [-16, 8] in interval notation.

The domain of g(x) is the set of all x for which the function g(x) is defined. If g(x) = f(-2x), then the domain of g(x) is the same as the domain of -2x, subject to the restriction that f(x) is defined for the corresponding values of x.

In interval notation, the domain of -2x is (-∞, ∞).

However, since f(x) is defined only on the interval [-8, 4], the domain of g(x) must be restricted to values of x that correspond to values of -2x within the interval [-8, 4].

To find the corresponding values of x, we need to solve the equation -2x = t for x, where t is a number in the interval [-8, 4].

Solving for x, we get x = -t/2. So, the domain of g(x) is the set of all x such that -t/2 is in the interval [-8, 4], or equivalently, t is in the interval [-16, 8]. In interval notation, this is [-16, 8].

So, the domain of g(x) is [-16, 8] in interval notation.

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The area needed to be iced is 263.76 inches².

The circular cake is 12 inches in diameter and 4 inches high. The side and top of the cake are to be covered with icing. The area of the cake that will be iced can be found as follows;

The area to to be iced is the top and the lateral area.

Therefore,

area to be iced = πr² + 2πrh

area to be iced = πr(r + 2h)

Therefore,

r = 12 / 2 = 6 inches

h = 4 inches

Hence,

area to be iced = 6π(6 + 2(4))

area to be iced = 6π(14)

area to be iced = 84π

area to be iced = 263.76 inches²

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We can use the two points given to find the slope of the line (which represents the population growth) and then use the point-slope form of the equation of a line to write an equation.

The population at time t=4 is 1580, which means P(4) = 1580. The population at time t=7 is 2000, which means P(7) = 2000. We can use these two points to find the slope:

slope = (P(7) - P(4)) / (7 - 4) = (2000 - 1580) / 3 = 140

So the slope of the line representing population growth is 140. Now we can use the point-slope form of the equation of a line to write an equation:

P - 1580 = 140(t - 4)

Simplifying and rearranging, we get:

P = 140t - 380

So the correct equation that represents the situation is:

P(t) = 140t - 380.