Which represents the solution(s) of the system of equations, y + 4 = x² and y - x = 2?
graphing.
O (-2, 0)
O (-2, 0) and (2, 0)
O (-2, 0) and (3, 5)
Ono solutions

Statement-Reason Proof:

If the circle has center O, then:

1.) BD = CA [Definition of Diameters of a Circle]

2.) Angle BAD = Angle CDA [Angle of Semicircle are Right Angles (90°)]

3.) AD = AD [Reflexive Property]

4.) Triangle DCA ≅ Triangle ABD [RHS Congruency Rule]

The distance between the points (-3.5, 0), and (1.5, 0), shown on the coordinate plane, obtained using the distance formula; is 5 units

The correct option is; 5 units

The distance formula is a formula that can be used to calculate the distance between the points (x₁, y₁), and (x₂, y₂) on the coordinate plane using the following equation;

d = √((x₂ - x₁)² + (y₂ - y₁)²).

The distance between the points (-3.5, 0), and (1.5, 0), on the graph can be obtained using the distance formula which is; d = √((x₂ - x₁)² + (y₂ - y₁)²

Where;

(x₁, y₁) = (-3.5, 0)

(x₂, y₂) = (1.5, 0), we get;

d = √((1.5 – (-3.5))² – (0 – 0)²) = 5

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Answer:

x = 8

Step-by-step explanation:

We can write the following equation to find the value of x based on above mentioned information:

10x - 20 = 7x + 4

10x - 7x = 20 + 4

3x = 24

x = 8

To find each angle measure, replace x with 8:

10x - 20 would be 10 × 8 - 20 = 60

Since angles are congruent the other one also would be 60°.

Answer:

a = 2

Step-by-step explanation:

Geometric series:

          r = 3

          n = 6

         [tex]S_n=728[/tex]

      [tex]\boxed{\bf S_n = \dfrac{a(r^n - 1)}{r- 1}}[/tex]

           [tex]\dfrac{a*(3^6 - 1)}{3-1}=728\\\\ \dfrac{a * (729 -1)}{2}= 728\\\\ \dfrac{a * 728}{2} = 728[/tex]

                   [tex]a = 728 * \dfrac{2}{728}\\\\a = 2[/tex]

Amplitude of attached graph is 800 and here amplitude explains the maximum change in volume as compare to average volume.

Let us consider two point on the attached graph.

Lowest point as ( 0.5, 1000 )

Highest point as ( 2.5 , 2600 )

In a periodic function the volume of air in a person's lungs over time,

The amplitude is the distance between the maximum value of the function and its average value.

It is represented by y-coordinate.

Amplitude  = ( 2600 - 1000 ) / 2

                  = 1600 / 2

                   = 800

In the context of the volume of air in a person's lungs,

The amplitude represents the maximum change in the volume of air from the average volume.

This is an important measure of lung function.

As it indicates how much air a person can take in and expel from their lungs with each breath.

The higher the amplitude, the greater the lung capacity and respiratory function of the person.

Therefore, the amplitude in the graph is equal to 800 and it represents the maximum variation in the volume of air from the average volume.

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The above question is incomplete, the complete question is:

The volume of air in a persons lungs can be molded with a periodic function the graph below represents the volume of air ,in mL, in a persons long overtime measured in seconds, t. What is the amplitude and what does it represent in this context?

Graph is attached.

Answer:

The slope of the curve ƒ(x) = x^2 + 2 at x = 3 can be found by taking the derivative of the function with respect to x and evaluating it at x = 3.

ƒ(x) = x^2 + 2

Taking the derivative:

ƒ'(x) = 2x

Substituting x = 3:

ƒ'(3) = 2(3) = 6

Therefore, the slope of the curve ƒ(x) = x^2 + 2 at x = 3 is 6.

The area of the triangle is 4.64 square meters and that of the trapezoid is 61.6 square inches.

A triangle is a type of polygon, which has three sides, and the two sides are joined end to end is called the vertex of the triangle. An angle is formed between two sides.

A trapezoid is a polygon that has only one pair of parallel sides. These parallel sides are also called parallel bases of trapezoid. The other two sides of trapezoids are non-parallel and called legs of trapezoids.

The formula for the area of a triangle is:

A = (1/2) * b * h

where b is the base of the triangle and h is the height of the triangle.

Substituting the given values, we get:

A = (1/2) * 2.9 m * 3.2 m

A = 4.64 square meters

Therefore, the area of the triangle is 4.64 square meters.

The formula for the area of a trapezoid is:

A = (a + b) * h / 2

where a and b are the lengths of the parallel bases, and h is the height of the trapezoid.

Substituting the given values, we get:

A = (10 + 12) * 5.6 / 2

A = 22 * 2.8

A = 61.6 square inches

Therefore, the area of the trapezoid is 61.6 square inches.

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It seems that the problem solved incorrectly is the one represented by letter A, which is trying to find the missing angle in a triangle. The correct answer is 74.1°, which can be obtained by subtracting the sum of the other two given angles (83.2° and 22.7°) from 180°.

The problem that Anna solved incorrectly is the last one: 32 + x = 108. The correct answer should be x = 76, not x = 108.

In this math problem, Anna seems to be solving for unknown angles in several triangle problems. An important principle here is that the sum of the angles in a triangle always adds up to 180 degrees. Looking at the problems she solved:

So, the problem that was solved incorrectly is the last one: 32 + x = 108.

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I believe you meant to write the expression as follows: 71 = -8x + 7y + 7z + 5. This equation represents a relation between the values of x, y, and z in a rhombus where 71 is the sum of the diagonals of the rhombus.

How to calculate value of x,y and z for the given rhombus?

To solve for x, y, and z, we need to use additional information about the rhombus. Without any further information, we cannot determine unique values for x, y, and z.

However, we can make some observations based on the given equation:

The coefficient of x is negative (-8), which means that increasing x would decrease the value of the left-hand side of the equation. Therefore, we can conclude that x must be positive to satisfy the equation.

The coefficients of y and z are positive (7 and 7, respectively), which means that increasing y and/or z would increase the value of the left-hand side of the equation. Therefore, we can conclude that y and z must be non-negative to satisfy the equation.

With these observations in mind, we can come up with multiple solutions for x, y, and z that satisfy the given equation. Here are a few examples:

If we let x = 0, y = 11, and z = 9, then the equation is satisfied:

71 = -8(0) + 7(11) + 7(9) + 5

71 = 77

If we let x = 2, y = 10, and z = 8, then the equation is also satisfied:

71 = -8(2) + 7(10) + 7(8) + 5

71 = 71

Therefore, we cannot determine a unique solution for x, y, and z based on the given equation alone.

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As a result, point C's coordinates are (-3/2, -21/4) as the section formula to determine the coordinates of point C .

A point together in two-dimensional plane can be found using coordinates, which are pairs of numbers. Each point is represented by an ordered pair of absolute values (x,y), where x represents the horizontal coordinate and y represents the vertical coordinate, in the Cartesian geometry. The x-axis is the horizontal axis, while the y-axis is the vertical axis. The origin is the intersection of the two axes and bears the following coordinates: (0,0). A point's coordinates might be plus, negative, or zero depending on where it is in relation to the axes and the origin.

given

We may use the section formula to determine the coordinates of point C, which divides line segment AB in a ratio of 1:3.

Let point C's coordinates be (x, y). Next, we have

x = [(3/4) * (-2)] + [(1/4) * 6] = -3/2

y = [(3/4) * (-5)] + [(1/4) * 3] = -21/4

As a result, point C's coordinates are (-3/2, -21/4) as the section formula to determine the coordinates of point C .

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Answer: To make "w" the subject of the formula "P+aw=b", we need to isolate "w" on one side of the equation.

First, we can subtract "P" from both sides of the equation to get:

aw = b - P

Next, we can divide both sides of the equation by "a" to get:

w = (b - P) / a

Therefore, the solution is:

w = (b - P) / a

Step-by-step explanation:

Answer:

integers 3 and 18

Step-by-step explanation:

The team that has the largest overall size hat for their players is the Seahawks; they have a larger mean value of about 23 inches. The correct option is b.

The two most frequently used measures of center are mean and median. When we compare the mean numbers for the Pelicans and Seahawks, we can see that the Pelicans have a mean of roughly 22 inches and the Seahawks have a mean of roughly 23 inches.

Nevertheless, when the data is skewed or contains outliers, the mean may not be the best approximation of the center because the mean can be altered by extreme values or outliers. Thus, we also need to compare the median values. The median is the midway value in the ordered set of data.

Thus, the correct option is b, Seahawks; they have a larger mean value of about 23 inches.

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Answer:

Step-by-step explanation:

the right answer is b 23 inches seahawkS BRAINLIST and verified answer wanted

Using the formula for calculating monthly mortgage payments, with a loan amount of $210,000, yearly rate of 6% and time period of 30 years, the monthly mortgage payment comes out to be approximately $1,259.81.

The calculation that needs to be done here involves a formula related to annuities, which is what monthly mortgage payments are classified as. The formula used to calculate a monthly mortgage payment is:

[tex]M = P [r(1 + r)^n]/[(1 + r)^n - 1][/tex]

Where:
M = monthly mortgage payment
P = loan amount (present value)
r = monthly interest rate
n = total number of payments (or total number of periods)

Plugging our given values into the equation:

P = $210,000 (this is the loan amount)
r = 6/100/12 = 0.005 (this is the monthly interest rate)
n = 30 x 12 = 360 (this is the number of periods, ie the total number of monthly payments over 30 years)

By substituting these values, one can calculate that:

M = [tex]210,000[0.005(1 + 0.005)^3^6^0] / [(1 + 0.005)^3^6^0 - 1][/tex]

Calculating this, we get M ≈ $1,259.81

So, the monthly mortgage payment would be approximately $1,259.81.

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So, the quotient is. [tex]Q(x) = x^3 - x^2 - x + 1/(x - 2)[/tex], and the remainder is. [tex]R(x) = 1.[/tex]Therefore, we can write:

[tex]f(x) / d(x) = Q(x) + R(x) / d(x)\\f(x) / d(x) = x^3 - x^2 - x + 1/(x - 2) + 1/(x - 2)[/tex].

Algebraic division is the process of dividing one algebraic expression by another. It involves applying the same rules of arithmetic division but with algebraic terms instead of numbers.

In algebraic division, the dividend, which is the expression being divided, is written on the top, while the divisor, which is the expression doing the dividing, is written below it. The division process involves finding how many times the divisor can fit into the dividend, and then subtracting that amount from the dividend. This process is repeated until there is no remainder left.

To divide [tex]f(x) = x^4 - 2x^3 + x^2 - 2x + 1[/tex] by[tex]d(x) = x - 2,[/tex] we can use long division as follows:

[tex]x^3 - x^2 - x + 1/ (x - 2)[/tex]

[tex]x - 2 | x^4 - 2x^3 + x^2 - 2x + 1[/tex]

     [tex]-x^4 + 2x^3[/tex]

      -----------

      [tex]0 - x^2[/tex]

      [tex]0 + x^2[/tex]

          ----------

                [tex]- 2x[/tex]

               [tex]+ 2x[/tex]

                  -----

                      1

                      1

                      -

                      0

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Answer:

6

Step-by-Step Explanation:

if you were to move the bottom triangle to the top, it would make the parallelogram a perfect rectangle.

the area is 60 units^2.

area=length*width

and the one side is 10. 60/10 =6 so 6 units is the answer

The function for the graph of the parabola given in the picture attached will be Option (H). f(x) = x² - 6x -1

What is the equation of the parabola?

The equation of a parabola depends on its vertex and focus. There are two possible orientations for a parabola, depending on whether it opens upward or downward (in the case of a vertical axis of symmetry) or leftward or rightward (in the case of a horizontal axis of symmetry).

Equation of a parabola in vertex form:

Equation of a parabola in vertex form is given by,

         y = a(x - h)² + k

         Here, (h, k) is the vertex of the parabola

Given in the graph,

Vertex of the parabola → (0, 2)

Parabola passes through the origin (4, 8).

The equation of the graph with vertex (0, 2) will be,

y = a(x - 0)² + 2

Since, the parabola passes through (4, 8),

8 = a(4 - 0)² + 2

8 = 16a + 2

a = 6/16

Substitute the value of 'a' in the equation of the parabola,

y = a(x - 0)² + 2

y = 6/16(x - 0)² + 2

y = 2/8(x - 0)² + 2

y = x² - 6x + 9 - 9

y = x² - 6x -1

Hence, the function representing the graph will be f(x) = x² - 6x -1

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Answer:

there is no image so i cannot solve your question.

Step-by-step explanation:

According to trigonometry, the ground distance covered by the plane is approximately 478.7 feet, rounded to the nearest tenth.

What is trigonometry?

The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations.

The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations.

There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc).

The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.

To draw a diagram of the situation:

[tex]tan(28°) = opposite / adjacent\\tan(28^{0}) = 250 / x\\x = 250 / tan(28^{0})\\ x= 478.7 ft[/tex]

Therefore, the ground distance covered by the plane is approximately 478.7 feet, rounded to the nearest tenth.

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Assume Z is a regular, standard random variable. The answer is P(Z 1.2), which is written as P(Z 1.2) = (1.2) =. 8849.

An variables is just a sum that can change according to the fundamental math concept. The generic letters x, y, and z are often employed in mathematical expressions and equations. Thus a variable is a sign for a numeric value that is unknown.

Every feature, number, or amount that can be gauged or quantified is referred to as a variable. A statistic may also be referred to as a data item. Examples of variables include age, sex, company revenue and costs, birth country, capital expenditures, class grades, eye colour, and vehicle kind.

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The probability of Z being greater than 1.2 is 0.11507, or approximately 11.51% (rounded to two decimal places).

Probability is a mathematical concept that expresses the possibility or chance of an event happening.

A number between 0 and 1, with 0 signifying impossibility and 1 signifying certainty, is used to symbolize it.

The likelihood of an event occurring increases as the probability approaches 1.

To find the probability P(Z > 1.2) where Z follows a standard normal distribution, we need to use the standard normal distribution table or a calculator with a normal distribution function.

Using a standard normal distribution table, we look for the probability value that corresponds to a standard normal deviate of 1.2.

The table gives us the area under the standard normal curve to the left of 1.2, which is 0.88493. Therefore, the probability of Z being greater than 1.2 is:

P(Z > 1.2) = 1 - P(Z ≤ 1.2)

= 1 - 0.88493

= 0.11507

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The tower is approximately 95 meters(m) tall.

What is a meter?

A meter is the basic unit of length in the International System of Units (SI). It is defined as the distance light travels in a vacuum in 1/299,792,458 of a second.

What kind of unit is meter?

The meter is a unit of measurement for length or distance. It is commonly used in science, engineering, and daily life to measure the size or distance between objects.

According to the given information

Let's call the height of the tower h. We can use similar triangles to set up a proportion:

3 / 1.55 = h / 49.25

Simplifying this expression gives:

h = (3 * 49.25) / 1.55

h = 95.48

Rounding this answer to the nearest meter gives:

h ≈ *95 meters*.

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Answer:

Step-by-step explanation:

blank 1. no

blank 2. not constant because it is a nonlinear function.

Answer: The Missouri Compromise of 1820 was a landmark agreement in American history that temporarily resolved the issue of slavery in the western territories. The compromise was driven by a sense of nationalism among Americans in the early 1800s, who were concerned about preserving the unity of the country and avoiding the outbreak of civil war.

The Missouri Compromise reflected this sense of nationalism by seeking to maintain a balance of power between the slave states and the free states. The compromise allowed Missouri to enter the Union as a slave state, but it also admitted Maine as a free state, and prohibited slavery in any new states formed north of the 36°30′ parallel. By preserving this balance of power, the Missouri Compromise helped to ease tensions between the North and the South, and prevent the outbreak of civil war for several decades.

John Quincy Adams's diary entry provides some insights into the political climate of the time, and the debates surrounding the Missouri Compromise. In his diary entry of February 24, 1820, Adams writes:

"The Missouri question still hangs over us like a black cloud. The ground of the controversy is evidently an apprehension of the preponderance of power in the Union, which by some is feared to be passing from the South to the North."

This quote suggests that there was a growing concern among some Southerners about the balance of power in the Union, and that this concern was driving the debates over the Missouri Compromise. Adams goes on to describe the debates in Congress, noting that "the debates upon the Missouri question are exceedingly able, ingenious, and eloquent." He also provides some insights into the strategies being used by different sides of the debate, noting that "the argument for restriction upon Missouri, is that it will preserve the balance of power in the Union; that the balance of power is a fundamental principle of the Constitution; and that this principle is essential to the preservation of the Union."

These quotes suggest that the Missouri Compromise was a highly contentious issue, and that the debates surrounding it were marked by a strong sense of nationalism among both supporters and opponents of the compromise. The compromise ultimately reflected a desire among Americans to maintain the unity and stability of the country, even as it grappled with the divisive issue of slavery.

Step-by-step explanation:

By SAS congruence, triangles ΔVTW and ΔUTX are congruent.

SAS congruence (Side-Angle-Side) is a criterion for the congruence of two triangles in Euclidean geometry. Two triangles are said to be congruent by SAS if they have two pairs of corresponding sides that are congruent, and the included angle between those sides is also congruent.

Formally, the SAS congruence theorem states that if two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle, then the triangles are congruent. In symbols, if triangle ABC is congruent to triangle DEF by SAS, we write:

AB = DE

AC = DF

∠A = ∠D

In the triangle ΔVTW and ΔUTX

TX/TW=TU/TV (given)

∠VTW=∠UTX(Vertically opposite angle)

By SAS congruence, ΔVTW≈ΔUTX

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Answer:

oc

Step-by-step explanation:

To calculate the interest that Margo will pay, we first need to determine how much interest she will accrue over the 17-month period.

We can use the formula:

Interest = Principal x Rate x Time

Where:

Principal is the amount borrowed, which is $700 in this case.

Rate is the annual interest rate, which is 3% or 0.03 as a decimal.

Time is the time period expressed in years, which is 17/12 or 1.4167 years in this case (since there are 12 months in a year).

Therefore, the interest that Margo will pay can be calculated as:

Interest = $700 x 0.03 x 1.4167

Interest = $29.75

So Margo will pay $29.75 in interest. Rounded to the nearest cent, the answer is $29.8.

Using quadratic equations, we can find the zeros of the equation are -4 and 12.

Quadratic equations are second-degree algebraic expressions because they have the form ax² + bx + c = 0. The word "quadratic" is derived from the Latin word "quadratus," which meaning "square," and alludes to the fact that the equation's variable x is squared. To put it another way, a "equation of degree 2" is a quadratic equation.

Given equation:

2x²-16x-96=0

Factor out of the terms on the left side:

2 × x² - 2 × 8x - 2 × 48 = 0

⇒ 2 (x² - 8x - 48) = 0

⇒ x² - 8x - 48 = 0

⇒ x² + 4x - 12x - 48 = 0

⇒ x (x+4) -12(x+4) = 0

⇒ (x+4) (x-12) = 0

⇒ x = -4 or x = 12.

Therefore, zeros of the equation are -4 and 12.

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