The graph of function f is shown. An exponential function with vertex at (1, 3) and passes through (minus 2, 10), (8, 2) also intercepts the y-axis at 4 units. Function g is represented by the equation. g ⁡ ( x ) = 4 ⁢ ( 1 4 ) x + 2 Which statement correctly compares the two functions? A. They have the same y-intercept but different end behavior. B. They have different y-intercepts and different end behavior. C. They have the same y-intercept and the same end behavior. D. They have different y-intercepts but the same end behavior.

Answer: In mathematics, the reciprocal of a number is 1 divided by that number. So the reciprocal of 7/9 is 1/(7/9) which can be simplified to 9/7.

Therefore, 9/7 is the number that when multiplied by 7/9 will result in the product of 1.

Another way of arriving at the same solution is to remember that the product of a number and its reciprocal is always 1. In this case, the number is 7/9, and its reciprocal is 9/7.

Step-by-step explanation:

70-70-40 is an isosceles triangle.

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a) The total amount of pizzas that they ate is given as follows: 2.92 pizzas.

b) The difference between the number of cheese pizzas and the number of vegetarian pizzas is given as follows: 4/3, which is the amount that they ate more of cheese pizzas than vegetarian pizzas.

The fractions relative to the amount of each type of pizza eaten are given as follows:

The total amount of pizzas eaten is given by the addition of these fractions, hence:

1/4 + 2 + 2/3 = 3/12 + 24/12 + 8/12

(as the least common factor between 4, 1 and 3 is of 12).

3/12 + 24/12 + 8/12 = (3 + 24 + 8)/12

(3 + 24 + 8)/12 = 35/12

2.92 pizzas.

The difference between the number of cheese pizzas and the number of vegetarian pizzas is obtained as follows:

2 - 2/3 = 6/3 - 2/3 = 4/3.

(as the least common factor of 1 and 3 is of 3).

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The graph of the linear equation 2x + 3y = 6 is a straight line that cuts the Y-axis at the point (0,2).

A linear equation is an equation in which the highest power of the variable is 1.

The general form of a linear equation is:ax + by = c where a, b and c are constants and x and y are variables. This equation represents a straight line when plotted on a graph.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept

To find the points at which the line will intersect y-axis,

take x=0 and substitute in the linear equation 2x+3y=6

2(0) + 3y = 6

3y = 6

y = 2

So the point where the line cuts the Y-axis is (0,2)

The straight line of the linear equation 2x+3y=6 intersects the y-axis at (0,2).

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Answer:

29

Step-by-step explanation:

when the area of the trapezoid is 70 units, and its first and second bases are at 4.6 units,

The size of a region on a flat or curved surface is expressed mathematically as area. The area of a form is defined as the "space encompassed inside the perimeter or the border." The area of various shapes is calculated using mathematical methods.

given

The trapezoid's surface area is 70 units.

first base is worth 20 units, while second base is worth 10 units.

how long CE

[tex]1/2(b1 + b2)*h is the area of a trapezoid.\\70= 1/2 (20 + 10 )*h\\70 = 1/2(30)*h\\4.6 units of h[/tex]

when the area of the trapezoid is 70 units, and its first and second bases are at 4.6 units,

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the cost of a broom is $62.50, and the cost of a mop is x + 15 = 62.5 + 15 = $77.50.

Therefore,

a) 1 mop cost $77.50

b) 1 broom cost $62.50

What is the system of equations?

A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied in other words, the locations at which all of these equations intersect.

To find the cost of a mop and a broom, we can set up a system of equations using the information given:

Let x be the cost of a broom

Let y be the cost of a mop (which is $15 more than a broom)

From the problem, we know that:

y = x + 15 (since a mop costs $15 more than a broom)

5x + 7y = 855 (since 5 mops and 7 brooms cost a total of $855)

We can substitute the first equation into the second equation:

5x + 7(x + 15) = 855

5x + 7x + 105 = 855

12x = 750

x = 62.5

Hence, the cost of a broom is $62.50, and the cost of a mop is x + 15 = 62.5 + 15 = $77.50.

Therefore,

a) 1 mop cost $77.50

b) 1 broom cost $62.50

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Answer:

The slope of line r is -3/4

Step-by-step explanation:

First, let's find the slope of line q. We can find the slope by finding the change in y over change in x.

[tex]\displaystyle{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Therefore, substitute in:

[tex]\displaystyle{m=\dfrac{8-4}{6-3}}\\\\\displaystyle{m=\dfrac{4}{3}}[/tex]

Therefore, the slope of line q is 4/3. Since we want to find the slope of line r and we know by the given that line r is perpendicular to line q. By the definition of perpendicular line is [tex]\displaystyle{m_1m_2=-1}[/tex].

Let [tex]m_1[/tex] be slope of the line q which is 4/3. Therefore, substitute in and solve for [tex]m_2[/tex] (slope of line r)

[tex]\displaystyle{\dfrac{4}{3}m_2=-1}\\\\\displaystyle{4m_2=-3}\\\\\displaystyle{m_2=-\dfrac{3}{4}}[/tex]

Therefore, the slope of line r is -3/4

You can identify equivalent expressions if one of the expressions can be written like the other and it is usually written by combining any like terms on each side of the equation such as x-terms with x-terms and constants with constants.

These are the type of expressions that have similar value or worth but do not look the same.

This type of expression can be identified if one of the expressions can be written like the other and example can be seen below:

3(x + 3) and 3x + 9

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The rounding off of 34.171875 to the nearest 100th gives us= 34.17

The nearest hundredth should be the second digit after the decimal point. To round off any decimal figures, we need to see if the digit after the hundredth is greater than or equal to 5. If such is the case, then add 1 to the hundredth, or else remove the digits.

Here, the nearest hundredth digit is 7, and the digit after it (i.e, the third place after decimal) is smaller than 5. So, there is no need of adding an extra 1 to the hundredth. Now, after casting off the remaining digits, we get 34.17.

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Answer:

it takes 110 minutes

Step-by-step explanation:

Answer:

it takes approximately 110 minutes

The midpoint of the x-intercept is (0,0).

By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the occurs when the x value is 0. Y = B when x = 0, since mx y-intercept = 0 at this point.

We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.

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No, 12, 20, and 16 do not form a Pythagorean triple. A Pythagorean triple is a set of three whole numbers, a, b, and c, such that a^2 + b^2 = c^2.

To determine if 12, 20, and 16 form a Pythagorean triple, we can substitute each number into the equation and solve for c.

Start by substituting 12 for a, 20 for b, and 16 for c:

12^2 + 20^2 = 16^2

144 + 400 = 256

544 ≠ 256

Since 544 does not equal 256, the numbers do not form a Pythagorean triple. We can also verify this by calculating the square of c to see if it is equal to the sum of the squares of a and b.

Start by substituting 12 for a, 20 for b, and 16 for c:

a^2 + b^2 = c^2

12^2 + 20^2 = c^2

144 + 400 = c^2

544 = c^2

Taking the square root of both sides:

√544 = √c^2

23.2 ≠ c

Since 23.2 does not equal c, the numbers do not form a Pythagorean triple.

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Step-by-step explanation:

EC = 165 cm (Given) Tangent of circle also makes 90°.

a) sind = Perpendicular Hypotenuse = CD = EC 165 => 0 = Sin = 0.519 ~ 0.52 =29.7448 ~ 29.75° =<E

By angle sum property of triangle. <D+<E+ <C = 180°

90° + 29.75 + LC = 180°

<C = 180-90-29.75 = 60.25° <C= 60.25°

<DCE = <C = 60.25 x π/180 = 1.052 radians.

(b) Area of triangle DCE = 1/2 x b x h = 1/2 x ED X 4

ED² + CD² = EC² ED² + 4² = (√65)² => EC² = 65-16 = 49 ED=7

Area = 1/2 x 7 x 4 = 14 cm²

Area of sector a π x 4²x 60.25/360 = 8.4125 cm2

Area of shaded region= Area ADCE Area of sector -

= 14-8.4125 = 5.5875 cm²

(a) <DCE = 1.052 radians b) Area shaded of region = 5.5875cm²

The spring constant is 30 N/m and the stretch when the 420 N force is applied is 14 cm.

The force needed or applied to compress or extend a spring on any attached object is known as the spring force.

A spring exerts an equal and opposite force on an object when the object exerts a force on it. It always takes action to get mass back to where it should be for equilibrium. 

Given that when 180 N force is applied the spring stretched by 6 cm. The spring stretch when the 420 N force is applied is calculated as,

First, calculate the spring constant,

F = kx

180 = k x 6

k = 30 N / m

Calculate the deformation,

x = F / k

x = 420 / 30

x = 14 cm

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Answer:

1/8

Step-by-step explanation:

total probability = 1

total probability = probability of red + probability of green + probability of yellow

1 = 1/4 + 5/8 + yellow

we want to find a common denominator

in this case, we know 4 * 2 = 8, so we can multiply 1/4 by 2/2 = 1 to get

1/4 * 2/2 = 2/8

1 = 2/8 + 5/8 + yellow

1 = 7/8 + yellow

subtract 7/8 from both sides to isolate yellow

1 = 8/8

1 - 7/8 = 8/8 - 7/8 = 1/8 = yellow

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Now, According to the question:

How do you find the domain?

Let y = f(x) be a function with an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.

How do you find the range?

The range is calculated by subtracting the lowest value from the highest value.

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Answer:

I think it would be 10 inches but I am not sure

Answer:

FALSE

Step-by-step explanation:

It is not necessarily true that ƒ(5)=8 just because ƒ(1)=0, ƒ(3)=0, and ƒ(4)=0. In fact, it is possible for ƒ(x) to be a cubic function and for ƒ(5) to equal any number, depending on the specific form of the function and the values of its coefficients.

No. the sum of any two lengths of the triangle is greater than the third length.

Option (A) is correct.

A triangle is a polygon with three edges and three vertices. In Euclidean geometry, a triangle is completely determined by the three points that make up its vertices.

Kathy wants to place a printer 9ft from the filing cabinet. Can the other two distances are shown to be 7ft and 2ft.

No the sum of any two lengths of the triangle should be greater than the third side.

but 7 + 2 = 9, so the condition for a triangle is false.

Hence, the correct explanation would be "No. the sum of any two lengths of the triangle is greater than the third length."

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Kathy wants to place a printer 9ft from the filing cabinet. Can the other two distances shown be 7ft and 2ft? Identify the answer with the correct explanation. Printer Desk Filing Cabinet

O Yes; the sum of any two lengths is greater than the third length.

O No; the sum of any two lengths is not greater than the third length.

O Yes; the sum of any two lengths is equal to the third length.

O No; the sum of any two lengths is greater than the third length

Answer:

No; The sum of any two lengths is NOT greater than the third length

Step-by-step explanation:

It is given that three objects, a desk, a filing cabinet, and a printer, form a triangle.

Use the Triangle Inequality Theorem to determine whether the given distances can be the lengths of the sides of a triangle.

9+7=16>2

9+2=11>7

7+2=9=9

The sum of one pair of lengths is equal to the third length. Therefore, the distances between the desk, the printer, and the desk and the filing cabinet cannot be 7ft and 2ft since 7+2 equals 9.

Therefore, the answer to the provided problem of tractable problem turns out to be the most common problem that has been shown to be insoluble.

a method that takes a polynomial amount of time to finish a manageable task. It makes advantage of the polynomial upper bound. Intractable refers to a problem that cannot be addressed in a polynomial amount of time. The bound has an exponential minimum.

Here,

It is the most common issue that has been shown to be intractable since there is no program that can fix the stopping trouble for sufficiently general computer programs.

We need to be clear about the kind of computer program we're talking about.

Therefore, the answer to the provided problem of tractability turns out to be the most common problem that has been shown to be insoluble.

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The coefficients in the expression [tex]12x^{3} (2x^{3}) + y^{3}[/tex] are , coefficient of of x⁹ is 24 and coefficient of of y³  is 1   .

The Coefficients are defined as a multiplicative factor in some term of a polynomial , series or an expression , the coefficient is usually a number .

the expression is given as [tex]12x^{3} (2x^{3}) + y^{3}[/tex] ;

to find the coefficients we first simplify the expression ,

we get ;

= [tex]12x^{3} \times2x^{3} + y^{3}[/tex]

= [tex]24x^{9} +y^{3}[/tex] ;

so , the numerical term with x⁹  is 24 and the numerical term with y³ is 1 .

Therefore , the coefficient of x⁹ is 24 and the coefficient of  y³ is 1 .

The given question is incomplete , the complete question is

What is the coefficient of x⁹ and y³ in the expression [tex]12x^{3} (2x^{3}) + y^{3}[/tex] ?

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The required length of the side AC of the given right triangle is 32 units.

A right triangle is a triangle with one right angle or two perpendicular sides.

It is also referred to as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle.

The relationship between the sides and various angles of the right triangle serves as the basis for trigonometry.

A triangle is referred to be a right triangle when one of the interior angles is 90 degrees or a right angle.

So, using the hypotenuse AC as the point of convergence for the right triangle ABC,

AB is 8 and AD is 2.

Verify whether the triangle ΔABD resembles ΔACB.

∠ BCA = ∠ DBA (90 - ∠ DBC)

∠ A = ∠ A

As a result, ΔABD and ΔACB share an AAS resemblance.

Utilize the similarity property to determine the length of AC.

AC/AB = AB/AD

x / 8 = 8 / 2

x = 32

Therefore, the required length of the side AC of the given right triangle is 32 units.

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Correct question:

Given a right triangle, ABC with altitude BD drawn to hypotenuse AC. If AB = 8 and AD = 2, what is the length of AC?

Answer:

x = -4

y = 29

Step-by-step explanation:

Let's take our two equations and turn the decimals into fractions for simplicity's sake. We get:

x/4 + 5y/100 = 9    x + y = 25

Simplifying a bit gives us:

x/4 + y/20 = 9       x + y = 25

Now, we will take the first equation and multiply it by 20 to get rid of the fractions. We get:

5x + y = 9

We will rearrange numbers to give us an answer to y that we can substitute in. we get:

y = 9 - 5x

Then, we will plug this into our second equation giving us:

x + 9 - 5x = 25

Combining like terms and subtracting 9 from both sides gives us:

-4x = 16

Dividing by -4 gives us:

x = -4

Then, we can substitute this into our second equation giving us:

-4 + y = 25

We will add 4 to both sides giving us:

y = 29

Hope this helped!

The variable terms in the expression 3[tex]x^{3}[/tex]y + 5[tex]x^{2}[/tex] + y + 9 are [tex]x^{3}[/tex]y, [tex]x^{2}[/tex], and y.

The expression provided is

3[tex]x^{3}[/tex]y + 5[tex]x^{2}[/tex] + y + 9

In the expression, each variable is represented by a letter.

Let's look at the variables for each term.

The variable in the first term, 3[tex]x^{3}[/tex]y, is [tex]x^{3}[/tex]y.

The variable in the second term, 5[tex]x^{2}[/tex] , is [tex]x^{2}[/tex] .

Y is the variable in the third term.

There is no variable in term 9's final equation.

The variables in the expression are [tex]x^{3}[/tex]y, [tex]x^{2}[/tex] , and y.

As a result, the variables [tex]x^{3}[/tex] and y are the variable terms.

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The area of the garage door on the blueprint is 0.55 ft^2.

The size of a patch on a surface is determined by its area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given in question,

Scale factor = 0.05

Since this scale factor is for length.

The scale factor for the area = 0.05*0.05

                                          = 0.0025

Original Area = 220

The area on the blueprint = 0.0025*220

                                       = 0.55

Hence, the area of the garage door on the blueprint is 0.55 ft^2.

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The formula yields the radius $r$ of a circle that is inscribed within three circles with radii $a$, $b$, and $c$ that are mutually external tangents.

[tex][\frac{1}{r} = \frac{1}{a} + \frac{1}{b} + \frac{1}{c}][/tex]

The radius of the inscribed circle is related to the radii of the three mutually externally tangent circles using a method known as the radical centre formula. According to this equation, the reciprocals of the radii of the three externally tangent circles add up to the radius of the circle that is inscribed.

The power of point theorem states that the product of the distance between the point and the three points of tangency is equal to the product of the distance between the point and the centres of the circles. This formula is based on the fact that the circles are mutually externally tangent and their centres are collinear. It is crucial to note that the formula can only be used if the circles are mutually externally tangent; otherwise, it is invalid.

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By the concept of the proportional method we determine that the height of the tower would be 48 feet.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

The model given can be interpreted by the concept of proportional method

a : b : : c : d.

Therefore,

5 : 6 : : 40 : x.

5/6 = 40/x.

5x = 240.

x = 240/5.

x = 48 feet.

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The vector equivalent to the directed line segment from the point (x1, y1) to the point (x2, y2) is the vector <x2-x1, y2-y1>.

The vector of a directed line segment is the difference between the two endpoints of the line segment. In this case, the endpoints are the points (x1, y1) and (x2, y2). Therefore, the vector of the directed line segment is equal to the vector <x2-x1, y2-y1>.

The vector equivalent of a directed line segment from the point (x1, y1) to the point (x2, y2) is the vector with initial point (x1, y1) and terminal point (x2, y2). This vector is equal to the vector form <x2-x1, y2-y1>, which describes the displacement from the initial point to the terminal point. This vector can also be written in component form, meaning the magnitude of the vector in the x-direction is x2-x1, and the magnitude of the vector in the y-direction is y2-y1.

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