Which set of ordered pairs could be generated by an exponential function?

Final answer:

The base and height of the triangle are found using the area formula for triangles, with the base being 7 feet more than the height. Using this relationship and the fact that the area is 114 square feet, we solve a quadratic equation to find the height to be 12 feet and the base to be 19 feet.

Explanation:

The student is given that the base of a triangle exceeds the height by 7 feet and that the area of the triangle is 114 square feet. To find the base and height of the triangle, we can use the area of a triangle formula A = (1/2) × base × height. Let's denote the base as b and the height as h. From the given information, b = h + 7.

Substituting the values into the area formula, we get:
114 = (1/2) × (h + 7) × h. Simplifying this, we get 114 = (1/2) × h² + 7/2 × h. Multiplying both sides by 2 to clear the fraction, we obtain 228 = h² + 7h. This is a quadratic equation in the form of h² + 7h - 228 = 0, which we can solve by factoring or using the quadratic formula. Factoring gives us (h + 19)(h - 12) = 0, leading to two potential solutions for h: -19 or 12. Since a height cannot be negative, we discard -19, leaving us with h = 12 feet. Therefore, the base b = h + 7 = 19 feet

The base of the triangle is 19 feet, and the height is 12 feet.

The focus point of the satellite is (-5.5,0).

This is a parabola by the looks of the equation and the fact that it's a satellite dish. The vertex of the equation is (-6,0) and the focus is 2/4, 1/2. 1/2 plus -6 is -5.5. the focus is (-5.5,0).

This refers to the plane curve that is U-shaped and is formed by the intersection of a cone.

Hence, we can see that based on the equation, y^2=2(x+6), we can see that the adjustments made by Samara where the x and y are in inches, the focal point based on the vertex of the equation which is (-6,0) and the focus is 2/4, 1/2.

Therefore, the focal point is 1/2 + -6 which is -5.5.

Read more about parabolas here:

https://brainly.com/question/25651698

#SPJ2

Answer:

the answer is (x - 1)(6 x-1) on edge, option D.

The product is (x - 1) (6x - 1).

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

The given expression is [6(x² - 1) (6x - 1)] / [6 (x + 1)]

6 is in the numerator as well as denominator. Cancel it.

[6(x² - 1) (6x - 1)] / [6 (x + 1)] =  [(x² - 1) (6x - 1)] / [(x + 1)]

We have to use one of the algebraic identity here.

a² - b² = (a + b) (a - b)

Using this,

x² - 1 = x² - 1² = (x - 1)(x + 1)

[6(x² - 1) (6x - 1)] / [6 (x + 1)] =  [(x² - 1) (6x - 1)] / [(x + 1)]

                                            = [(x - 1)(x + 1)(6x - 1)] / [(x + 1)]

Again, x + 1 is both in the numerator as well as denominator. Cancel it.

[6(x² - 1) (6x - 1)] / [6 (x + 1)] = (x – 1)(6x – 1)

Hence the product is (x – 1)(6x – 1).

Learn more about Multiplication here :

https://brainly.com/question/29404443

#SPJ2                        

The equation to model the total income, y, for selling x calendars will be y=5x.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, each calendar will sell for $5.00. the total income is y and the calendars to be sold be x.

Since each calendar costs $5, the total revenue (y) is equal to the number of calendars sold (x).

y=5x

The above equation is in the one variable known as the linear equation in one variable. It had the form y = mx. x and y are the variables in the equation.

Thus, the equation to model the total income, y, for selling x calendars will be y=5x.

Learn more about the equation here,

https://brainly.com/question/10413253

#SPJ2

The volume of the solid formed by revolving the region bounded by the graphs of the given functions is (25π) / 2.

Integration is a method of adding or summing up the parts to find the whole. It is a reverse process of differentiation, where we reduce the functions into parts.

The region bound by all three functions is in the first quadrant. If this region were rotated about the y-axis, the solid formed would have washer-shaped cross-sections.

Therefore, we can use the Washer method: V = π∫ (ROuter)² - (RInner)² dy

R(outer) = 3 and R(inner) = √y  (Note: the inner radius is formed by the function y = x2 which we solve in terms of y since we are rotating about the y-axis).

V = π∫ (3)2 - (√y)2 dy

(the limits of integration are from y = 4 to y = 9, so a = 4 and b = 9)

= π∫  9 - y dy where a = 4 and b = 9

Integrate this definite integral to find the volume,

=  (25π) / 2.

Hence, the volume of the solid formed by revolving the region bounded by the graphs of the given functions is (25π) / 2.

Learn more about integration, click;

https://brainly.com/question/18125359

#SPJ3

Answer:

[tex]\textsf{A)} \quad \dfrac{25\pi}{2}[/tex]

Step-by-step explanation:

To find the volume of the solid of revolution created by rotating the region bounded by the curve y = x², x = 3, and y = 4 about the y-axis, we can use the method of cylindrical shells.

As the region of revolution is bounded by the graphs of two functions, y = x² and y = 4, the volume of a solid of revolution using cylindrical shells is given by the integral:

[tex]\displaystyle V=2\pi\int^b_ax\left(f(x)-g(x)\right)\;\text{d}x[/tex]

where:

The height of the shell, f(x) - g(x), is determined by the vertical distance between the curve y = x² and the line y = 4. Therefore, the height is:

[tex]f(x)-g(x)=x^2-4[/tex]

The upper bound of the integral is b = 3, since the region is bounded by x = 3.

The lower bound is the x-value of the point of intersection of the two functions y = x² and y = 4. These two functions intersect when x = 2. Therefore, the lower bound of the integral is a = 2.

Substitute these values into the integral:

[tex]\displaystyle V=2\pi\int^3_2x\left(x^2-4\right)\;\text{d}x[/tex]

Expand the brackets:

[tex]\displaystyle V=2\pi\int^3_2\left(x^3-4x\right)\;\text{d}x[/tex]

Evaluate the integral by using the power rule:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

Therefore:

[tex]V=2\pi\left[\dfrac{x^4}{4}-\dfrac{4x^2}{2}\right]^3_2[/tex]

[tex]V=2\pi\left[\dfrac{x^4}{4}-2x^2\right]^3_2[/tex]

[tex]V=2\pi\left[\left(\dfrac{(3)^4}{4}-2(3)^2\right)-\left(\dfrac{(2)^4}{4}-2(2)^2\right)\right][/tex]

[tex]V=2\pi\left[\left(\dfrac{81}{4}-18\right)-\left(4-8\right)\right][/tex]

[tex]V=2\pi\left[\left(\dfrac{9}{4}\right)-\left(-4\right)\right][/tex]

[tex]V=2\pi\left(\dfrac{25}{4}\right)[/tex]

[tex]V=\dfrac{25\pi}{2}[/tex]

Therefore, the volume of the solid formed by revolving the region bounded by the graphs of y = x², x = 3, and y = 4 about the y-axis is:

[tex]\Large\boxed{\boxed{\dfrac{25\pi}{2}}}[/tex]

The area of the blue glass that will be needed to fill each butterfly dot would be 144π.

The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

We have given the distance around each dot is 24pi inches.

So, The circumference of the circle = 2πr

                                                 24π = 2πr

                                                 r = 12

The artist plans to fill the inside of each dot with blue-colored glass.

Now, we know that

The area of the circle = [tex]\pi r^{2}[/tex]

                                    = π x 12 x 12

                                    = 144π

Thus, the area of the blue glass that will be needed to fill each butterfly dot would be 144π.

Learn more about circumference here;

brainly.com/question/12512221

#SPJ3

A fraction is a way to describe a part of a whole. The number of students who voted is 401. The correct option is B.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

Given that the total number of students in the senior class is 535. Now, if  3/4 of the class voted. Then we can write,

The number of seniors who voted = 3/4 of 535

                                                         = (3/4) ×  535

                                                         = 401.25 ≈ 401

Hence, the number of students who voted is 401.

Learn more about Fraction here:

https://brainly.com/question/1301963

#SPJ2

Answer:

The second choice is correct.

Step-by-step explanation:

Reflecting ABC across the y-axis will negate the x-coordinates, which will place it directly above triangle DEF.  Counting down from A to D, B to E and C to F, we see that each is 5 units above the image; this means a translation 5 units down will finish mapping the pre-image to the image.  Since they are mapped on top of each other, they are congruent.

x = hot dogs

y = snacks

x +y = 175

x = 175-y

2.50x + 0.75y = 262.50

2.50(175-y) +0.75y = 262.50

437.50-2.50y + 0.75y = 262.50

-1.75y = -175

y = -175 / -1.75 = 100

100 snacks & 75 hot dogs

The number of hot dogs sold is 75 while the number of snacks sold is 100.

Based on the information, the equation to solve the question will be:

x + y = 175 ....... i

2.50x + 0.75y = 262.50 ....... ii

From equation i, x = 175 - y.

We'll put the value of x into 2.50x + 0.75y = 262.50 and this will be:

2.50x + 0.75y = 262.50

2.50(175 - y) + 0.75y = 262.50

437.50 - 2.50y + 0.75y = 262.50

Collect like terms

-2.50y + 0.75y = 262.50 - 437.50

-1.75y = -175

y = 175/1.75

y = 100

The number of snacks sold is 100.

Since x + y = 175

x = 175 - 100

x = 75

The number of hot dogs sold is 75

Therefore, 75 hot dogs and 100 snacks were sold.

Read related link on:

https://brainly.com/question/5715622

The correct answers are:

Answer:

ABC would be right angle triangle if C(1,-1) or C(-3,2)

Step-by-step explanation:

In △ABC , the coordinates of vertices A and B are A(1,2), and B(−3,−1)

We need to find the third vertex of triangle ABC.

ABC is a right angle triangle.

A(1,2) and B(-3,-1)

Using A and B, Two possible right angle triangle.

Case 1: If we draw a vertical line at A and horizontal line at B then intersection point of vertical and horizontal would be third vertex of triangle ABC.

Vertical line at A, x=1

Horizontal line at B, y=-1

Vertex C: (1,-1)

Case 2: If we draw a horizontal line at A and vertical line at B then intersection point of vertical and horizontal would be third vertex of triangle ABC.

Vertical line at B, x=-3

Horizontal line at C, y=2

Vertex C: (-3,2)

Thus, ABC would be right angle triangle if C(1,-1) or C(-3,2)

Please see the attachment to see the process graphically.

Final answer:

The closed form sum of the given expression is obtained by expanding and simplifying it. Comparing this with the given expression, we can find the values of a and b.

Explanation:

The closed form sum of $$12 \left[ 1² \cdot 2 + 2²\cdot 3 + \ldots + n² (n+1) \right]$$ for $n \geq 1$ is $n(n+1)(n+2)(an+b).$ To find $an + b$, we can simplify the expression by expanding it:

Expanding the sum, we have:

$$\begin{align*} 12 &\left[ 1² \cdot 2 + 2² \cdot 3 + \ldots + n² (n+1) \right] \\ &= 2[1 + (n-1) + 3 + \ldots + (2n-3) + (2n-1)-(n-1)] \\ &= 2[n + 3 + \ldots + (2n-3) + n] \\ &= 2n² \end{align*}$$

Comparing this with the given expression $n(n+1)(n+2)(an+b)$, we can see that $2n² = n(n+1)(n+2)(an+b)$. So, $an+b = \boxed{2}$.

To solve for 'a' in the equation 5a^2 = 320, first divide both sides of the equation by 5 to get a^2 = 64. Then, take the square root of both sides which provides two possible solutions, a = 8, and a = -8.

The student is asking to solve for 'a' in the algebraic equation 5a2 = 320. To find the solution, we first need to isolate 'a' on one side of the equation. Begin by dividing both sides of the equation by 5:

a2 = 320 / 5

This simplifies to:

a2 = 64

To solve for 'a', we take the square root of both sides:

a = √64

Therefore, the solutions are:

a = 8, a = -8

https://brainly.com/question/32436021

#SPJ2

Answer:

192 feet fence would be used for 6 cows.

Step-by-step explanation:

Given,

64 feet of fence is used for 2 cows,

Ratio in fence and cows = [tex]\frac{64}{2}[/tex] = 32,

96 feet of fence is used for 3 cows,

Ratio in fence and cows = [tex]\frac{96}{3}[/tex] = 32,

128 feet of fence is used for 4 cows,

Ratio in fence and cows = [tex]\frac{128}{4}[/tex] = 32,

Thus, by the above explanation it is clear that in every case the ratio of the length of fence and number of cows is 32,

Let x be the length of cows that is used for x cows,

[tex]\implies \frac{x}{6}=32[/tex]

[tex]\implies x = 192[/tex]

Hence, 192 feet fence would be used for 6 cows.

The interior angles on the same side of a transversal cutting parallel lines are always congruent.

The interior angles on the same side of a transversal cutting parallel lines are always congruent.

When a transversal intersects two parallel lines, it creates several pairs of corresponding angles. The corresponding angles that are on the same side of the transversal are congruent or equal in measure. This is known as the Alternate Interior Angles Theorem.

For example, if line m is parallel to line n and a transversal line t cuts both lines at points A and B, then the angle formed by the intersection of line t and line m, and the angle formed by the intersection of line t and line n on the same side of the transversal are congruent.

https://brainly.com/question/32955275

#SPJ3

1 is the answer bruvy

Answer: 1

Step-by-step explanation:

From the given picture, it can be seen that there is a plane H on which two pints J and K are located.

One of the Axiom in Euclid's geometry says that "Through any given two points X and Y, only one and only one  line can be drawn "

Therefore by Axiom in Euclid's geometry , for the given points J and K in plane H , only one line can be drawn  through points J and K.

The expression for the sum of these integers is 3n

Let the first number be n-2

Let the middle number be n

Let the third number be n+2

The expression for the sum of these integers will be:

=(n - 2) + n + (n + 2)

= n - 2 + n + n + 2

Collect like terms

= 3n

The expression for the sum of these integers is 3n

Read related link on:

https://brainly.com/question/5760634

Answer:

i need helppp

Step-by-step explanation:

this same problems but where is everyone getting the 6.25 from.

Answer:

Step-by-step explanation:

repeating or circulating decimal is decimal representation of a number whose digits are periodic or infinitely repeated.

To convert a fraction into decimal form we have to divide numerator by denominator.

a.  2/3 = 0.666666

b.  9/11 = 0.8181818

c.  2/9 = 0.222222

d.  11/3 = 3.666666

e.  5/6 = 0.833333

f.  14/3 = 4.666666

Answer:

y = 75

Step-by-step explanation:

23 + y - 19 = 79

We are to solve for y.

To solve for y, we are to follow the step below

23 + y - 19 = 79

subtract nineteen from twenty three

y + 4 = 79

Subtract four(4) from both-side of the equation

y + 4 - 4 = 79 - 4

On the left hand-side of the equation, 4-4=0 leaving us with just y

y = 79 - 4

y =75

Therefore y = 75