What is the slope of the line in the graph?

The sum of the first six terms of the geometric series will be -364. Hence, option (B) will be correct.

A geometric series is a series in which the division of any consecutive two terms will be the same.

For example 3, 6, 12, 24 here if you divide 6 by 3 then it gives you 2, and if you divide 12 by 6 then also it gives you 2, and so on.

here, we have,

Given up series is 2, – 6, 18, – 54

The common ratio of this GP is -3 by that

The remaining elements of this gp will be 162, -486

So the sum will be 2 - 6 + 18 - 54 + 162 - 486 = -364 so it will the summation of the given gp.

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There are 21 books Jason's have and 24 books Nathan's have.

Given

Six times Jason's collection of books and one-third of Nathan's collection add up to 134 books.

One-third of Jason's collection and Nathan's entire collection add up to 31 books.

Let the number of collection of books Jason's be x.

And the number of collection of books Nathan's be y.

Six times Jason's collection of books and one-third of Nathan's collection add up to 134 books.

[tex]\rm 6x+\dfrac{1}{3} y=134\\\\\dfrac{18x+y}{3} =134\\\\ 18x+y = 134\times 3\\\\18x+y=402[/tex]

One-third of Jason's collection and Nathan's entire collection add up to 31 books.

[tex]\rm \dfrac{1}{3}x+y=31\\\\\dfrac{x+3y}{3} =31\\\\x+3y=31\times 3\\\\x+3y=93[/tex]

On solving both the equations;

From equation 1;

[tex]\rm 18x+y=402\\\\y = 402-18x[/tex]

Substitute the value of y in equation 2

[tex]\rm x+3y=93\\\\x+ 3(402-18x)=93\\\\x+1206 -54x=93\\\\-53x = 93-1206\\\\-53x =-1113\\\\x = \dfrac{-1113}{-53}\\\\x=21[/tex]

Substitute the value of x in equation 2

[tex]\rm x+3y=93\\\\21+3y=93\\\\3y=93-21\\\\ 3y =72\\\\ y = \dfrac{72}{3} \\\\ y=24[/tex]

Hence, there are 21 books Jason's have and 24 books Nathan's have.

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Answer:

The domain is all real numbers and the range is non-negative real numbers

(y ≥ 0) ⇒ answer B

Step-by-step explanation:

* Lets revise the parent function of the absolute value

- The absolute value or modulus |x| of a real number x is the

  non-negative value of x

- The absolute value of a number means the magnitude of the number

  without regard to its sign

- The parent function of the absolute value is f(x) = IxI

∵ The domain of the function is all the values of x which make the

  function defined

∵ In the function f(x) = IxI, x can be any number

∴ The domain of the f(x) is any real number

∴ The domain is (-∞ , ∞) or {x : x ∈ R}

∵ The range is the set of values of y that corresponding with the

   domain

∵ f(x) = IxI is non-negative value

∴ f(x) ≥ 0

∵ f(x) = y

∴ y ≥ 0

∴ The range is the set of real numbers greater than or equal zero

∴ The range is [0 , ∞) or {y : y ≥ 0}

* The true statement is: The domain is all real numbers and the range is

  non-negative real numbers (y ≥ 0)

Answer:

Step-by-step explanation:

ANSWER

Point if discontinuity:  

{x}=  \pm3

Zero of the function is  

x = 0

EXPLANATION

The given rational function is:

f(x) =  \frac{3x}{ {x}^{2}  - 9}  

This function is not continous when  

{x}^{2}  - 9 = 0

{x}=  \pm \sqrt{9}  

{x}=  \pm3

The function is zero when,

3x = 0

x = 0

Answer:

x = 0 is the zero of this function and at x = ±4 function is discontinuous.

Step-by-step explanation:

The given function is [tex]f(x) = \frac{4x}{x^{2}-16}[/tex]

For this function we have to find the discontinuity and zeros of this function.

For zeros of the function [tex]0 = \frac{4x}{x^{2}-16}[/tex]

so zero of the function is x = 0

For x² - 16 = 0 this function not defined therefore, x = ± 4 function will be discontinuous.

Finally, x = 0 is the zero of this function and at x = ±4 function is discontinuous.

Answer:

Symbol                    Words                              Open dot or closed dot

     >                        greater than                      open dot

    [tex] \ge [/tex]                     greater than                      closed dot

                                 or equal to

    <                          less than                          open dot

    [tex] \le [/tex]                        less than                         closed dot

                                or equal to

Answer:

B.

Step-by-step explanation:

Quarterly interest rate is 4.5 / 4 = 1.125%.

Monthly rate is 4.5 / 12 = 0.375%.

Answer:

B 1.25%-0.375%

Step-by-step explanation:

Compounded quarterly means there are 4 interest periods in 1 year, so divide the annual interest rate by 4.

4.5% ÷ 4 = 1.125%

Compounded monthly means there are 12 interest periods in 1 year, so divide the annual interest rate by 12.

4.5% ÷ 12 = 0.375%

The value of y from the given equation with x=2+i is y= 7(i+2).

The given equation is y= x²+3x+5.

We need to evaluate y from the given equation for x= 2+i.

A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value 'a' is called the real part which is denoted by Re(z), and 'b' is called the imaginary part Im(z).  Also, ib is called an imaginary number.

The alphabet i is referred to as the iota and is helpful to represent the imaginary part of the complex number. Further the iota(i) is very helpful to find the square root of negative numbers.

Now, put x= 2+i in y= x²+3x+5 and simplify.

That is, (2+i)²+3(2+i)+5

=4+i²+4i+6+3i+5

=15-1+7i

=7i+14

=7(i+2)

Therefore, the value of y from the given equation with x=2+i is y= 7(i+2).

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Answer:

18, 5, 2

Step-by-step explanation:

its pretty much X times 2 to find Y and to find X with Y you must divide Y by 2

Answer:

18, 5, and 2

Step-by-step explanation:

#1 Plug in 9 for x

y = 2(9)

y = 18

#2 Plug in 10 for y

10 = 2x

Divide by 2 on Both sides

5 = x or x = 5

#3 Plug in 1 for x

y = 2(1)

y = 2

Hope this helps!

Answer:

Step-by-step explanation:

[tex]f(x)=(x-6)^2(x+2)^2\to y=(x-6)^2(x+2)^2[/tex]

x-intercepts are for y = 0.

Put y = 0 to the equation:

[tex](x-6)^2(x+2)^2=0\iff(x-6)^2=0\ \vee\ (x+2)^2=0\\\\(x-6)^2=0\iff x-6=0\qquad\text{add 6 to both sides}\\\\x=6\\\\(x+2)^2=0\iff x+2=0\qquad\text{subtract 2 from both sides}\\x=-2[/tex]

Answer:

the awnser is 2

Step-by-step explanation:

Answer:

488 = r

Step-by-step explanation:

362 = -126 + r

126 +126

----------------

488 = r

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Answer: 117°

Step-by-step explanation:

Use the Law of Cosines:

c² = a² + b² - 2ab · cos C

12² = 6² + 8² - 2(6)(8)(cos C)

144 = 36 + 64 - 96 cos C

144 = 100 - 96 cos C

44 = -96 cos C

[tex]-\dfrac{44}{96}=cosC\\\\\\cos^{-1}\bigg(-\dfrac{44}{96}\bigg)=C[/tex]

117° = C

Answer:

[tex]\large\boxed{\dfrac{5}{-7x}\cdot\dfrac{-9y}{8}=\dfrac{45y}{56x}}[/tex]

Step-by-step explanation:

[tex]\dfrac{5}{-7x}\cdot\dfrac{-9y}{8}=\dfrac{(5)(-9y)}{(-7x)(8)}=\dfrac{-45y}{-56x}=\dfrac{45y}{56x}[/tex]

Answer:

a  x+2y =5

b  x=1  y=2

Step-by-step explanation:

4x+3y = 10

So the cost of 1 banana is x and the cost of 1 peach is y

a) we want the cost of 1 banana and 2 peaches

1x+2y

That is equal to 5 dollars

1x+2y =5

x+2y =5

b

The matrixes are

1   2         x              5

         *           =

4   3          y            10

Using my calculator, x=1  y=2

Answer:

A:A(6t)=πp^2

B: about 7234.56

Step-by-step explanation:

First find A[p(t)], Since this is a composite function so whenever you see p(t), you replace it with 6t, that is the value of p(t).

This is a simplified version of the area of the circle as a function of time A(6t)=πp^2

To find how large the area of paint spilled plug in 8 for t because t represents time.

A(48)≈3.14(48)^2

A(48)≈3.14*2304

A(48)≈7234.56

Final answer:

To find the area of spilled paint over time, we replace the time-dependent spread 'p(t)' in the area function 'A(p) = πp²' with '6t'. This results in the equation 'A[p(t)] = 36πt²'. After 8 minutes, the area is approximately 7233.76 square units when using 3.14 for π.

Explanation:

To solve for the area of the circle of spilled paint as a function of time, we need to use the given functions. We are given p(t) = 6t, which represents how far the paint spreads over time in minutes. The area of the circular pattern is given by A(p) = πp².

Part A

To find A[p(t)], we substitute the expression for p(t) into the equation for A(p):

A[p(t)] = π(6t)²
= π(36t²)
= 36πt²

Part B

After 8 minutes, the area of spilled paint can be calculated by substituting t=8 into the function A[p(t)]:

A[p(8)] = 36π(8)²
= 36π(64)
= 2304π
≈ 2304(3.14)
≈ 7233.76 square units

Answer:

A) 760 ft³

Step-by-step explanation:

The surface area of the figure has to be calculated.

Step 1: Divide the figure

The figure is divided into the following parts to calculate the volume.

Part 1: Box without ledge

Formula for volume of rectangle = length x width x height

Volume = 14.3 x 7.8 x 6.6

Volume = 736.164 ft³

Part 2: Box with ledge-we will only calculate height and width since the length has already been included in part 1 therefore including it again would result in double counting and give the wrong answer.

Volume = height x width

Volume = 2.7 x 7.8

Volume = 21.06 ft³

Step 2: Add both volumes to find the total volume

Volume part 1 + Volume part 2 = 736.164 ft³ + 21.06 ft³

= 757.224 ft³ rounded off to nearest tenth = 760 ft³

Therefore, answer A is correct.

!!

Answer:

D

Step-by-step explanation:

for the 2 lines to be parallel, they have to have the same slope

its y-axis for the first answer and the other one its, y=-x

The line of reflection which maps the point K to K' and L to L' is Y axis.

Reflection is the transformation where the image is flipped.

Line of reflection is the line for which a figure has a mirror image over that line.

Given a triangle JKL.

Let the coordinate of the triangle be J(4, 5), K(5, 2) and L(2, 3).

When a coordinate (x, y) is reflected over the X axis, then the coordinates changes to (x, -y).

When a coordinate (x, y) is reflected over the Y axis, then the coordinates changes to (-x, y).

Here,

K(5, 2) changes to K'(-5, 2).

Here x coordinate changes sign.

So the line of reflection is Y axis.

Similarly, the line of reflection for the other transformation is also Y axis.

Hence the line of reflection is Y axis.

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Answer:

18 since f(3)=18

Step-by-step explanation:

f(x)=2x^2 is give as our function. To find f(3) we need to replace x with 3.

f(3)=2(3)^2   (Replaced x with 3.)

f(3)=2(9)   (Did 3^2 which was 3*3=9)

f(3)=18    (Did 2(9) which was 18)

[tex]f(3)=2\cdot 3^2=18[/tex]

Answer:

10.2 inches

Step-by-step explanation:

Ok let's assume we don't know the larger (the c value).

So this means using [tex]a^2+b^2=c^2[/tex] we have:

[tex]12^2+15^2=c^2[/tex]

[tex]144+225=c^2[/tex]

[tex]369=c^2[/tex]

Square both sides:

[tex]c=\sqrt{369} \aprox 19.2[/tex

Now assume we know the larger is 15 (this means c=15 now), then we have

[tex]a^2+12^2=15^2[/tex]

[tex]a^2+144=225[/tex]

Subtract 144 on both sides:

[tex]a^2=225-144[/tex]

Simplify:

[tex]a^2=81[/tex]

Square root both sides:

[tex]a=9[/tex]

The difference between 19.2 and 9 is 19.2-9=10.2.

Answer:

Option 1 - 10.2 inches.                            

Step-by-step explanation:

Given : The lengths of two sides of a right triangle are 12 inches and 15 inches.

To find : What is the difference between the two possible  lengths of the third side of the triangle?

Solution :

Since, It is a right angle triangle so we apply Pythagoras theorem,

[tex]C^2=A^2+B^2[/tex]

Where, C is the hypotenuse the longer side of the triangle

A is the perpendicular

B is the base

There will be two cases,

1) Assume that C=15 inches and B = 12 inches

Substitute the value in the formula,

[tex]15^2=A^2+12^2[/tex]

[tex]225=A^2+144[/tex]

[tex]A^2=225-144[/tex]

[tex]A^2=81[/tex]

[tex]A=\sqrt{81}[/tex]

[tex]A=9[/tex]

Assume that A=15 inches and B = 12 inches

Substitute the value in the formula,

[tex]C^2=15^2+12^2[/tex]

[tex]C^2=225+144[/tex]

[tex]C^2=369[/tex]

[tex]C=\sqrt{369}[/tex]

[tex]C=19.2[/tex]

Therefore, The possible length of the third side of the triangle is

[tex]L=C-A[/tex]

[tex]L=19.2-9[/tex]

[tex]L=10.2[/tex]

Therefore, The difference between the two possible  lengths of the third side of the triangle is 10.2 inches.

So, Option 1 is correct.

Answer:

$1x + $3y = c

Step-by-step explanation:

To write an expression you need to pick a variable to represent the cups of orange juice and lemonade.

x = cups of lemonade sold

y = cups of orange juice sold

Now you have the variables to represent the amount of cups sold, so now you need a variable to represent the total cost.

c = amount of money earned from selling drinks

Now you have all the variables, so you need to write how much is cost for that drink.

$1 for one cup of lemonade so $1x

$3 for one cup of orange juice so $3x

Now put the expression together:

$1x + $3y = c

The expression that represents the amount of money that Alice selling drinks​ is $ (a+ 3b)

An expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.

According to the problem,

Let the number of cups of lemonade sold are a and the cups of orange juice sold are b.

Cost of 1 cup of lemonade is $ 1

∴Cost of a cups of lemonade = $ a

Similarly we can say,

Cost of 1 cup of orange juice is $ 3

∴ Cost of b cups of orange juice is $ 3b

So the total cost is represented by the expression : $(a + 3b)

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Answer:

The answer is c.

This is because when it rotates a 180 degrees around its center it maps a parallelogram on to itself.

Answer:

Option D is correct.

Step-by-step explanation:

Option D is correct.

y < 2 and y >= x

Because the dotted line shows that y < 2 and y >=x is shown is represented by diagonal line.

Option: D is the correct answer.

      D.    y<2   and    y≥x

The graph of the system of linear inequalities are two lines:

1)

The first is a solid line which passes through (0,0) , (1,1)

i.e. the equation of the line is: y=x

and the inequality will be a inequality with a equality sign ( since the line is solid ) and the shaded region is above the line .

Hence, the inequality is: y≥x

2)

The second line is a dotted line.

This means that the inequality is strict.

Also, the line is a horizontal line parallel to the x-axis and the line pass through (0,2) and the shaded region is below the line.

Hence, the inequality is given by:

                    y<2

Answer:

[x + 3][2x² - 7]

Step-by-step explanation:

Start out by doing this: [2x³ + 6x² ] - [7x - 21]

↑ ⤻ ↑

GCF: 2x² GCF: -7

Do as so: 2x²[x + 3] -7[x + 3]

You see, one factor is already found [x + 3]. You only use it ONCE. Now, the other factor comes from your two Greatest Common Factors from both groups [2x² - 7]. Together, you end up with the above answer. That arrow under the negative tells you that it is attached to the 3 [distribution of the negative].

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Answer:

(C) 3

Step-by-step explanation:

Let us define the degree of polynomial first

"The degree of a polynomial is the highest power of the variable in the given expression"

Now,

Given expression is:

3x^3+0x^4+8

The highest degree from first observation seems to be 4 but the term with exponent 4 is being multiplied with zero so the degree is then 3 ..

Therefore the correct answer is C. 3 ..

Final answer:

The expression 7x = 8 evaluated with x = 2 results in 14, not 8. There was a misunderstanding in the question as it was not asking for a solution to the equation but rather an evaluation of the expression with a given value of x.

Explanation:

The question asks us to evaluate the expression 7x = 8 when x = 2. However, there seems to be a misunderstanding in the way the question is framed. Normally, an expression such as 7x = 8 would be an equation we solve to find the value of x. But since we are given that x = 2, it appears the task is to substitute this value into the expression 7x and see if it equals 8. Let's clarify and solve accordingly.

First, substitute x = 2 into the expression 7x:

7 * 2 = 14

Therefore, when we substitute x = 2 into the expression 7x, we get 14, not 8. It seems there was confusion in the question regarding what was being asked. If the task was to solve 7x = 8, then x would not equal 2 since 7*2 = 14. However, the original instruction was misunderstood, and the correct task was to substitute x = 2 into the expression and evaluate it, which we did correctly.

Answer:

[tex]a=\pm i\sqrt{26}}[/tex]

Step-by-step explanation:

[tex]6^2+a^2=10\\\\36+a^2=10\qquad\text{subtract 36 from both sides}\\\\a^2=-26<0\\\\\bold{NO\ REAL\ SOLUTIONS}\\\\\text{In the set of complex numbers:}\\\\i=\sqrt{-1}\\\\a^2=-26\to a=\pm\sqrt{-26}\\\\a=\pm\sqrt{(-1)(26)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\a=\pm\sqrt{-1}\cdot\sqrt{26}\\\\a=\pm i\sqrt{26}[/tex]

Answer:

Step-by-step explanation:

the graph of x + y = 4 is the line passes by the point A(2,2) and the slope -1

because 2+2 =4  and y = -x +4

Answer:

Step-by-step explanation:

The formula of a slope:

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

We have the points (-1, 5) and (3, 5). Substitute:

[tex]m=\dfrac{5-5}{3-(-1)}=\dfrac{0}{4}=0[/tex]

It's a horizontal line y = 5.

Step-by-step explanation:

Rectangles, rhombuses, and squares all have angles that add up to 360°.

Rectangles, rhombuses, and squares all have opposite angles that are congruent.

Rectangles and squares have four right angles.

the square has 4 right angles, the rectangle has both pairs of opposite angles that are congruent, and the rhombus has angles where the sum is 360 degrees.

Answer:

54

Step-by-step explanation:

234-126 = 108

108/2 = 54