Given the geometric sequence where a1=3 and the common ratio is -1, what is the domain for n?

Answer:

#1 (1,10),(2,9),(2,8),(4,7),(5,6),(6,5),(7,4),(8,3),(9,2),(10,1). #2 (1,18),(2,9),(3,6),(6,3),(9,2),(18,1)

Answer:

  1 : 4

Step-by-step explanation:

Let x represent the amount of 30% solution for 1 unit of 5% solution. Then the amount of acid in the mix is ...

  0.30x + 0.05·1 = 0.10·(x +1)

  0.30x + 0.05 = 0.10x + 0.10 . . . . eliminate parentheses

  0.20x = 0.05 . . . . . . . . . . . . . . . . subtract 0.05+0.10x

  x = 0.05/0.20 = 1/4

That is, the ratio x : 1 is 1 : 4.

Answer:

The ratio of the amount of the 30% solution to the amount of 5% solution will be 1 : 4.

Step-by-step explanation:

Suppose, the amount of 30% acid solution is [tex]x[/tex] and the amount of 5% acid solution is [tex]y[/tex].

So, the total amount of the mixture [tex]= x+y[/tex], which is 10% acid solution.

Amount of acid in 30% solution [tex]= 30\%\ of\ x=0.30x[/tex]

Amount of acid in 5% solution [tex]=5\%\ of\ y= 0.05y[/tex]

Amount of acid in the mixture [tex]=10\%\ of\ (x+y)=0.10(x+y)[/tex]

Now, the equation will be......

[tex]0.30x+0.05y=0.10(x+y)\\ \\ 0.30x+0.05y=0.10x+0.10y\\ \\ 0.30x-0.10x=0.10y-0.05y\\ \\ 0.20x=0.05y\\ \\ \frac{x}{y} =\frac{0.05}{0.20} =\frac{5}{20}=\frac{1}{4}\\ \\ x:y=1:4[/tex]

So, the ratio of the amount of the 30% solution to the amount of 5% solution will be 1 : 4.

Answer: [tex]a^2+a-6[/tex]

Step-by-step explanation:

To solve the exercise you must apply the following proccedure:

- Apply the distributive property.

- Keepn on mind that when you multiply two powers with equal base, you must add the exponents.

- Add like terms.

Then:

[tex](a)(a)-(a)(2)+(3)(a)-(3)(2)=a^2-2a+3a-6=a^2+a-6[/tex]

Answer:

[tex]\large\boxed{(a+3)(a-2)=a^2+a-6}[/tex]

Step-by-step explanation:

Use FOIL: (a + b)(c + d) = ac + ad + bc + bd

[tex](a+3)(a-2)=(a)(a)+(a)(-2)+(3)(a)+(3)(-2)\\\\=a^2-2a+3a-6\qquad\text{combine like terms}\\\\=a^2+a-6[/tex]

The correct formulas for the composite shape are A. [tex]\( A = 2bh \)[/tex] and B. [tex]\( A = 2\left(\frac{1}{2}bh\right) \)[/tex].

1. Find the area of the composite figure.

You can use the formula for the area of a parallelogram: [tex]$A = bh$[/tex]. Since there are two parallelograms, you add their areas:

[tex]\[ A = 2bh \][/tex]

2. The previous diagram represents a scale drawing of a hexagonal garden. The scale factor is 1cm=0.5m. What is the area of the garden?

If the scale factor is 1 cm = 0.5 m, the area in the drawing needs to be scaled up. The scale factor squared is used for areas. Therefore,

[tex]\[ \text{Area in meters}^2 = (\text{Area in centimeters}^2) \times (\text{Scale factor})^2 \][/tex]

3. For which shape would you use the formula [tex]\((bh) + \left(\frac{1}{2}bh\right)\)[/tex] to find the area?

This formula represents the sum of the areas of a parallelogram and a triangle. So, you would use this formula for a shape that consists of both a parallelogram and a triangle.

4. Which shapes could this hexagon be decomposed into to find its area? Choose all that apply.

Since a hexagon has six sides, it can be decomposed into various combinations of shapes. All the given options are valid:

- A. Two trapezoids

- B. Six triangles

- C. One rectangle and two triangles

- D. Two parallelograms

5. Which formulas could be used to find the area of the composite shape? Choose all that apply.

The correct formulas for finding the area of the composite shape (made up of two parallelograms) are:

- A. [tex]\(A = 2bh\)[/tex]

- B. [tex]\(A = 2\left(\frac{1}{2}bh\right)\)[/tex]

So, the correct choices are A and B.

Answer:

25

Step-by-step explanation:

10*100/40

10*100= 1000

1000/40= 25

Answer:

x=25

explanation:

so we have 40% of x, x =10

40/100 x, x=10

multiplying both sides by 100 and dividing both sides by 40

x=25

calculator check~

10x100÷40 which also gives you the answer of  25

❤️ hope this helps -bangtanboys7❤️

Answer:

100

Step-by-step explanation:

Because it is an issoceles triangle, the sides are equal,making 40 on 1 side be the same on the other side, then since its not obtuse, it should add up to 180, subtract 80 from 180, and get the answer

Answer:

9/5

Step-by-step explanation:

To find the slope, use the slope formula.

[tex]m = \frac{y_2 - y_1}{x_2-x_1} = \frac{18 - -18}{6--14} = \frac{36}{20} =\frac{9}{5}[/tex]

Answer:

{x = 1/2 , y = 3/2

Step-by-step explanation:

Solve the following system:

{3 x + y = 3 | (equation 1)

{x + y = 2 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{3 x + y = 3 | (equation 1)

{0 x+(2 y)/3 = 1 | (equation 2)

Multiply equation 2 by 3:

{3 x + y = 3 | (equation 1)

{0 x+2 y = 3 | (equation 2)

Divide equation 2 by 2:

{3 x + y = 3 | (equation 1)

{0 x+y = 3/2 | (equation 2)

Subtract equation 2 from equation 1:

{3 x+0 y = 3/2 | (equation 1)

{0 x+y = 3/2 | (equation 2)

Divide equation 1 by 3:

{x+0 y = 1/2 | (equation 1)

{0 x+y = 3/2 | (equation 2)

Collect results:

Answer:  {x = 1/2 , y = 3/2

Answer:

[tex]\large\boxed{x=\dfrac{1}{2}\ and\ y=1\dfrac{1}{2}\to\left(\dfrac{1}{2},\ 1\dfrac{1}{2}\right)}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3x+y=3\\x+y=2&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3x+y=3\\-x-y=-2\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=1\qquad\text{divide both sides by 2}\\.\qquad\boxed{x=\dfrac{1}{2}}\\\\\text{Put the value of x to the second equation:}\\\dfrac{1}{2}+y=2\qquad\text{subtract}\ \dfrac{1}{2}\ \text{from both sides}\\\boxed{y=1\dfrac{1}{2}}[/tex]

Answer:  a) x² - 3x - 18 = 0

Step-by-step explanation:

[tex]\dfrac{x}{3}-\dfrac{6}{x}=1\\\\\\\text{Multiply everything by the LCD (3x) to clear the denominator:}\\\\\dfrac{x}{3}(3x)-\dfrac{6}{x}(3x)=1(3x)\\\\\\x^2-18=3x\\\\\\\text{Subtract 3x from both sides:}\\x^2-3x-18=0[/tex]

Answer:

x = 1

Step-by-step explanation:

Given in the question the equation

y = -x² + 2x - 1

To find the x-intercept, substitute in 0 for y

0 = -x² + 2x - 1

To find value of x use quadratic equation

x = -b ± √b²-4ac / 2a

  here a = -1

           b = 2

           c = -1

x1 = -2 + √2²-4(-1)(-1) / 2(-1)

   = -2 + 0 / -2

   = -2 / -2

   = 1

x2 = -2 - √2²-4(-1)(-1) / 2(-1)

   = -2 - 0 / -2

   = -2 / -2

   = 1

The circumference is 6 and the arc is 1.

This means that the arc is 1/6 of the circumference.

A full circle is 360 degrees, since the arc is 1/6 of the circle, the central angle would be 1/6 of 360.

360 x 1/6 = 60

The central angle is 60 degrees.

Answer:  [tex]\bold{12\sqrt2}[/tex]

Step-by-step explanation:

A 45-45-90 triangle has corresponding sides of: a - a - a√2

Since the side that corresponds to the 90° angle = a√2, then

[tex]a\sqrt2=24\\\\a=\dfrac{24}{\sqrt2}\\\\\\.\ =\dfrac{24}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\\\\\\,\ =\dfrac{24\sqrt2}{2}\\\\\\.\ =\boxed{12\sqrt2}[/tex]

12 square root of 2 will be the answer

Answer:

33 cents

Step-by-step explanation:

4/12=1/3=0.33=33 cents

Answer:

= $1/3

Step-by-step explanation:

A dozen contains 12 items

Therefore;

a dozen of doughnuts contains 12 doughnuts

12 doughnuts = $ 4.00

1 doughnuts = 4/12

                    = $ 1/3

Answer:

c= (-10)

Step-by-step explanation:

Simplify both sides of the equation then isolate the variable.

Answer:

c= 15.9

Step-by-step explanation:

well.. what are the statements?

Answer: The function that best represents the data is f(x)=24,512(0.755)^x.

The function decrease indefinitely.

It is reasonable to interpolate to the value of the car at 4.5 years.

Step-by-step explanation:

took the test

Answer:

A. 40°

Step-by-step explanation:

Hello, there! The angle is across from (vertical to) the angle given. Therefore, the 2 angles are the same.

I hope I helped!

Let me know if you need anything else!

~ Zoe

Answer:

x = 40°, or A)

Step-by-step explanation:

The Vertical Angle Theorem states that if the angles are vertically (directly) opposite of each other, the measurements will be the same.

Therefore, if the opposite angle of x is 40, then x also = 40.

~

If the circumference is 34 Times PI that means that 34 is the diameter.

So that means that you can just divide the diameter by 2 to get the radius (Because the radius is half of the diameter.)

So the answer is the diameter is 34 and the radius is 17

Final answer:

The diameter of the circle with a circumference of 34π is 34 units, and the radius is half the diameter, which is 17 units.

Explanation:

The circumference of a circle is given by the formula C = πd, where C is the circumference, π (Pi) is approximately 3.14159, and d is the diameter of the circle. Given that the circumference of the circle is 34π, we can find the diameter by dividing the circumference by π:

d = C / π = 34π / π = 34

Therefore, the diameter is 34 units. The radius r is half of the diameter, so:

r = d / 2 = 34 / 2 = 17

Thus, the radius of the circle is 17 units.

Answer:  B) The parabola is narrower.

Step-by-step explanation:

[tex]y=ax^2+bx+c[/tex] is the Standard form of a quadratic function, where a, b and c are coefficients ([tex]a\neq0[/tex]).

With the coefiicient "a" you can determine how narrow or wide the parabola is:

[tex]|a|>1[/tex] makes the parabola narrow.

[tex]0<|a|<1[/tex] makes the parabola wide.

Given the transformation of the parent function: [tex]f(x)=3x^2[/tex], you can identify that:

[tex]a=3[/tex]

Then:

[tex]|a|>1[/tex]

Therefore, as the parent function is multiplied by 3 and know [tex]|a|>1[/tex],   the parabola if narrower than the parabola of the quadratic parent function [tex]f(x)=x^2[/tex].

Answer:

Option B - The parabola is narrower.

Step-by-step explanation:

Given : The function [tex]f(x)=x^2[/tex] is transformed to  [tex]f(x)=3x^2[/tex]

To find : Which statement describes the effect(s) of the transformation on the graph of the original function?

Solution :

When the function of parabola [tex]f(x)=x^2[/tex] is transformed by 'a' unit [tex]f(x)=ax^2[/tex]

Then, [tex]|a|>1[/tex] makes the parabola narrow.

and [tex]0<|a|<1[/tex] makes the parabola wide.

On comparing with given function,

|a|=|3| >1 which is greater than 1.

Which means it makes the parabola narrow.

Therefore, the parabola is narrower.

So, Option B is correct.

Answer:

Step-by-step explanation:

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\k\ \parallel\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\=============================\\\\\text{We have the equation}\ y=\dfrac{1}{2}x+3\to m_1=\dfrac{1}{2}.\ \text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2.\\\\\text{We have the equation}\ y=-2x+b\\\\\text{Put the coordinates of the point (10, -5) to the equation and solve}\\\text{for}\ b:\\\\-5=-2(10)+b\\-5=-20+b\qquad\text{add 20 to both sides}\\15=b\\\\\text{Finally we have:}\\\\y=-2x+15[/tex]

Answer: OPTION B.

Step-by-step explanation:

The number that are inside of the square root are called "radicands".

To subtract the expressions shown in the image attached, the radicands must be the same.

As you can see, both are equal, therefore, you can subtract the numbers that are in front of the square roots.

Then, you obtain the following result:

[tex]3\sqrt{2}-\sqrt{2}=(3-1)\sqrt{2}=2\sqrt{2}[/tex]

The answer is the option B.

Answer:

The correct answer is option B.  2√2

Step-by-step explanation:

It is given an expression, 3√2 - √2

Simplify the expression

The expression is 3√2 - √2

3√2 - √2 = √2(3 - 1)   ( taking √2 as common)

= √2 x  2

= 2√2

Therefore the simplified form of given expression(3√2 - √2) is 2√2

The correct answer is option B.  2√2

Answer:

[tex]\large\boxed{y=2(x+1)^2-3}[/tex]

Step-by-step explanation:

The vertex form of an equation of a parabola:

[tex]y=a(x-h)^2+k[/tex]

(h, k) - vertex

We have

[tex]y=2x^2+4x-1=2\left(x^2+2x-\dfrac{1}{2}\right)[/tex]

We must use the formula: [tex](a+b)^2=a^2+2ab+b^2\qquad(*)[/tex]

[tex]2\left(x^2+2(x)(1)-\dfrac{1}{2}\right)=2\bigg(\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-\dfrac{1}{2}\bigg)\\\\=2\left((x+1)^2-1-\dfrac{1}{2}\right)=2\left((x+1)^2-\dfrac{3}{2}\right)[/tex]

Use the distributive formula a(b + c) = ab + ac

[tex]2(x+1)^2+2\left(-\dfrac{3}{2}\right)=2(x+1)^2-3[/tex]

The answer to you question is = c) 68 bookmarks

The correct answer is D.

0.96 x 72 = 69.12

Hope this helps. Please mark brainliest and comment if correct.

Answer:

add up all numbers

then divide that number by the amount of numbers.

Step-by-step explanation:

mad is basically finding the average of a set of numbers.

and how do you do that?

first, add up all numbers

ex: 1, 5,3,10,6,20,15,15,14  --> this adds up to 90.

then divide that number by the amount of numbers.

count how much numbers ehere are: there are 9 numbers.

divide 90 by 9 and the mad/average is 10.

plz give brainliestttt

Answer:

Here is an example..:

Find the M.A.D of the set of data

10.2 , 9.4, 11.3, 12.9

( so, we just have to add up all numbers )

10.2 + 9.4 + 11.3 + 12.9 = 43.8

Then we divide them by 4, you might be wondering..why 4?

that's because there are about 4 numbers in the data set.

So:

43.8

____= 10.95 (we found the mean! :D)

  4

After that, we just have to subtract the mean (10.95) to the same numbers (or the so called data set)

10.95 - 10.2 = 0.75

10.95 - 9.4 = 1.55

10.95 - 11.3 = 0.35

10.95 - 12.9 = 1.95

For our final step, we just add up all the difference, then,  divide it by 4 again.

0.75 + 1.55 + 0.35 + 1.95 = 4.6

                                          --------- = 1.15

                                              4

~hope this helps, have a good day/afternoon/night~

I think that is line 5

Answer:

Lines 3 & 4

Step-by-step explanation: To find slope you calculate rise/run.

Line 1: 6/2= 3

Line 2: 6/3= 2

Line 3: 6/4= 1.5

Line 4: 6/5 = 1.2

Line 5: 6/6= 1

Lines 3 and 4 are the only two that have a slope that fall between 1 and 2. Notice it said greater than and less than but not equal to.

Answer:

A

Step-by-step explanation:

Answer:

Option D.  23.4 pounds

Step-by-step explanation:

step 1

Find the pieces of glass for 22.5 pounds of copper in the sculpture.

using proportion

[tex]\frac{12}{1}=\frac{x}{22.5} \\ \\x=22.5*12\\ \\x=270\ piece\ of\ glass[/tex]

step 2

Find the pounds of bronze used in the sculpture

using proportion

[tex]\frac{6.5}{75}=\frac{x}{270} \\ \\x=270*6.5/75\\ \\x=23.4\ pounds[/tex]

Answer:

1. B 2. C

Step-by-step explanation:

1. x^2-18x+(18/2)^2=19+(18/2)^2

(x-18/2)^2=100

(x-9)^2=100

x1= -1 x2= 19

2. x^2=81

x=+-9

x1=-9 x2=9

The difference of two numbers is 15, and their product is 700. The numbers are 25 and 10.

The two numbers are 25 and 10.

The two numbers are 35 and 20, or -20 and -35.

The problem states that the difference of two numbers is 15, and their product is 700. Let's denote the two numbers as x and y.

We have the following system of equations:

From equation (1), we can express x in terms of y:

Substituting this into equation (2) gives:

To solve this quadratic equation, we use the quadratic formula: y = (-b ± √(b² - 4ac)) / 2a

Here, a = 1, b = 15, and c = -700. Plugging in these values, we get:

We have two solutions:

The corresponding values for x are:

Therefore, the two pairs of numbers are (35, 20) and (-20, -35).

Answer:

First, you add 6.8 and 6.8 together, since it's a rectangular garden and the length is the same on both sides of the rectangle. This will equal 13.6. Then you subtract 13.6 from 20.6. You will get 7. Divide this in half and you will get 3.5. 3.5 is the width.

Step-by-step explanation:

Answer:

x = ±4

Step-by-step explanation:

we are given  |x|-4=0

The first step is to add 4 on both sides of the equation;

|x|-4+4=0+4

|x|=4

Getting rid of the absolute symbol implies we have to add the positive and negative symbols to the right hand side of the equation;

x = ±4