A geometric series has a common ratio of (-2) and the first term is 3.
Show that the sum of the first eight positive terms of the series is 65 535.

Answer:

8

Step-by-step explanation:

x+37+x+37+90 = 180

2x + 74 = 90

2x = 16

x = 8

Answer:

x=8°

Step-by-step explanation:

JI is a diameter and K is on the circumference of a circle.

∴∠JKI=90°

also KJ=KI=x(say)

tan (x+37)=y/y=1=tan 45

so x+37=45

x=45-37=8°

Answer:

(8, -7)

Step-by-step explanation:

Hi there!

We are given this system:

y=-3x+17

2x+3y=5

And we want to solve the system

Let's solve it by substitution.

In the first equation, we are given y=-3x+17, which we can substitute -3x+17 as y into the second equation

2x+3(-3x+17)=5

Now do the distributive property

2x+-9x+51=-5

Combine like terms

-7x+51=-5

Subtract 51 from both sides

-7x=-56

Divide both sides by -7

x=8

Now substitute 8 as the value of x in y=-3x+17 to find the value of y

y=-3(8)+17

y=-24+17

y=-7

The answer is x=8, y=-7. If you need it as a point, it's (8, -7)

Hope this helps!

Answer:

0.375

Step-by-step explanation:

0.125 x 3 = 0.375

Answer:

0.375

Step-by-step explanation:

3 x 125

8 x 125

=

375

1000

=

0.375

Other sample problem:

5 = 5×125 = 625 = 0.625

8         8×125         1000

Hope this helps, have a good day :)

Answer:

59.5 feet

Step-by-step explanation:

The second tree is 59.5 feet tall.

Two trees are growing in a clearing.

The first tree is 17 feet tall and casts a 10-foot shadow.

The second tree casts a 35-foot shadow.

Let x be the tall is the second tree.

Then,

The ratio of the height of the tree is;

[tex]\rm \dfrac{17}{10} = \dfrac{x}{35}\\\\17 \times 35 = x \times 10\\\\595 = 10x\\\\x = \dfrac{595}{10}\\\\x = 59.5 \ feet[/tex]

Hence, the second tree is 59.5 feet tall.

To know more about Ratio click the link given below.

https://brainly.com/question/8677748

Answer:

false it would be something like x root 2

Step-by-step explanation:

Answer:

∠ G = 121°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 given angles and equate to 180

x + 3x + 25 + x - 5 = 180 , that is

5x + 20 = 180 ( subtract 20 from both sides )

5x = 160 ( divide both sides by 5 )

x = 32

Thus

∠ G = 3x + 25 = 3(32) + 25 = 96 + 25 = 121°

Answer:

121

Step-by-step explanation:

The inverse function [tex]f^{-1}(x)[/tex] is such that

[tex]f\left(f^{-1}(x)\right) = x[/tex]

Plugging [tex]f^{-1}(x)[/tex] into [tex]f(x)[/tex] gives us

[tex]f\left(f^{-1}(x)\right) = \dfrac{3f^{-1}(x) + 3}{5f^{-1}(x) + 6} = x[/tex]

Solve for [tex]f^{-1}(x)[/tex] :

[tex]\dfrac{3f^{-1}(x) + 3}{5f^{-1}(x) + 6} = x \\\\ 3f^{-1}(x)+3=x\left(5f^{-1}(x)+6\right) \\\\ 3f^{-1}(x) + 3 = 5x f^{-1}(x)+6x \\\\ 5xf^{-1}(x)-3f^{-1}(x) = 3 - 6x \\\\ (5x-3)f^{-1}(x)=3-6x \\\\ \boxed{f^{-1}(x)=\dfrac{3-6x}{5x-3}}[/tex]

Answer:

First choice: (1/4)(2 + v) = 3; v = 10 pounds of chopped vegetables

Step-by-step explanation:

"2 pounds of meat with some chopped vegetables"

2 + v

"She divides the mixture into 4 equal portions."

(1/4)(2 + v)

"Each portion weighs 3 pounds."

(1/4)(2 + v) = 3

2 + v = 12

v = 10

Answer: (1/4)(2 + v) = 3; v = 10 pounds of chopped vegetables

Answer:

(2+v)=3   v=10

Step-by-step explanation:

Answer:

The total duration of the trip is 48 hours.

Step-by-step explanation:

Let suppose that ship travels at constant speed during its travel. Each stage is represented by the following kinematic equation:

[tex]v =\frac{\Delta s}{\Delta t}[/tex]

Where:

[tex]\Delta s[/tex] - Travelled distance, measured in kilometers.

[tex]\Delta t[/tex] - Time, measured in hours.

[tex]v[/tex] - Speed, measured in kilometers per hour.

Now, each stage is represented by the following expressions:

Outbound trip

[tex]v = \frac{700\,km}{\Delta t}[/tex]

Return trip

[tex]v + 10\,\frac{km}{h} = \frac{700\,kh}{\Delta t - 8\,h}[/tex]

By eliminating [tex]v[/tex] and simplifying the resulting expression algebraically:

[tex]\frac{700\,km}{\Delta t} + 10\,\frac{km}{h} = \frac{700\,km}{\Delta t -8\,h}[/tex]

[tex](700\,km)\cdot \left(\frac{1}{\Delta t - 8\,h}-\frac{1}{\Delta t} \right) = 10\,\frac{km}{h}[/tex]

[tex]\frac{1}{\Delta t - 8\,h}-\frac{1}{\Delta t} = \frac{1}{70}\,\frac{1}{h}[/tex]

[tex]\frac{8\,h}{\Delta t \cdot (\Delta t-8\,h)} = \frac{1}{70}\,\frac{1}{h}[/tex]

[tex]560\,h^{2} = \Delta t\cdot (\Delta t - 8\,h)[/tex]

[tex](\Delta t )^{2}-8\cdot \Delta t - 560 = 0[/tex]

This equation can be solved by means of the Quadratic Formula, whose roots are presented below:

[tex]\Delta t_{1} = 28\,h[/tex] and [tex]\Delta t_{2} = -20\,h[/tex]

Only the first roots offers a physically resonable solution. Then, total duration of the trip is:

[tex]t_{T} = 28\,h +20\,h[/tex]

[tex]t_{T} = 48\,h[/tex]

The total duration of the trip is 48 hours.

Answer:

D

Step-by-step explanation:

As the graph depicts, the function is increasing in the interval [-2,3]

Answer:

see below

Step-by-step explanation:

10c + 5 < 45

Subtract 5 from each side

10c + 5-5 < 45-5

10c < 40

Divide by 10 on each side

10c/10 < 40/10

c < 4

Open circle at 4 and the line going to the left

Answer:

15.56

Step-by-step explanation:

Total flour available=35 cups

Each cake=2 1/4 cups

Find how many cakes Pauline can bake with 35 cups of flour

Let the number of cakes she can bake with 35 cups of flour=x

x=35 cups / 2 1/4 cups

=35÷9/4

=35×4/9

=140/9

=15 5/9 cakes

=15.56 cakes approximately

Answer:

x=30

Step-by-step explanation:

to find the value of x you have to find K(constant number).

[tex]\frac{x}{45}=\frac{18}{27}\\\frac{x}{45}=\frac{2}{3}\\ 3(x)=45*2\\3x=90\\x=\frac{90}{3}\\ x=30[/tex]

Answer:

The value of x is 30

Step-by-step explanation:

Step 1: Find the scale factor

[tex]\frac{FA}{F B} =\frac{45}{27}[/tex]

Step 2: Use the scale factor to solve for x

[tex]\frac{45}{27} =\frac{x}{18}[/tex]

[tex](45)(18) = 27x[/tex]

[tex]810 = 27x[/tex]

[tex]x = 30[/tex]

Therefore x = 30

Answer:

Hello,

Answer m=-1, n=-6,l=2

Step-by-step explanation:

[tex]A*U=B\\\begin{bmatrix}3&-1&0\\0&1&3\\0&0&2\end{bmatrix}*\begin{bmatrix}m\\n\\l\end{bmatrix}=\begin{bmatrix}3\\0\\4 \end{bmatrix}\\\\\\A^{-1}=\begin{bmatrix}\dfrac{1}{3}&\dfrac{1}{3}&\dfrac{-1}{2}\\\\0&1&\dfrac{-3}{2} \\\\0&0&\frac{1}{2}\end{bmatrix}\\\\\\A^{-1}*A*U=A^{-1}*B\\[/tex]

[tex]U=\begin{bmatrix}\dfrac{1}{3}&\dfrac{1}{3}&\dfrac{-1}{2}\\\\0&1&\dfrac{-3}{2}\\\\0&0&\dfrac{1}{2}\end{bmatrix}*\begin{bmatrix}3\\0\\4\\\end{bmatrix}=\begin{bmatrix}-1\\-6\\2\end{bmatrix}\\\\[/tex]

Answer:

10t+2

Step-by-step explanation:

2-5t+8+5t-8

10t+2

Answer:

Step-by-step explanation:

(a+2,b)=(4,5)

Since the points are equal we can equate them to find a

Comparing a + 2 to 4

We have

a + 2 = 4

Send 2 to the right side of the equation

a = 4 - 2

We have the final answer as

Hope this helps you

Step-by-step explanation:

Here,

according to the question,

(a+2, b)=(4,5)

since, they are equal, equating with their corresponding elements we get,

(a+2)=4

or, a= 4-2

Therefore, the value of a is 2.

Also you can find value of b in same way,

b=5.

Therefore, the value of a abd b are 2 and 5 respectively.

Hope it helps...

Answer:

Step-by-step explanation:

Hey there!!!,

in this problem we are expected to present an equation for the given scenario, and a way out is to model it after the equation of line

i.e y= mx+c

From the problem statement we can see that the constant amount Myles have is $635, and also earnings of $120 weekly.

Comparing the statement withe equation of line we have

  y= 120x+ 635

as "x" is the number of weeks worked and $635 is the constant amount at hand.

Should you need further clarification on this, let me know

Answer:

The conditions for a substance to float on liquid are given below:

[tex] \mathrm{Hope \: I \: helped!}[/tex]

[tex] \mathrm{Best \: regards!}[/tex]

Answer:

The simplest form of the given expression is 8.

Step-by-step explanation:

(-11/2x + 3) - 2(-11/4x - 5/2)

Distribute 2 to (-11/4x - 5/2)

(-11/2x + 3) - (-11/2x - 5)

Now, combine like terms. The terms with the x value will cancel each other out because a negative plus a positive of the same number will equal zero. For example, -2 + 2 = 0.

So, the expression in the simplest form is going to be 8. The x values have cancelled each other out so all there is left is the constant number which is 8.

Answer:

The answer is 4.75

Step-by-step explanation:

Since six months is 28.50 then 1 month is equal to x

       28.50: 6 months

           x     : 1 month

 After this  you cross multiple so u divide by 6 both side to get 4.75

   6x/6: 28.50/6

   x=4.75

Answer:

42,44,46

Step-by-step explanation:

we first divide the 132 by the 3 which gives 44

since the numbers involved are even numbers and we know even numbers are numbers divisible by 2 we subtract 2 from the 44 and also add 2 to the 44 the get the rest of the two numbers which is from the above explanation

(44-2),44,(44+2)

42,44,46

we can check whether the above numbers are correct by adding to see whether we get 132

42+44+46=132 which are consecutive even numbers

Answer: 42, 44, and 46

Explanation: Make sure you read through the problem carefully so that you recognize that we are dealing with consecutive even numbers here.

So we can represent our numbers as follows.

X ⇒ first even integer

X + 2 ⇒ second even integer

X + 4 ⇒ third even integer

Since their sum is 132, our equation reads x + (x + 2) + (x + 4) = 132.

Solving from here, we find that x = 42.

So x + 2 is 44 and x + 4 is 46.

Answer:

[tex]\huge\boxed{Answer=>silver}[/tex]

Step-by-step explanation:

Information given:

1. 11 red bikes

2. 3 blue bikes

3. 4 orange bikes

4. 12 silver bikes

...........................................................

For every 1 orange bike, there are 3 ______

Note: there is 4 orange bikes.

(Denominator will be 4 since 4 orange bikes)

Red: [tex]11/4[/tex]

Blue: [tex]3/4[/tex]

(Don’t include orange)

Silver: [tex]12/4[/tex] (which equals 3)

We can’t divide any of the fractions accept for silver.

So the answer is silver. Hope this helps! ✨by: RobloxYt ✨

Answer:

-31/26

Step-by-step explanation:

To find the slope

m= ( y2-y1)/(x2-x1)

   = ( 15 - -16)/(-7 - 19)

   = ( 15+16)/(-7-19)

    = 31/ -26

-31/26

━━━━━━━☆☆━━━━━━━

▹ Answer

-1 - 1/2x

▹ Step-by-Step Explanation

3x ÷ x - 4 + x - 3 ÷ 2x

Divide and Rewrite:

3 * 1 - 4 + x - 3 ÷ 2 * x

Calculate:

3 - 4 + x - 3/2x

-1 + x - 3/2x

= -1 - 1/2x

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

Step-by-step explanation:

[tex]\frac{3x}{x-4}+\frac{x-3}{2x}[/tex]

Make them into common denominators. To do so, multiply by the LCM of the denominators. The LCM of the denominators is (x-4)(2x). Thus, we multiply 2x to the first term and (x-4) to the second:

[tex](\frac{2x}{2x}) \frac{3x}{x-4}+(\frac{x-4}{x-4}) \frac{x-3}{2x}[/tex]

Simplify:

[tex]\frac{6x^2}{2x(x-4)}+\frac{x^2-7x+12}{2x(x-4)} \\=\frac{7x^2-7x+12}{2x(x-4)}[/tex]

And this cannot be simplified further (you can also distribute the denominator if preferred).

Answer:

3.2768 feet

Step-by-step explanation:

The situation can be model by h(x)=8*(4/5)^(n-1). For the 5th jump, n=5. The height will be 8*(4/5)^4=3.2768

Answer:

[tex]\Large \boxed{\mathrm{Option \ 2}}[/tex]

Step-by-step explanation:

[tex]2x^2 =16[/tex]

The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is x, so divide both sides by 2 before applying the square root property.

The x variable should be isolated on one side of the equation. The x variable is squared so before performing the square root property where we take the square root of both sides, we divide both sides by 2, then take the square root of both sides.

Dividing both sides by 2.

[tex]\displaystyle \frac{2x^2 }{2} =\frac{16}{2}[/tex]

[tex]x^2 =8[/tex]

Taking the square root of both sides.

[tex]\sqrt{x^2 } =\pm \sqrt{8}[/tex]

[tex]x=\pm 2\sqrt{2}[/tex]

Answer:

Option 2

Step-by-step explanation:

2x² = 16

Since x is completely squared and and 2 isn't , so we need to divide both sides by 2. As to find x , we need to "isolate" x first so that is why we need to get rid of 2 with the x². We'll divide both sides by 2 in order to get rid of 2.

Dividing both sides by 2

=> x² = 8

Now , that is the x is isolated so we'll take square root on both sides

=> x = ±2√2

Answer:

y=3/4x-2

Step-by-step explanation:

two points from graph (0-2) and (8,4)

find slope m: y2-y1/x2-x1

m=4+2/8-0

m=6/8=3/4

x=0 then y=b=-2

y=3/4x-2

Answer:

8

Step-by-step explanation:

-4(2)+8(-3)+12-8(2)-2(-3)+6=-8-24+12-16+6+6=8

Answer:

-24

Step-by-step explanation:

-4b + 8c + 12 - 8b - 2c + 6

Combine like terms

6c+18-12b

Let b=2  c=-3

6(-3) +18-12(2)

-18 +18 -24

-24

Answer:

4m/3m

Step-by-step explanation:

1km = 1000m

750m : 1km

750m : 1000m

Reduce ratio in simplest form.

HCF of 1000 and 750 is 250

750  ÷ 250 / 1000  ÷ 250

= 4/3

Hence, the simplest form of the ratio 750m : 1km is 4m/3m