the sum of the first six terms of a geometric series is 21/16 . if the common ratio is -1/2 , what is the first term?

Answer:

Area = 81; Side Length = 3

Step-by-step explanation:

The area of a square is the side lenght squared, and 9² is 81.

The side lengh can be found by taking the square root of the area. √9 = 3

Answer:

it's 10 all you had to do was count the boxes from a to b

Step-by-step explanation:

Answer:

The value of b is 6 and the value of c is also 6

Step-by-step explanation:

We know that given triangles are congruent. When two triangles are congruent then their respective sides are also equal/congruent.

So,

ΔUWV≅ΔEDF

Then

WV ≅ DF

WU ≅ DE

UV ≅ EF

So,

Putting their respective value equal:

WV = DF

[tex]9c = 10c-6\\10c-6 = 9c\\10c-6+6 = 9c+6\\10c = 9c+6\\10c-9c = 9c+6-9c\\c = 6\\and\\10b = b+54\\10b-b = b+54-b\\9b = 54\\\frac{9b}{9} = \frac{54}{9}\\b = 6[/tex]

Hence,

The value of b is 6 and the value of c is also 6

Answer:

You will need 18

Step-by-step explanation:

Answer:

u = -5/9

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define equation

-3(u + 2) = 5u - 1 + 5(2u + 1)

Step 2: Solve for u

Step 3: Check

Plug in u into the original equation to verify it's a solution.

Here we see that -13/3 does indeed equal -13/3.

∴ u = -5/9 is a solution of the equation.

Answer:

[tex] \sf u = -\dfrac{5}{9} [/tex]

Step-by-step explanation:

Expand the following:

[tex] \longrightarrow [/tex] -3(u + 2) = 5u - 1 + 5(2u + 1)

5(2u + 1) = 10u + 5:

[tex] \longrightarrow [/tex] -3(u + 2) = 5u - 1 + 10u + 5

-3(u + 2) = -3u - 6:

[tex] \longrightarrow [/tex] -3u - 6= 10 u + 5 u - 1 + 5

Grouping like terms,

5u - 1 + 10u + 5 = (5u + 10u) + (-1 + 5):

[tex] \longrightarrow [/tex] -3u - 6 = (5u + 10u) + (-1 + 5)

5u + 10u = 15u:

[tex] \longrightarrow [/tex] -3u - 6 = 15u + (-1 + 5)

5 - 1 = 4:

[tex] \longrightarrow [/tex] -3u - 6 = 15u + 4

Subtract 15 u from both sides:

[tex] \longrightarrow [/tex] (-3u - 15u) - 6 = (15u - 15u) + 4

-3u - 15u = -18u:

[tex] \longrightarrow [/tex] -18u - 6 = (15u - 15u) + 4

15u - 15u = 0:

[tex] \longrightarrow [/tex] -18u - 6 = 4

Add 6 to both sides:

[tex] \longrightarrow [/tex] (6 - 6) - 18u = 6 + 4

6 - 6 = 0:

[tex] \longrightarrow [/tex] -18u = 4 + 6

4 + 6 = 10:

[tex] \longrightarrow [/tex] -18u = 10

Divide both sides of -18 u = 10 by -18:

[tex] \longrightarrow [/tex] [tex] \sf \dfrac{-18u}{-18}= \dfrac{10}{-18} [/tex]

[tex] \sf \dfrac{-18}{-18}=1: [/tex]

[tex] \longrightarrow [/tex] [tex] \sf u = \dfrac{10}{-18} [/tex]

[tex] \sf \dfrac{10}{-18}=\dfrac{5}{-9}: [/tex]

[tex] \longrightarrow [/tex] [tex] \sf u = \dfrac{5}{-9} [/tex]

Multiply numerator and denominator of [tex] \sf \dfrac{10}{-18} [/tex] by -1:

[tex] \longrightarrow [/tex] [tex] \sf u = \dfrac{-5}{9} [/tex]

Answer:

The angle measure is 35°.

Step-by-step explanation:

Complementary angles in geometry are angles that summate to exactly 90 degrees. If an angle measures 20 degrees less than the measure of its complementary angle, we can create an equation to find the measure of this angle.

The complementary angle is going to equal 90 - x, so this becomes a term in our equation: (90 - x)

Both angles need to add up to 90 degrees, so we can set up this equation:

x = (90 - x) - 20, where x is our unknown angle.

Now, we can just solve for x.

[tex]x = (90-x)-20\\\\x = 90 - x - 20\\\\x = 70 - x \\\\2x = 70\\\\\bold{x = 35}[/tex]

Therefore, the angle that measures 20 degrees less than its complementary angle is 35°. We can check this by using substitution:

[tex]90 = x + 35\\\\55 = x \rightarrow x = 55\\\\55 - 35 = 20[/tex]

Therefore, the two angles are 55° and 35°, but the angle that measures 20° less than the measure of its complementary angle is 35°.

Answer:

The dependent variable is the hour.

Answer: The remainder is 6

Step-by-step explanation:

you divide using long division

8 goes into 4 zero times

8 goes into 47 5 times. 5 times 8 is 40. 47-40=7 then you bring down the 8 and 8 would go into 78 9 times. then you would subtract 78 from 72 and you get 6, so 6 is the remainder.

Answer:

Step-by-step explanation:

-2/3 and -8/22

No, they are not.

-2/3 = -0.6

-8/22= -4/11 or -0.36

Answer:

43.75

Step-by-step explanation:

It you want to find the speed of the cat, all you have to do is divide 35 by 0.8.

Answer:

The answer is B formal

Answer:

B on edge 2021

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

because 16+16 is 32

Answer:

[tex]\displaystyle -\frac{4}{13},~-\frac{3}{13},~-\frac{1}{13},~0[/tex]

Step-by-step explanation:

Rational Numbers

The rational numbers are defined as numbers of the form [tex]\frac{a}{b}[/tex] where a and b are integer numbers and b is not zero.

Two rational numbers expressed as fractions can be better compared if they have the same denominator. For example, 5/11 is greater than 3/11 because they have the same denominator and 5 is greater than 3.

Similarly, if we have the fractions -5/13 and 1/13, it's clear that the first fraction is less than the second. If we wanted to have some rational numbers between them we only have to play around with the numerators: any number between -5 and 1 will do.

Examples of the required numbers:

[tex]\displaystyle -\frac{4}{13},~-\frac{3}{13},~-\frac{1}{13},~0[/tex]

Answer:

A. Horizontal and slope is 0

B. Horizontal and slope is 0

C. Vertical and slope is undefined

D. Vertical and slope is undefined

Step-by-step explanation:

Answer:

4x - 9y = 3

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

4x - 8 = 9y - 5 ( subtract 9y from both sides )

4x - 9y - 8 = - 5 ( add 8 to both sides )

4x - 9y = 3 ← in standard form

Answer:

Iscoccecles

Sorry if i spelled it wrong.

Step-by-step explanation:

Answer:

A. 3s + 2

Step-by-step explanation:

6s - (3s - 2)

6s - 3s +2

3s + 2

A. 3s + 2

Answer:

 [tex]\boxed{3s+2}[/tex]

Solution Steps:

__________________________________________________________

To find the opposite of 3s−2, find the opposite of each term:

Combine 6s and −3s:

Rewrite:

__________________________________________________________

 [tex]\bold{Hope~this~helps~Mate!}\\\bold{If~you~need~anything~else,~feel~free~to~ask!}\\\\\bold{~~~~-Your~friendly~answerer,~Shane.}[/tex]

Answer:

[tex]Z(x,y) = (-18,7)[/tex]

Step-by-step explanation:

Given

[tex]X = (10,9)[/tex]

[tex]Y = (-4,8)[/tex]

Required

Determine the coordinates of Z

From the question, we understand that Y is the midpoint

And the midpoint is calculated as:

[tex](x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

In this case:

[tex]Y(x,y) = (-4,8)[/tex]

[tex]X(x_1,y_1) = (10,9)[/tex]

[tex]Z = (x_2,y_2)[/tex]

So: This gives

[tex](x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

[tex](-4,8) = (\frac{10+x_2}{2},\frac{9+y_2}{2})[/tex]

Multiply through by 2

[tex](-8,16) = (10 + x_2,9+y_2)[/tex]

By comparison:

[tex]-8 = 10 + x_2[/tex] and [tex]16 = 9 + y_2[/tex]

Solving for x2

[tex]-8 = 10 + x_2[/tex]

[tex]-8 - 10 = x_2[/tex]

[tex]-18 = x_2[/tex]

[tex]x_2 = -18[/tex]

Solving for y2

[tex]16 = 9 + y_2[/tex]

[tex]16 - 9 = y_2[/tex]

[tex]7 = y_2[/tex]

[tex]y_2 = 7[/tex]

Hence, the coordinates of Z is:

[tex]Z(x,y) = (-18,7)[/tex]

Answer:

609

Step-by-step explanation:

609

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

Answer:

389 people

Step-by-step explanation:

Step 1

we convert 1500 inches to feet

1 inch = 0.0833 feet

1500 inches = x feet

x = 1500 × 0.0833

x = 125 feet

Step 2

We create a proportion

Since it is on both sides

20/9ft × 10ft = x/7 feet × 125 feet × 2

20/90 = x/1750

Cross Multiply

90 × x = 20 × 1750

x = 20 × 1750/90

x = 35000/90

x = 388.88888889

approximately = 389 people

Answer:

option 1

Step-by-step explanation:

hope that helps you :)

Answer:

y>/ 2x -4

Step-by-step explanation:

This >/ means the line underneath

Answer:

9

Step-by-step explanation:

f(1/2)=8+2(1/2)

f(1/2)=8+1

f(1/2)=9

Answer:

f ( 1/2 ) = 9

Step-by-step explanation:

Step 1:

f ( x ) = 8 + 2x          Function

Step 2:

x = 1/2              Given

Step 3:

f ( 1/2 ) = 8 + 2 ( 1/2 )        Input x value

Step 4:

f ( 1/2 ) = 8 + 1        Multiply

Answer:

f ( 1/2 ) = 9

Hope This Helps :)

Answer:

1+1=2

Step-by-step explanation:

1 as a single number plus another 1 as a single number is 2. like this:+=.

Answer:

x = 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=3 because if you subtract 1 its 4x=12 which is 3