2(6x+5)=58
(solve for x)

Answer:

[tex]x = \frac{5 + \sqrt{53}}{2}[/tex]  or  [tex]x = \frac{5 - \sqrt{53}}{2}[/tex]

Step-by-step explanation:

Given

[tex]x^2 - 5x - 7 = 0[/tex]

Required

Solve for x using:

[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

First, we need to identify a, b and c

The general form of a quadratic equation is:

[tex]ax^2 + bx + c = 0[/tex]

So, by comparison with [tex]x^2 - 5x - 7 = 0[/tex]

[tex]a = 1[/tex]     [tex]b = -5[/tex]      [tex]c = -7[/tex]

Substitute these values of a, b and c in

[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]x = \frac{-(-5) \± \sqrt{(-5)^2 - 4 * 1 * -7}}{2 * 1}[/tex]

[tex]x = \frac{5 \± \sqrt{25 +28}}{2}[/tex]

[tex]x = \frac{5 \± \sqrt{53}}{2}[/tex]

Split the expression to two

[tex]x = \frac{5 + \sqrt{53}}{2}[/tex]  or  [tex]x = \frac{5 - \sqrt{53}}{2}[/tex]

To solve further in decimal form, we have

[tex]x = \frac{5 + 7.28}{2}[/tex]  or  [tex]x = \frac{5 - 7.28}{2}[/tex]

[tex]x = \frac{12.28}{2}[/tex]  or  [tex]x = \frac{-2.28}{2}[/tex]

[tex]x = 6.14[/tex] or [tex]x = -1.14[/tex]

Answer:

D {36,47,60}

Step-by-step explanation:

it would have to be {37,48,60} for it to be a right triangle

hope this helps you out

Answer:

5) option c

6) option d

7) option d

8) option b

Answer:

The maximum volume the cube could have is 729 cubic inches

Step-by-step explanation:

The total surface area of the cube equals the total area of material used.

Let A = total surface area of cube = 6L² where L = length of side of cube

Since A = total area of material used, A = 486 in²

So 486 in² = 6L²

L = √(486 in²/6)

= √81 in²

= 9 in

The volume of the cube V = L³ where L = length of side of cube

So, V = (9 in)³

= 729 in³

So the maximum volume the cube could have is 729 cubic inches.

The maximum volume that the box could have will be 729inches³.

Based on the information given, the first thing to do is to find the length of the shape. This will be:

Length = ✓(486/6)

Length = ✓81

Length = 9

Therefore, the volume of the cube will be:

= 9³

= 9 × 9 × 9

= 729 in³.

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Answer:

-3x-6

Step-by-step explanation:

distribute the -3

Answer:

-3x-6

Step-by-step explanation:

Answer:Example 1:

Find the sum of the first 8 terms of the geometric series if a1=1 and r=2.

S8=1(1−28)1−2=255

Example 2:

Find S10 of the geometric sequence 24,12,6,⋯.

First, find r.  

r=r2r1=1224=12

Now, find the sum:

S10=24(1−(12)10)1−12=306964

Example 3:

Evaluate.

∑n=1103(−2)n−1

(You are finding S10 for the series 3−6+12−24+⋯, whose common ratio is −2.)

Sn=a1(1−rn)1−rS10=3[1−(−2)10]1−(−2)=3(1−1024)3=−1023  

In order for an infinite geometric series to have a sum, the common ratio r must be between −1 and 1.  Then as n increases, rn gets closer and closer to 0.  To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r, where a1 is the first term and r is the common ratio.

Example 4:

Find the sum of the infinite geometric sequence

27,18,12,8,⋯.

First find r:  

r=a2a1=1827=23

Then find the sum:

S=a11−r

S=271−23=81

Example 5:

Find the sum of the infinite geometric sequence

8,12,18,27,⋯ if it exists.

First find r:  

r=a2a1=128=32

Since r=32 is not less than one the series has no sum.

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = - 3x

Answer:

A is 6 23/56

B is 3 4/15

Step-by-step explanation:

Answer:

a. 6 23/56

b. 3 4/15

Step-by-step explanation:

1. First you need have the same denominators.

5 16/56 and  1 7/56

5 16/56 + 1 7/56 = 6 23/56

2. Again you have to find the same denominators.

4 10/15 and 1 6/15

4 10/15 - 1 6/15 = 3 4/15

3 4/15

Answer:

A. $99,195.055

B. $72,000

C. $27,195.055

Step-by-step explanation:

A. Calculation for How much will you have in the account in 30 years

Using future annuity formula

Future value=[Deposit amount* (1+Interest rate^n-1)/Interest rate]

Let plug in the formula

Where,

Deposit amount=$200

Number of days=30*12=360

Interest rate=0.02/12=0.0017

Let plug in the formula

Future value=[$200*(1+0.0017^360-1)/0.0/17]

Future value=[$200*(1+0.0017^360-1)/0.0/17]

Future value=[$200*(1.0017^360-1)/0.0/17]

Future value=$99,195.055

Therefore the amount you will have in the account in 30 years will be $99,195.055

B. Calculation for How much total money will you put into the account

Using this formula

Total money=Deposit amount*Number of days

Let plug in the formula

Total money=$200*360 days

Total money=$72,000

Therefore the total money you will put into the account is $72,000

C. Calculation for How much total interest will you earn

Total Interest=$99,195.055-$72,000

Total Interest=$27,195.055

Therefore the total Interest you will earn is $27,195.055

Answer:

Conclusion:

Both sets represent the function.

Step-by-step explanation:

For example, a certain plant grows 10 cm each year. Thus, the height of the plant is associated with its age using the function

h (age) = age × 10

Thus, if the age of the plant is 2 years, the height is:

h(10) = 2 × 10 = 20 cm

Set P

P = {(6, −7), (3, −2), (−9, 2), (−5, −7)}

The set P represents the function because the function relates an input to an output. In other words, here each input is related to exactly one output.

The x-values are 6, 3, -9, and -5.

Thus, there are no duplicated inputs or x-values.

Set Q

Q = {(−7, 8), (4, −6), (−3, 1), (1, 5)}

The set P represents the function because the function relates an input to an output. In other words, here each input is related to exactly one output.

The x-values are -7, 4, -3, and 1.

Thus, there are no duplicated inputs or x-values.

Conclusion:

Both sets represent the function.

Answer:

yes i think so it looks quite accurate

Answer:

This does look like the right answer. I think you filled it out right

Step-by-step explanation:

Answer:

[tex]r \cdot 4 = z[/tex]

Step-by-step explanation:

An expression means that we don't know enough to create an equation. So, this means we will mostly be using variables.

John runs r amount every day. We need to create an expression for if he runs r amount for 4 days.

[tex]r \cdot 4 = z[/tex]

r = how much he runs per day

4 = how many days he runs

z = how much he runs this week

This is your expression!

Answer:

r * 4 = a

Step-by-step explanation:

If John runs the same amount everyday (r) for the past four days, we can multiply 4 by r

r * 4

We don't have enough information to write the answer to the expression so in its place we can put a variable. (In this case, I chose a)

r * 4 = a

So a possible expression for this problem is r *4 = a

Hope this helps! Have a great day! :)

Answer:

[tex]B. \: \: y = 3x - 2[/tex]

Step-by-step explanation:

I how this HELPS you!

Answer:

18 dots

____________________________________________________

The number of dots in the step 4 are eighteen.

A number system is defined as a system of writing to express numbers.

From the figure, In step 0 there are two dots.

In step 1 there are three dots

In step 2 there are six dots

In step 3 there are eleven dots

We need to find the number of dots in step 4.

2+ 1=3

3 + 3 = 6

6 + 5 = 11

11+7=18

The sequence of odd numbers are added.

Hence, in step 4 there are 18 dots

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#SPJ2

Answer:

40 games will be played in total.

Step-by-step explanation:

Answer:

will it be b

Step-by-step explanation:

Answer:

step-by-step explanation

130% ×××××

hai

i'll be friend, babai

Answer:

8.1%

Step-by-step explanation:

Step one:

given

initial price = $8.72 per pound

final price=  $9.43 per pound

Required

the % increase

Step two:

% increase= (final-initial)/initial*100

substituting we have

[tex]percent- increase= (9.43-8.72)/8.72*100\\\\percent- increase= 0.71/8.72*100\\\\percent- increase= 0.081*100\\\\percent- increase= 8.1%[/tex]

Answer:

A circle of radius = 14 or diameter = 28 or circumference = 87.96 meters has an area of: 0.0006158 square kilometers (km²) 615.8 square meters (m²) 6.158 × 10 6 square centimeters (cm²) 6.158 × 10 8 square millimeters (mm²) 0.000237762 square miles (mi²) 736.491 square yards (yd²) 6628.42 square feet (ft²) 9.54492 × 10 5 square inches (in²)

Step-by-step explanation:

Answer:

a. True

b. True

c. True

d. False

e. False

I hope this helped! Thank You!

Answer:

a. False

b. True

c. True

d. False

e. False

Answer: c=(220)^1/2

^1/2 is the square root

Step-by-step explanation:

c^2=a^2+b^2

c^2=14^2+(24^1/2)^2

c^2=196 +24

c^2=220

c=(220)^1/2

Answer:

Shell is under Red color cup

Step-by-step explanation:

We have 3 cups and 3 objects which they cover under them.

Taking into consideration (4) and (2) as they both describe the position related to bean

(4) Gray cup  →Bean (right)     (2) coin ← bean (left)  

that means coin can either under Gray cup or left to gray cup.

Now

(1) Red ← White (left)  (3) Shell → Gray  (right)

This means if we consider coin to be left of gray cup then we can't place shell to the left of gray cup as required in (3)

so coin will be under gray cup

on forming the Color of cups and the coin below them

C1             C2         C3

Red       Gray      White

 __           __          __

Shell        coin        Bean

So Shell is under Red color cup

Answer:

scooby-dooby-doooby-dooooby-doooooby-D000000000000000000000000000000Step-by-step explanation:

Answer:

$0.32, so a quarter a nickel and 2 pennies

Step-by-step explanation:

Answer:

$0.32

Step-by-step explanation:

First, add $1.29+$0.39 to get the total amount of the transaction.

$1.29+$0.39 = 1.68

Then, subtract that from the amount paid.

$2.00-$1.68

= $0.32