The sum of two numbers is 39, One number is 7 more than the other. Find the two numbers.

Answer:

The fifth term is -1/4.

Step-by-step explanation:

We know that the first three terms of the geometric sequence is x, x + 2, and x + 3.

So, our first term is x.

Then our second term will be our first term multiplied by the common ratio r. So:

[tex]x+2=xr[/tex]

And our third term will be our first term multiplied by the common ratio r twice. Therefore:

[tex]x+3=xr^2[/tex]

Solve for x. From the second term, we can divide both sides by x:

[tex]\displaystyle r=\frac{x+2}{x}[/tex]

Substitute this into the third equation:

[tex]\displaystyle x+3=x\Big(\frac{x+2}{x}\Big)^2[/tex]

Square:

[tex]\displaystyle x+3 = x\Big( \frac{(x+2)^2}{x^2} \Big)[/tex]

Simplify:

[tex]\displaystyle x+3=\frac{(x+2)^2}{x}[/tex]

We can multiply both sides by x:

[tex]x(x+3)=(x+2)^2[/tex]

Expand:

[tex]x^2+3x=x^2+4x+4[/tex]

Isolate the x:

[tex]-x=4[/tex]

Hence, our first term is:

[tex]x=-4[/tex]

Then our common ratio r is:

[tex]\displaystyle r=\frac{(-4)+2}{-4}=\frac{-2}{-4}=\frac{1}{2}[/tex]

So, our first term is -4 and our common ratio is 1/2.

Then our sequence will be -4, -2, -1, -1/2, -1/4.

You can verify that the first three terms indeed follow the pattern of x, x + 2, and x + 3.

So, our fifth term is -1/4.

The equation of the line that passes through the point(1, 3) and is perpendicular to the line 2x + 3y = 15 is y = 3 / 2x + 3 / 2.

The line passing through (1, 3) is perpendicular to the equation 2x+3y=15.

Therefore,

y = mx + b

where

Hence,

3y = -2x + 15

y = -2 / 3 x + 5

For line to be perpendicular it must follow the following rules;

m₁m₂ = -1

m₁(-2 / 3) = -1

-2m₁ = -3

m₁ = 3 / 2

Therefore, the equation can be found as follows:

3 = 3 / 2(1) + b

3 = 3 / 2 + b

b = 3 - 3 / 2

b = 6 - 3 / 2

b = 3 / 2

Hence,

y = 3 / 2x + 3 / 2

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Answer:

I need more clarification for anythng else, this is the best i can do

Step-by-step explanation:

Answer:

I guess 7/2

Step-by-step explanation:

2x - 7 = 0

2x = 7

x= 7/2 ?

You didnt give us what the equation equals to

Answer:

f(x)=3√x f ( x ) = x 3

Step-by-step explanation:

Answer:

Q1: B. UHWXUQV

Q2: None of these answers equal 12 so I'll just tell you the answers for all of them in case you mistyped.

a. 66

b. 82

c. 120

d. 109

Im assuming you meant 120. If so, your answer is c.

C. -4/3

[tex]slope = \frac{(y _{2} - y _{1}) }{(x _{2} - x _{1} )} \\ = \frac{( - 6 - 2)}{(0 -( - 6)} \\ = \frac{ - 8}{ 6} \\ = - \frac{4}{3} [/tex]

Answer:

5 cm

Step-by-step explanation:

Area= 1/2 base×altitude

let base be x cm hence altitude = x+7 cm

30 = 1/2 (x) (x+7)

60= x^2 + 7x

x = 5 or - 12

but measurements can't be in negative form hence -12 is discarded. Thus x= 5 cm

x= base hence base = 5cm

Answer:

base = 5 cm

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the altitude )

let base be b then h = b + 7

Given A = 30, then

[tex]\frac{1}{2}[/tex]b(b + 7) = 30 ( multiply both sides by 2 to clear the fraction )

b(b + 7) = 60 ← distribute left side

b² + 7 = 60 ( subtract 60 from both sides )

b² + 7 - 60 = 0 ← in standard form

(b + 12)(b - 5) = 0 ← in factored form

Equate each factor to zero and solve for b

b + 12 = 0 ⇒ b = - 12

b - 5 = 0 ⇒ b = 5

However, b > 0, thus b = 5

That is the base is 5 cm

Answer:

-30m^11n^5

Step-by-step explanation:

the length of a rectangle is width times length (or base times height).

5m^7n^3 times -6m^4n^2 = -30m^11n^5

I hope this helped, please give brainliest if this is correct! Thank you!

Rise/Run

5/4

You go to the point farthest to the left and count up. This will be your Rise. Then you count over to the point on the right. This will be your Run.

Answer:

83

Step-by-step explanation:

you go up so it is positive. it's up 83 so the number is 83.

Step-by-step explanation: The keyword is up. Since we're talking about integers and the keyword is up, the number is positive.

Therefore, the answer is 83, or say it like this, positive 83.

For example: Start at 0. Then go up by 83. (That's why there is a number line.

Answer:

10

Step-by-step explanation:

c²=b²+a²=100

so

c=10

jjthj

Answer:

the answer its 49

Step-by-step explanation:

simple math just subtract 90-41 and you will get 49

Answer:

The pdf wont work

Step-by-step explanation:

cant help

Answer:

p=13

Step-by-step explanation:

Answer:

32.8 is the answer

Step-by-step explanation:

hope it helps u

Answer:32.8

Step-by-step explanation:

Answer:

n > 10 is the inequality solved, but there is no way to graph this equation.

Step-by-step explanation:

Key skills: Inequalities, Division

1) You are given the inequality 2n > 20

2) To solve for n, you have to divide by 2 on both sides.

3) 2n/2 > 20/2

4) 2n/2 = n

5) 20/2 = 10

6) The inequality is n> 10

There is no way to graph this as it has no x or y values in it (coordinate graphing requires x or y in the inequality)

The solution to the inequality is n > 10

To solve the inequality 2n > 20, we need to isolate n by dividing both sides of the inequality by 2:

2n/2 > 20/2

n > 10

The solution to the inequality is n > 10, indicating that n must be greater than 10 for the inequality to hold true.

To graph the solution, we represent the solution on a number line. We start by marking a point at 10, and then shade the region to the right of 10 to indicate all values greater than 10.

Graphically, it would be represented as an open circle at 10 with a shaded line extending to the right.

This represents the solution n > 10.

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Step-by-step explanation:

the formula for the area of a circle is

πr²

plug 9 in for r (radius) to get

3.14 (81) = 254.34 cm² as our area

the circumference is equal to πd , with π being pi and d being diameter.

the circumference is then 3.14(100) = 314cm

Answer:

1609.8

Step-by-step explanation:

Answer:

1609.34

Step-by-step explanation:

1 meter = 3.28 feet

1 mile = 5280 feet

A linear inequality is given to us and we need to drag each number to show whether or not it is a

solution to the inequality .The given inequality to us is ,

[tex]\bf\implies 4x - 12 \leq 24 \\\\\bf\implies 4x \leq 24+12 \\\\\bf\implies 4x \leq 36 \\\\\bf\implies x \leq \dfrac{36}{4}\\\\\bf\implies x\leq 9\\\\\bf\implies \boxed{\red{\bf x \in [9,-\infty ) }}[/tex]

Hence , x can have all values less than or equal to 9. That is x E [ 9 , -∞ ) .

Options provided to us are ,

Hence values less than or equal to 9 are 9 , 6 , (-5) and 0 .

Answer:

70/x

Step-by-step explanation:

Answer:

136.86 or 137

Step-by-step explanation:

21÷3x10+66.86

here's what I did...

as simplified its: 137

Answer:

5 pounds = $2.49

1 pound = $2.49 ÷ 5 = $0.50 (nearest hundredth)

Answer: $0.50/pound

Step-by-step explanation:

Answer:

x= 9°

Step-by-step explanation:

[tex]180 - 171 = 9[/tex]

[tex]x = 9[/tex]

Answer:

11 or 22 would be one of your answer i believe it is 11 though

Step-by-step explanation:

mark me brainly have an amazing day

sparkles and love

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9514 1404 393

Answer:

  176°

Step-by-step explanation:

The total of exterior angles is 360°, so one of those for the regular polygon will be 360°/90 = 4°. The adjacent interior angle is the supplement of this.

The interior angles measure 180° -4° = 176°.

Answer:

Option B: $20x + $30 < $170 is the correct answer.

Step-by-step explanation:

Given that:

Service fee of Tina's business = $30

Per day charges = $20

Number of days =  x

Customer's budget = less than $170

According to given statement;

20x + 30 < 170

Hence,

Option B: $20x + $30 < $170 is the correct answer.

Answer:

the answers are the x and the star (or just B and C)

Step-by-step explanation:

How do I know? I just know...

JK

Rotational semetry is if one shape looks the same, even fliped in a sort of way.

Answer:

$12

Step-by-step explanation:

Answer:

The statement that best interprets the z-score is;

D. The length of the gestation period was shorter than the mean length of gestation period by 1.7 standard deviations

Step-by-step explanation:

The given parameters are;

The length of the gestation period of the cattle breed = 284 days

The standard deviation = 5.5 days

The z-score of one length of gestation period was z = -1.70

The formula for finding the z-score, z is presented as follows

[tex]Z=\dfrac{x-\mu }{\sigma }[/tex]

Where;

x = The observed value for the gestation period

μ = The sample mean length for the gestation period = 284

σ = The gestation period standard deviation = 5.5

When Z = -1.70, we have;

[tex]-1.70 =\dfrac{x-\mu }{\sigma }[/tex]

∴ x - μ = -1.7 × σ

∴ x is shorter than μ by 1.7×σ

Therefore, the length of the gestation period, x, was shorter than the mean length of gestation period, μ, by 1.7 standard deviations, σ.

Answer:

D. The length of the gestation period was shorter than the mean length of gestation period by 1.7 standard deviations

Step-by-step explanation: