Mathematics High School

log x + log(x+3) = 1

Answers

Answer 1

9514 1404 393

Answer:

x = 2

Step-by-step explanation:

Taking antilogs, the equation becomes ...

x(x +3) = 10

x^2 +3x +2.25 = 12.25 . . . . add (3/2)² to complete the square

(x +1.5)² = 3.5² . . . . write as squares

x = -1.5 +3.5 . . . . . . take the positive square root*

x = 2

_____

* The negative square root gives an extraneous solution (x=-5).

I find that using a graphing calculator with the original equation avoids extraneous solutions. Here we transform the equation to the form f(x) = 0, so the x-intercept is the value of x we seek.

Related Questions

6) Two coastguard stations P and Q are 17km apart, with due East of P. A ship S is observed in distress on a bearing 048° fromP and 324 from Q. How far is the ship from each of the coastguard stations?

Answers

Answer:

The ship S is at 10.05 km to coastguard P, and 12.70 km to coastguard Q.

Step-by-step explanation:

Let the distance of the ship to coastguard P be represented by x, and its distance to coastguard Q be represented by y.

But,

<P = 048°

<Q = [tex]360^{o}[/tex] - [tex]324^{o}[/tex]

= 0[tex]36^{o}[/tex]

Sum of angles in a triangle = [tex]180^{o}[/tex]

<P + <Q + <S = [tex]180^{o}[/tex]

048° + 0[tex]36^{o}[/tex] + <S = [tex]180^{o}[/tex]

[tex]84^{o}[/tex] + <S = [tex]180^{o}[/tex]

<S = [tex]180^{o}[/tex] - [tex]84^{o}[/tex]

= [tex]96^{o}[/tex]

<S = [tex]96^{o}[/tex]

Applying the Sine rule,

[tex]\frac{y}{Sin P}[/tex] = [tex]\frac{x}{Sin Q}[/tex] = [tex]\frac{z}{Sin S}[/tex]

[tex]\frac{y}{Sin P}[/tex] = [tex]\frac{z}{Sin S}[/tex]

[tex]\frac{y}{Sin 48^{o} }[/tex] = [tex]\frac{17}{Sin 96^{o} }[/tex]

[tex]\frac{y}{0.74314}[/tex] = [tex]\frac{17}{0.99452}[/tex]

⇒ y = [tex]\frac{12.63338}{0.99452}[/tex]

= 12.703

y = 12.70 km

[tex]\frac{x}{Sin Q}[/tex] = [tex]\frac{z}{Sin S}[/tex]

[tex]\frac{x}{Sin 36^{o} }[/tex] = [tex]\frac{17}{Sin 96^{o} }[/tex]

[tex]\frac{x}{0.58779}[/tex] = [tex]\frac{17}{0.99452}[/tex]

⇒ x = [tex]\frac{9.992430}{0.99452}[/tex]

= 10.0475

x = 10.05 km

Thus,

the ship S is at a distance of 10.05 km to coastguard P, and 12.70 km to coastguard Q.

Helppppppppppppppppppppp
pleaseeeeee

Answers

Answer:

Question 3: x = 11

Question 4: x = -17

Question 5: x = 26

Question 6: 10 = x

Question 7: x = 36

Question 8: x = 88

Question 9: x = 81

Question 10: n = 36

Step-by-step explanation:

The distance between the longest and shortest sides of parallelogram are respectively 12 cm and 16 cm. If the longest side measures 24 cm find the perimeter of the parallelogram

Answers

Answer:

16c

Step-by-step explanation:

ANSWER

The length of side 24cm

Its corresponding height is 12cm

The area of parallelogram is 24×12=288cm

The length of another side is 18cm

The area of parallelogram is 288cm

Its corresponding height is

288

=16c

PLZ ANSWER BRAINLIEST

Tom needs to get on his roof to clean the gutters, his roof is 30ft. high, his ladder is 35ft. long. Tom places the ladder 4ft. away from his house. Will Tom need a longer ladder?
apply the Pythagorean Theorem

Answers

Answer:

Tom wont need a longer ladder.

Step-by-step explanation:

Answer:

No the ladder is long enough.

Step-by-step explanation:

30x30=900

4x4=16

Sq. Root of (900+16)= 30.27ft distance from the ground to the roof, 4 ft away from the house.

Find the length of the missing side plz

Answers

The answer is 87feet !!!!!!!!!

Describe a real life situation that uses the sum of the integers -8 and 12.

Answers

I had some cookies 8 of them fell and my mother gave me 12 more.

Landon rides his bike 178 feet in 8 seconds, find the unit rate

Answers

Answer:

22.25

Step-by-step explanation:

178/8=22.25

Answer:

22.25

Step-by-step explanation:

178 divided by 8

simplify f (x)=5x^2-10x+6

Answers

Step-by-step explanation:

[tex]f(x) = {x}^{2} - 5x + \frac{6}{5} [/tex]

[tex]f(x) = {x}^{2} - 5x + \frac{25}{4} - \frac{9}{5} [/tex]

f(x) =(x-5/2)^2-9/5

I needddd helppppp pleaseee

Answers

Answer:

ok this triangle is an isosceles triangle because when you tell sit and look at the base sides that is 55° and be those are the base angles so if one is 55 the other one is also 55 So B is 55

Answer:

B=55°

Step-by-step explanation:

That is an isosceles triangle TS and US are the same size. So the 2 angles at the base (TU) will be the same. so b=55°

Find the perimeter of this figure. Enter your answer in the box.

Answers

Answer:

I think you forgot to put the figure

Apples: $(2x) per pound
Grapes: $(6x – 5) per pound
Oranges: $(x + 2) per pound
A shopper purchases one pound each of
apples, grapes, and oranges and spends
$10.50. How much is spent on each type
of fruit?

Answers

Answer:

Shopper spend $3 on Apples, $4 on Grapes and $3.5 on Oranges

Step-by-step explanation:

Cost of one pound of Apple = $2x

Cost of one pound of Grapes = $(6x-5)

Cost of one pound of Oranges = $(x+2)

A shopper purchases one pound each of apples, grapes, and oranges and spends $10.50.

It can be written as: [tex]2x+6x-5+x+2=10.50[/tex]

We need to find how much the shopper spend on each fruit.

First we need to find value of x by solving equation

[tex]2x+6x-5+x+2=10.50[/tex]

Solving:

[tex]2x+6x+x+2-5=10.50\\9x-3=10.50\\9x=10.50+3\\9x=13.5\\x=\frac{13.5}{9}\\x=1.5[/tex]

The value of x is: x=1.5

Now finding cost of one pound each fruit by putting x=1.5

Cost of one pound of Apple = $2x = 2(1.5) = $3

Cost of one pound of Grapes = $(6x-5) = (6(1.5)-5)= $4

Cost of one pound of Oranges = $(x+2)=(1.5+2)=$3.5

So,

Cost of one pound of Apple = $3

Cost of one pound of Grapes = $4

Cost of one pound of Oranges = $3.5

So, shopper spend $3 on apples, $4 on Grapes and $3.5 on Oranges

Anyone can help me on this

Answers

Answer:

f(1)=5 f(0)=0 f(-1)=-3

Step-by-step explanation:

by pluging it in.

answer this please

Answers

Answer5 times 6=30 divide bc its a triangle the answer is 15

Step-by-step explanation:

PLS HELP ME I’VE ASKED THIS TWICE AND NOBODY HAD ANSWER THIS IS REALLY EASY TO DO

I HAVE THE ANSWER I JUST NEED TO SHOW THE WORK. PLS HELP MEEEE!!!

The answer is x = 9

Answers

Answer:

Step-by-step explanation:

All the angles within a triangle equals to 180, and that square thing at a corner of the triangle means that the angle is 90 degrees, so:

20+6x+16+90=180

add stuff

6x+126=180

subtract 126 from both sides

6x=54

divide 6 from both sides

x=9

Use the properties of operations to write an
expression equivalent to:
4x + 1/2 + 2x - 3

Answers

Answer:

6x * 1/2 - 3 (* means multiplying)

Step-by-step explanation:

In this problem, you are using communitive property and so you are just changing the problem to an equal situation.

The equivalent expression of 4x + 1/2 + 2x - 3 is 6x - 8/3.

What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.

Given is the expression -

4x + 1/2 + 2x - 3

We have the following expression -

4x + 1/2 + 2x - 3

Solving further -

4x + 2x - 3 + 1/3

6x + 1/3 - 3

6x + (1 - 9)/3

6x - 8/3

Therefore, the equivalent expression of 4x + 1/2 + 2x - 3 is 6x - 8/3.

To solve more questions on functions, expressions and polynomials, visit the link below -

brainly.com/question/17421223

#SPJ2

Find m and n if if the sum of zeros of mx²-2x + n is 4, and product is 4

Answers

Answer:

dont know

Step-by-step explanation:

HELP! i can not figure this out! y=4x+1

Answers

Answer:

Step-by-step explanation:

Does the equation 600 ÷ 120 = 5 represent this tape diagram? Explain your reasoning.

Answers

hey bae u gotta show us the tape diagram

PLEASE HELP WILL GIVE BRAINLY

(USE BAR NOTATION IF NEEDED!!!!!!
CONVERT TO DECIMAL

Answers

Answer:

3.34 is the decimal form but the question is unclear, what is it that you need?

Step-by-step explanation:

The answer is 3.3408 as a decimal, does that help?

(-1)^39=

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Answers

19-6=13

i hope this helps

Answer:

Step-by-step explanation:

: Add 6 to both sides.

a−6+6=13+6

a=19

factories
x⁴ y⁴- xy

Answers

Answer:

xy (x³y³-1) this is the correct answer. check my explanation to understand

Step-by-step explanation:

x⁴y⁴-XY =

xy (x³y³-1)

help please I'm to stupid for this

Answers

Answer:

X>0, so the second one

Step-by-step explanation:

Since the point on 0 is OPEN that means the number (0) is NOT part of the solution. Therefore, X is greater than 0.

Cassie works at the apple store. She earns $12 plus $8 for each hour she works. Write an equation to represent her earnings.

Answers

Answer:

8h+12=E

h: hours worked

E: total Earnings

it's about proportion and stuff but I'm confused on this one can someone please explain?

Answers

Answer:

the one clue you have is "30,12" on the left. try to understand how they relate to each other. maybe how many times 12 goes into 30. or maybe how many times it goes into 32 with no decimal so what number do you have to add (sometimes work doesnt mean it like that so that might be wrong). but if you want the answers, they are:

35/5/15/30

14/2/6/12

the way i did it was if it was on the bottom (y) i did 2.5 times the number. if on the top (x) i did the number divided by 2.5. 2.5 was the rate of change (is that the word i think it is but if it isnt just blame me im sorry).

Step-by-step explanation:

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