write each decimal as a fraction in simplest form 0.5​

QUESTION 1

[tex] {3}^{x + 1} = {9}^{x + 3} [/tex]

This is the same as:

[tex] {3}^{x + 1} = {3}^{2(x + 3)} [/tex]

Equate the exponents.

x+1=2(x+3)

Expand:

x+1=2x+6

Group similar terms;

2x-x=1-6

x=-5

QUESTION 2

[tex] log(9x - 2) = log(4x + 3) [/tex]

Equate the arguments.

9x-2=4x+3

Group similar terms;

9x-4x=3+2

5x=5

Divide through by 5

x=1

QUESTION 3

[tex] log_{6}(5x + 4) = 2[/tex]

Take antilogarithm to obtain,

[tex]5x + 4 = {6}^{2} [/tex]

This implies that,

5x+4=36

5x=36-4

5x=32

x=32/5

or

[tex]x = 6 \frac{2}{5} [/tex]

QUESTION 4

[tex] log_{2}(x) + log_{2}(x - 3) = 2[/tex]

Use the product rule of logarithms:

[tex]log_{2}x(x - 3) = 2[/tex]

Take antilogarithm,

[tex] {x}^{2} - 3x = {2}^{2} [/tex]

[tex] {x}^{2} - 3x - 4 = 0[/tex]

Factor:

[tex](x + 1)(x - 4) = 0[/tex]

This implies that,

[tex]x = - 1 \: or \: x = 4[/tex]

But the domain is x>0, therefore the solution is

x=4

QUESTION 5

[tex]x=\log_{4}(11.2)[/tex]

[tex]x=\log_{4}(\frac{56}{5})[/tex]

[tex]x=\log_{4}(56)-\log_{4}(5)[/tex]

x=1.7 to the nearest tenth.

QUESTION 6

[tex]2e^{8x}=9.2[/tex]

Divide both sides by 2.

[tex]e^{8x}=4.6[/tex]

Take natural log of both sides

[tex]{8x}=\ln(4.6)[/tex]

[tex]{x}=\ln(4.6)\div 8[/tex]

x=0.2 to the nearest tenth.

Answer:

# The solution x = -5

# The solution is x = 1

# The solution is x = 6.4

# The solution is x = 4

# The solution is 1.7427

# The solution is 0.190757

Step-by-step explanation:

* Lets revise some rules of the exponents and the logarithmic equation

# Exponent rules:

1- b^m  ×  b^n  =  b^(m + n) ⇒ in multiplication if they have same base

  we add  the power

2- b^m  ÷  b^n =  b^(m – n) ⇒  in division if they have same base we

   subtract  the power

3- (b^m)^n = b^(mn) ⇒ if we have power over power we multiply

   them

4- a^m × b^m = (ab)^m ⇒ if we multiply different bases with same  

   power then we multiply them ad put over the answer the power

5- b^(-m) = 1/(b^m)  (for all nonzero real numbers b) ⇒ If we have

   negative power we reciprocal the base to get positive power

6- If  a^m  =  a^n  ,  then  m  =  n ⇒ equal bases get equal powers

7- If  a^m  =  b^m  ,  then  a  =  b    or    m  =  0

# Logarithmic rules:

1- [tex]log_{a}b=n-----a^{n}=b[/tex]

2- [tex]loga_{1}=0---log_{a}a=1---ln(e)=1[/tex]

3- [tex]log_{a}q+log_{a}p=log_{a}qp[/tex]

4- [tex]log_{a}q-log_{a}p=log_{a}\frac{q}{p}[/tex]

5- [tex]log_{a}q^{n}=nlog_{a}q[/tex]

* Now lets solve the problems

# [tex]3^{x+1}=9^{x+3}[/tex]

- Change the base 9 to 3²

∴ [tex]9^{x+3}=3^{2(x+3)}=3^{2x+6}[/tex]

∴ [tex]3^{x+1}=3^{2x+6}[/tex]

- Same bases have equal powers

∴ x + 1 = 2x + 6 ⇒ subtract x and 6 from both sides

∴ 1 - 6 = 2x - x

∴ -5 = x

* The solution x = -5

# ㏒(9x - 2) = ㏒(4x + 3)

- If ㏒(a) = ㏒(b), then a = b

∴ 9x - 2 = 4x + 3 ⇒ subtract 4x from both sides and add 2 to both sides

∴ 5x = 5 ⇒ divide both sides by 5

∴ x = 1

* The solution is x = 1

# [tex]log_{6}(5x+4)=2[/tex]

- Use the 1st rule in the logarithmic equation

∴ 6² = 5x + 4

∴ 36 = 5x + 4 ⇒ subtract 4 from both sides

∴ 32 = 5x ⇒ divide both sides by 5

∴ 6.4 = x

* The solution is x = 6.4

# [tex]log_{2}x+log_{2}(x-3)=2[/tex]

- Use the rule 3 in the logarithmic equation

∴ [tex]log_{2}x(x-3)=2[/tex]

- Use the 1st rule in the logarithmic equation

∴ 2² = x(x - 3) ⇒ simplify

∴ 4 = x² - 3x ⇒ subtract 4 from both sides

∴ x² - 3x - 4 = 0 ⇒ factorize it into two brackets

∴ (x - 4)(x + 1) = 0 ⇒ equate each bract by 0

∴ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

OR

∵ x + 1 = 0 ⇒ subtract 1 from both sides

∴ x = -1

- We will reject this answer because when we substitute the value

 of x in the given equation we will find [tex]log_{2}(-1)[/tex] and this

 value is undefined, there is no logarithm for negative number

* The solution is x = 4

# [tex]log_{4}11.2=x[/tex]

- You can use the calculator directly to find x

∴ x = 1.7427

* The solution is 1.7427

# [tex]2e^{8x}=9.2[/tex] ⇒ divide the both sides by 2

∴ [tex]e^{8x}=4.6[/tex]

- Insert ln for both sides

∴ [tex]lne^{8x}=ln(4.6)[/tex]

- Use the rule [tex]ln(e^{n})=nln(e)[/tex] ⇒ ln(e) = 1

∴ 8x = ln(4.6) ⇒ divide both sides by 8

∴ x = ln(4.6)/8 = 0.190757

* The solution is 0.190757

Answer:

Stay friends. Make him think you are over him.

Step-by-step explanation:

This will make him question if maybe you have found someone else. An opportunity to get back together might pop up out of it.

Answer:

Honestly as a boy I think that you should start talking to him again.

Step-by-step explanation:

Like we cant read minds. If you miss him then maybe if he sees that u have feelings for him then maybe yall can work things out. Also it depends on the boy. What type is he. and it depends on you. what type of girl are you. If you like can I please get brainliest

Final answer:

The system of equations y = −x² + x + 7 and y = x² + 3x + 7 can be solved by setting them equal to each other and simplifying, which reveals the solutions (0, 7) and (−1, 7).

Explanation:

The solution to the system of equations y = −x² + x + 7 and y = x² + 3x + 7 involves finding the set of x and y values that satisfy both equations simultaneously. To solve this system, we can set the two equations equal to each other since they both equal y:

−x² + x + 7 = x² + 3x + 7.

Combining like terms, we get:

−x² − x² + x − 3x = 0,

which simplifies to:

−2x² − 2x = 0.

Factoring out -2x gives us:

− 2x(x + 1) = 0.

So we have two solutions for x:

x = 0

x = −1

We now substitute these x values back into either of the original equations to find the corresponding y values. We get two pairs of solutions for the system of equations:

(0, 7) when substituting x = 0

(−1, 7) when substituting x = −1

Therefore, the graph that correctly solves the system of equations will show the intersection points at (0, 7) and (−1, 7).

Answer:

113.51

Step-by-step explanation:

y=2x

switch x and y

x=2y

solve for y

x/2 =y

this is the same as g(x)

Answer:

see explanation

Step-by-step explanation:

If f(x) and g(x) are inverses then

f(g(x)) = g(f(x)) = x

f(g(x)) = f([tex]\frac{x}{2}[/tex]) = 2 × [tex]\frac{x}{2}[/tex] = x

g(f(x)) = g(2x) = [tex]\frac{2x}{2}[/tex] = x

Hence

f(x) and g(x) are inverse functions

Answer: C. 390

Step-by-step explanation:

Firstly, we need to find the amount each of the categories.

House: 6500 * 0.25 = 1625

Bills: 6500 * 0.14 = 910

Food: 6500 * 0.19 = 1235

Other: 6500 * 0.42 = 2730

All of those add up to 6500.

House - Food

1625 - 1235 = 390

Without the specific percentages from the circle graph representing housing and food, we can't determine the exact dollar difference. But theoretically, we would multiply each percentage by the total budget ($6500) and subtract the food from the housing amount.

Without actual percentages or numbers for the family's expenditures on housing and food provided in the circle graph, we cannot determine the exact dollar amount difference. However, we can explain theoretically how you would do it with actual values. After identifying the percentages represented by housing and food on the graph, you would multiply each percentage by the total monthly budget of $6,500. Subtract the amount spent on food from the amount spent on housing to get the difference. Based on the choices given, it seems you want help in selecting the correct option. If you provide the specific percentages from the graph, I will gladly assist further in your mathematical problem.

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[tex]\frac{f(x)}{g(x)} =?[/tex]

Since you know f(x) = 2x and g(x) = 3x^3, you can substitute that into the function

[tex]\frac{f(x)}{g(x)} =?[/tex]

[tex]\frac{2x}{3x^3} =?[/tex]

When a variable(x or y) with an exponent is divided by another variable with an exponent, you subtract the exponents, only if the variables are the same.

For example:

[tex]\frac{x}{y}[/tex]   Since the variables on the top and bottom are not the same, you can't simplify it (or its already simplified)

[tex]\frac{x^3}{x^2} =x^{3-2} =x^1[/tex]

[tex]\frac{y^5}{y^7}=y^{5-7}=y^{-2} = \frac{1}{y^2}[/tex] (when an exponent is negative, you move it to the other side of the fraction to make the exponent positive)

[tex]\frac{2x}{3x^3} =?[/tex]

[tex]\frac{2x}{3x^3}= (\frac{2}{3})x^{1-3}= (\frac{2}{3})x^{-2} = (\frac{2}{3})\frac{1}{x^2}[/tex]  Since you can't simplify 2/3, you get:

(not sure if this is how it should look ---> (2/3)x^(1-3) but i'm assuming it is)

[tex]\frac{2}{3x^2}[/tex]

Answer:

First Integer = n = 45

Second Integer = n+1 = 45 + 1 = 46

And Third Integer = n+ 2 = 45 +2 = 47

Step-by-step explanation:

Let First integer = n

Second Integer = n+1

Third Integer = n+2

According to the question given (If the first of three consecutive integers is subtracted from 138, the result is the sum of the second and third) the equation will be:

138 - n = (n+1) + (n+2)

Solving the equation:

138 - n = n+1+n+2

138 - n = 2n+3

138 - 3 =2n +n

135 = 3n

135/3 = n

=> n= 45

So, First Integer = n = 45

Second Integer = n+1 = 45 + 1 = 46

And Third Integer = n+ 2 = 45 +2 = 47

There is only 1 number equal to 3 and that is 3.

Answer:

if your on plato that is wrong

Step-by-step explanation:

Answer:

37/40

Step-by-step explanation:

The correct choice is the second one which is 4(2 + y)

Answer:

4(2 + y)

Step-by-step explanation:

Answer:

9 movies

Step-by-step explanation:

If we let the number of movies watched is "x",

Duke's total cost:

111.60 + 4x

Tenneshia's total cost:

16.40x

Since, the cost needs to be equal, we equate both their equations and solve for x, the number of movies at which they will have paid the same amount. Thus:

111.60 + 4x = 16.40x

111.60 = 16.40 x - 4x

111.60 = 12.40 x

x = 111.60/12.40 = 9

Hence, after 9 movies, they will have paid the same amount.

Answer is 9 movies

n = no. of movies

111.6 +4n= 16.4 n

116.4= (16.4-4)n

116.4 = 12.4 n

n = 116.4/12.4

n = 9 movies

Answer:

t(ties) = $8,50 and s(shirts) = $19,50

Linda's purchase total price $36,50

Step-by-step explanation:

In mathematics, a system of linear equations is a set of two or more linear equations with more than one unknown that make up a mathematical problem that consists of finding the values ​​of the unknowns that satisfy those operations.  the unknowns are usually represented with letters of the alphabet

For this example, we can represent as a system of linear equations as follows:

For Ted

[tex]4s+2t=95[/tex] where s are shirts, t are ties, and 95 the total price of both products in $.

For Stephen

[tex]3s+3t=84[/tex] where s are shirts, t are ties, and 84 the total price of both products in $.

Each shirt and each tie were buying in the same clothing store which means that it has the same price and we can and we can relate both equations with a system of equations as follows:

[tex]\left \{ {{4s+2t=95} \atop {3s+3t=84}} \right.[/tex]

Using the reduction method, which is to clear in one of the equations with any unknown.

In this case the system has two unknowns, the selected one must be replaced by its equivalent value in the other equation.

Let's clear s in the second equation

[tex]3s+3t=84\\3s=84-3t\\s=\frac{84-3t}{3} \\s=28-t[/tex]

Substituting the value of [tex]s=28-t[/tex] in the first equation

[tex]4s+2t=95[/tex] with [tex]s=28-t[/tex]

[tex]4(28-t)+2t=95\\112-4t+2t=95\\-2t=95-112\\t=\frac{-17}{-2}=8.50[/tex]

We got that the price of a tie is t = $8,50

Substituting the value of t in the first equation in order to obtain the value of s

[tex]3s+3t=84\\3s+3(8.50)=84\\3s+25.50=84\\s=\frac{84-25.50}{3} = 19.50[/tex]

We got that the price of a shirt is s = $19,50

Checking if the result satisfies the equations

With t = 8.50 and s = 19.50

[tex]\left \{ {{4s+2t=95} \atop {3s+3t=2}} \right.\\\left \{ {{4(19.50)+2(8.50)=95} \atop {3(19.50)+3(8.50)=84}} \right.\\\left \{ {{78+17=95} \atop {58.50+25.50=84}} \right.[/tex]

Linda bought 1 shirt and 2 ties at the same store. What's the total price in dollars and cents of Linda's purchase?

If a shirt value is s = $19,50 and a tie value is t = $8,50

Then s + 2t = ?

$19,50 + 2($8,50) = $36,50

The system of equations can be used to find s, the cost of each shirt in dollars and t the cost of each tie in dollars is

4s + 2t = 95

4s + 2t = 953s + 3t = 84

Given:

Cost of shirt = s

Cost of tie = t

4s + 2t = 95 (1)

4s + 2t = 95 (1)3s + 3t = 84 (2)

Multiply (1) by 3 and (2) by 2

12s + 6t = 285 (3)

6s + 6t = 168 (4)

subtract (4) from (3)

12s - 6s = 285 - 168

6s = 117

s = 117/6

s = 19.5

substitute s = 19.5 into (1)

4s + 2t = 95 (1)

4(19.5) + 2t = 95

78 + 2t = 95

2t = 95 - 78

2t = 17

t = 17/2

t = 8.5

Therefore, the cost of each shirt is $19.5 and the cost of each tie is $8.5

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Answer:

Slope = -1/4

Step-by-step explanation:

Slope = (-8 + 5)/(0 + 12) = -3/12 = -1/4

Answer:

-1/4

Step-by-step explanation:

Slope is found by using

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

   = (-8--5)/(0--12)

   = (-8+5)/(0+12)

  = -3/12

   =-1/4

Answer:

not sure, not enough info given

Step-by-step explanation:

what to do is

sin 45=AC/BC

or

cos 45=AB/BC

or

tan 45=AC/AB

Answer:

it is 144.

I think.

The measure of angle 5 would be equal to 36°.

We know that for two similar figures, the pair by pair similar angles of those two similar figures are called corresponding angles. They are of same measurement.

Since straight angle is a 180-degree angle.

Now,

From the figure, we can see that line a and b are parallel to each other.

m∠1=36°

Therefore, m∠1= m∠5

This makes the angle corresponding to each other.

Hence, m∠5=36°

Learn more about angles here:

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70 beats per minute

24*60=1440 minutes in one day

70*1440=100,800 beats per day

Answer:

The number of minutes per day is 60 × 24 = 1440 (minutes)

Since we know that human heart beats about 70 times every minute, the number of times the human heart beats in one day should be:

70 × 1440 = 100800 (times)

Answer:

0.345%

Step-by-step explanation:

you multiply is by 100

Answer:

A

Step-by-step explanation:

When converting from a decimal to a percent, you always multiply the decimal by 100, and in this case, multiplying the number 0.00345 gets us 0.345. This number is the percent, in this case 0.345%, or answer choice A.

Answer:

The length of OA = 10 cm

Step-by-step explanation:

* Lets revise some facts about the circle

- If two tangents drawn from a point outside the circle, then

 they are equal in lengths

- The radii of the circle are perpendicular to the tangents at the

 point of tang-ency

- The line from the center to the angle between the two tangents

 bisects it

* Now lets solve the problem

∵ The sides of ∠A are tangents to circle O

∴ The radius of the circle O ⊥ to the tangent at the point of tang-ency

∴ The line OA bisects ∠A

- The measure of ∠A = 60°

∴ The measure of the angle between line OA and the tangent

  is equal to 1/2 × 60° = 30°

* Now we have right angle triangle formed from the line OA as a  

 hypotenuse two legs of the right angle one of them is the

 tangent and the other is the radius

∵ r = 5 cm

∵ The measure of the angel opposite to r is 30°

∵ OA is the hypotenuse

- By using trigonometry function

∴ sin(30°) = 5/OA

∵ sin(30°) = 1/2

∴1/2 = 5/OA ⇒ by using cross multiplication

∴ OA = 2 × 5 = 10 cm

* The length of OA = 10 cm

*Image Linked Below*

I think it’s B.

I did 9 times 7

The area is going to be 63

Answer:

The image of p is (2.5x , 2.5y)

Step-by-step explanation:

* Lets talk about dilation

- A dilation is a transformation that changes the size of a figure.  

- It can become larger or smaller, but the shape of the

 figure does not change.  

- The scale factor, measures how much larger or smaller  

 the image will be

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

* In our problem

- Point p is (x , y)

- Center of dilation is (0 , 0)

- The scale factor is 2.5

* To get the image multiply each coordinates of p by 2.5

∴ The image of p is (2.5x , 2.5y)

He originally had 24

4 For himself

5 for his four children

5*4= 20+4= 24

Answer:

24

Step-by-step explanation:

24-4=20/5=4

He ate four pieces of his candy which leaves him with twenty pieces. Then multiply five by four and you get 20 pieces of candy.

Answer:

[tex]a=-2\\b=4\\c=-3[/tex]

Step-by-step explanation:

In a quadratic equation in the Standard form

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

You need to remember that "a", "b" and "c" are the numerical coefficients (Where "a" is the leading coefficient and it cannot be zero: [tex]a\neq0[/tex]).

You can observe that the given quadratic equation is written in the Standard form mentioned before. This is:

[tex]-2x^2+4x-3=0[/tex]

Therefore, you can identify that the values of "a", "b" and "c" are the following:

[tex]a=-2\\b=4\\c=-3[/tex]

Answer:

a = -2

b = 4 and

c = -3

Step-by-step explanation:

A standard form of a quadratic equation is

ax₂ + bx + c = 0, where a, b and c are coefficients

To find the value of a, b, and c

The given equation is -2x² + 4x - 3 = 0

The degree of equation is 2, therefore it is a quadratic equation.

here a = -2, b = 4 and c = -3

I guess you mean [tex]\cos a=-\dfrac25[/tex]. Since [tex]a[/tex] is in quadrant III, we expect [tex]\sin a<0[/tex]. Then

[tex]\sin a=-\sqrt{1-\cos^2a}=-\dfrac{\sqrt{21}}5[/tex]

Since [tex]b[/tex] is in quadrant I, we expect [tex]\sin b>0[/tex], so that

[tex]\sin b=\sqrt{1-\cos^2b}=\dfrac{\sqrt{15}}4[/tex]

Now,

[tex]\sin(a+b)=\sin a\cos b+\cos a\sin b=-\dfrac{2\sqrt{15}+\sqrt{21}}{20}[/tex]

[tex]\cos(a+b)=\cos a\cos b-\sin a\sin b=\dfrac{3\sqrt{35}-2}{20}[/tex]

and

[tex]\tan(a+b)=\dfrac{\sin(a+b)}{\cos(a+b)}=-\dfrac{2\sqrt{15}+\sqrt{21}}{3\sqrt{35}-2}[/tex]

Answer:

No, the area will not be doubled. Instead, it will be quadrupled

Step-by-step explanation:

Let the length of the base be b and the height be h.

Original area = b x h

= 3 x 5

= 15 square feet

New area = b x h

= (2 x 3) x (2 x 5)

= 6 x 10

= 60 square feet

Therefore, the area is quadrupled when both the base and the height are doubled.

Answer:

Sample response: No, the area will be multiplied by 4. The original area is 3 × 5 = 15 square feet. If the base and the height are both doubled, then the new area will be 6 × 10 = 60. 60 is 4 times 15.

Answer: The answer is 3/4

Step-by-step explanation:

Answer:

1 cupcake = $3.75

1 ice-cream = $4.50

1 doughnut = $1.50

Step-by-step explanation:

2 ice-cream + 1 cup cake = $12.75 ------------ [ 1 ]

1 ice-cream + 2 doughnuts = $7.50 ------------ [ 2 ]

1 cup cake + 1 doughnut + 1 ice-cream = $9.75 ------------ [ 3 ]

From [ 1 ] :

2 ice-cream + 1 cup cake = $12.75

1 cupcake = $12.75 - 2 ice-cream

Substitute [ 1 ] into [ 3 ]:

1 cup cake + 1 doughnut + 1 ice-cream = $9.75

$12.75 - 2 ice-cream + 1 doughnut + 1 ice-cream = $9.75

1 doughnut - 1 ice-cream = -$3  ------------ [ 4 ]

[ 2 ] + [ 4 ] :

3 doughnuts = $4.75

1 doughnut = $1.50

Substitute (1 doughnut = $1.50) into [ 2] :

1 ice-cream + 2 doughnuts = $7.50

1 ice-cream + 2 x $1.50 = $7.50

1 ice-cream + $3 = $7.50

1 ice-cream = $4.50

Substitute (1 ice-cream = $4.50) into [ 1 ]:

2 ice-cream + 1 cup cake = $12.75

2 x $4.50 + 1 cup cake = $12.75

1 cupcake = $12.75 - $9

1 cupcake = $3.75

To find the cost of each in a system of equations, you need to solve the equations simultaneously. You can solve for one variable first and substitute it into the other equation to find the value of the second variable. Once you have the value of one variable, you can substitute it back into one of the original equations to find the value of the other variable.

In the field of Mathematics, specifically in algebra, a system of equations is a set of equations with the same variables. When you're asked to find the cost of each one, you're actually being asked to solve this system of equations. Let's assume your system of equations is:

You can solve for one variable first from either equation and substitute it into the other. For example, from Equation 1 you can solve for x: x = (40 - 2y)/5. Substituting x into Equation 2 gives us: 3((40 - 2y)/5) + 4y = 35. Solving this will give you the value of y which can then be substituted into any of the original equations to find the cost of x.

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Answer:

B is the greatest being 5.

Step-by-step explanation:

A.

[tex]-2-(-3)\\-2+3\\1[/tex]

B.

[tex]2-(-3)\\2+3\\5[/tex]

C.

[tex]-2-3\\-5[/tex]

D.

[tex]2+(-3)\\-1[/tex]

The expression 2-(-3) is determined to have the greatest value.

To determine which expression has the greatest value:

A: -2-(-3) = -2 + 3 = 1

B: 2-(-3) = 2 + 3 = 5

C: -2-3 = -5

D: 2+(-3) = 2 - 3 = -1

Answer:

4 1/10 kg

Step-by-step explanation:

To find the total mass, we add the mass of the three baskets

1 1/10 + 1 3/10 + 1 7/10

Since they have the same denominator

 1   1/10

 1   3/10

 1   7/10

-------------

 3  11/10

Change the improper fraction to a mixed number

11/10 = 1 1/10

3 + 1 1/10

4  1/10

the answer is:

Area =518

Volume =735

hope this helps you good luck!!