For a field trip 8 students rode in cars and the rest filled ten buses. How many students were in each bus if 538 students were on the trip?

the answer is:

Area =518

Volume =735

hope this helps you good luck!!

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

[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:

The height of the prism is [tex]24\ in[/tex]

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

[tex]V=LWH[/tex]

In this problem we have

[tex]V=5,376\ in^{3}[/tex]

[tex]L=14\ in[/tex]

[tex]W=16\ in[/tex]

substitute in the formula and solve for H

[tex]5,376=(14)(16)H[/tex]

[tex]H=5,376/[(14)(16)][/tex]

[tex]H=24\ in[/tex]

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:

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:

-1/2

explanation

1-2 / 4-2 = -1/2

Slope between two points

 [tex](x_{1},y_{1}) \text{and},(x_{2},y_{2}) \text{is equal to}\\\\\text{and}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{1-2}{4-2}\\\\=\frac{-1}{2}[/tex]

Option D                                

  [tex]\frac{-1}{2}[/tex]

Answer:

[tex]\boxed{\frac{1}{8}}[/tex]

Step-by-step explanation:

You are starting with ½ pie. Then you cut it into four pieces.

You want to evaluate ½ ÷ 4

Step 1. Treat the integer as a fraction

[tex]\frac{1}{2}\div{\frac{4}{1}}[/tex]

Step 2. Invert the divisor and change divide to multiply

[tex]\frac{1}{2}\times{\frac{1}{4}}[/tex]

Step 3. Multiply numerators and denominators

[tex]\frac{1}{2}\times{\frac{1}{4}} = \mathbf{\frac{1}{8}}\\\\\text{Each piece is } \boxed{\mathbf{\frac{1}{8}}} \text{ of a whole pie.}[/tex]

Answer:

1/8

Step-by-step explanation:

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)

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:

113.51

Step-by-step explanation:

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

Answer:

4(2 + y)

Step-by-step explanation:

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:

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

Answer:

[tex]y=B(2+0.1x)[/tex]

Step-by-step explanation:

B = number of sponsors

x = number of pins

Equation :

[tex]y=B(2+0.1x)[/tex]

Answer:

(7,2)

y= -47 or (0,-47)

Step-by-step explanation:

You can use a graphing calculator to find the vertex and y intercept

The coordinates of the vertex are - V(7, 2) and the y - intercept will have coordinates - Y(0, - 47).

Given is the following equation -

- x² + 14x - 47

We can write the vertex as -

[tex]{\displaystyle V=\left(-{\frac {b}{2a}},{\frac {4ac-b^{2}}{4a}}\right)}[/tex]

So, we can write -

V = (-14/-2, {4 x -1 x -47 - 196}/{-4})

V = (7, 2)

and the point of the parabola intersecting the y - axis has coordinates -

(0, c)

(0, - 47)

Therefore, the coordinates of the vertex are - V(7, 2) and the y - intercept will have coordinates - Y(0, - 47).

To solve more questions on Parabolas, visit the link below-

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Answer:

153.86

Step-by-step explanation:

To find the area the equation is pi* radius squared

so it's 3.14*7 squared it's

3.14*49

The answer is 153.86

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

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:

(-1,4)(1,4)

2

Step-by-step explanation:

Answer:

37/40

Step-by-step explanation:

Answer:

hello :  x=1

Step-by-step explanation:

look this solution  :

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

Read more:

https://brainly.com/question/15165519

Answer:

£ 1.96

Hope this helps :)

Have a great day !

5INGH

Step-by-step explanation:

1 kg = £ 4.90

( ÷ 10 )

100 g = £ 0.49

( × 4 )

400 g = £ 1.96

Answer:

£1.96

Step-by-step explanation:

1kg = 1000g

1 kg = £4.90

1000g = £4.90

1000g = £4.90

100 g = 4.90 ÷ 10 = £0.49

100g = £0.49

400g = 0.49 x 4 = £1.96

Answer: The answer is 3/4

Step-by-step explanation:

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

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:

Step-by-step explanation:

Look at the picture.

We have the triangles 45° - 45° - 90° and 30° - 60° - 90°.

The sides of those triangles are in ratio:

1 : 1 : √2 and 1 : √3 : 2

Therefore

If AC = 6√2 then AB = BC = 6

If BC = 6 then x = 6 : 2 = 3

Answer:$2700

Step-by-step explanation: Really depends on the kind of interest, but you would take the initial amount, and multiply it by the APR for the amount of interest, then add the interest to the initial amount.

To repay the full principle and interest in the first year of the loan with an interest rate of 8%, David borrowed $2500 from his local bank, would need to pay a total of $2700 to the bank.

To answer your question, we first need to calculate the interest David needs to pay. The formula used to calculate the interest on a loan is: Principal sum x Annual interest rate. David's principal sum is $2500 and the annual interest rate is 8%.

Here's the calculation step-by-step:

So, if David pays the full principle and interest in the first year of the loan, he will pay a total of $2700 to the bank.

Learn more about Interest Calculation here:

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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