Ben climbed 15 feet up a hill,8 feet down a hill, and 11 feet up another hill. What is his overall change in elevation?

Answer:

2y + 3x = 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x + 2y = - 4 into this form

Subtract 3x from both sides

2y = - 3x - 4 ( divide all terms by 2 )

y = - [tex]\frac{3}{2}[/tex] x - 2 ← in slope- intercept form

with slope m = - [tex]\frac{3}{2}[/tex]

• Parallel lines have equal slopes, thus

y = - [tex]\frac{3}{2}[/tex] x + c ← partial equation of parallel line

To find c substitute (4, - 1) into the partial equation

- 1 = - 6 + c ⇒ c = - 1 + 6 = 5

y = - [tex]\frac{3}{2}[/tex] x + 5 ← in slope- intercept form

Multiply through by 2

2y = - 3x + 10 ( add 3x to both sides )

3x + 2y = 10 ← in standard form

The equation of the line parallel to 3x+2y= -4 goes through the point (4,-1).

The general equation of a straight line exists y = mx + c, where m is the gradient, and y = c exists the value where the line cuts the y-axis. This number c is named the intercept on the y-axis. The equation of a straight line with gradient m and intercept c on the y-axis stands y = mx + c.

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x + 2y = - 4 into this form

Subtract 3x from both sides

2y = - 3x - 4 ( divide all terms by 2 )

y = -  x - 2 ← in slope- intercept form

with slope m = -

• Parallel lines have equal slopes, thus

y = -  x + c ← partial equation of parallel line

To find c substitute (4, - 1) into the partial equation

- 1 = - 6 + c ⇒ c = - 1 + 6 = 5

y = -  x + 5 ← in slope- intercept form

Multiply through by 2

2y = - 3x + 10 ( add 3x to both sides )

3x + 2y = 10 ← in standard form.

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The total amount that all three friends have is $84.

Let's assume that Ami, Jan, and Toy have x, y, and z dollars respectively. After the first redistribution, we know that:

x - a = 2(y + z)

y + a = 2(x + z)

z + a = 2(x + y)

where a is the amount of money that Ami gives to Jan and Toy.

Solving these equations, we get:

x = 5z - 4a

y = 5z - 6a

z = z

After the second redistribution, the new amounts are:

x + b = 2(y + c)

y - b + c = 2(x + c)

z + b + c = 2(x + y)

where b is the amount that Jan gives to Ami and Toy, and c is the amount that Toy gives to Ami and Jan.

Solving these equations, we get:

x = 14c

y = 11c

z = 6c

Finally, after the third redistribution, the new amounts are:

x + 2d = 2(y + 2d)

y + 2d = 2(x + 2d)

z - 2d + 2c = 2(x + y)

where d is the amount that Toy gives to Ami and Jan.

Solving these equations, we get:

x = 8d

y = 10d

z = 18d

Since we know that z = $36, we can solve for d and get d = $2. Therefore, the total amount that all three friends have is:

x + y + z = 8d + 10d + 36 = $84.

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Answer:

m(h) = 5.25h

$11.81 for 2 hours and 15 minutes

Step-by-step explanation:

Answer:

13. part a

What Lenora did wrong is that when you multiply 2 terms, the exponents are added not multiplied. It would be 10x^4y^6

13. part b

2xy^4

when the terms are divided, the exponents are subtracted

Answer:

13. part a

What Lenora did wrong is that when you multiply 2 terms, the exponents are added not multiplied. It would be 10x^4y^6

13. part b

2xy^4

when the terms are divided, the exponents are subtracted

Step-by-step explanation:

Answer:

a + 2

Step-by-step explanation:

Given

[tex]\frac{a^2+3a+2}{a+1}[/tex] ← factor the numerator

= [tex]\frac{(a+1)(a+2)}{a+1}[/tex]

Cancel the factor (a + 1) on the numerator/denominator

= a + 2 ← quotient

Answer:

$480+$48=$528

Step-by-step explanation:

his friend paid him $480 and 10% so,

=10/100*480

=1/10*480

=480/10

=$48

so,his friend paid him $480+$48=$528.

Answer:

[tex]\large\boxed{\dfrac{x+5}{x^2}-\dfrac{2}{5x}=\dfrac{3x+25}{5x^2}}[/tex]

Step-by-step explanation:

[tex]\dfrac{x+5}{x^2}-\dfrac{2}{5x}=\dfrac{5(x+5)}{5x^2}-\dfrac{2x}{5x^2}\qquad\text{use the distributive property}\\\\=\dfrac{5x+25}{5x^2}-\dfrac{2x}{5x^2}=\dfrac{5x+25-2x}{5x^2}=\dfrac{3x+25}{5x^2}[/tex]

The difference between the rational expressions below will be,[tex]\frac{3x+25}{5x^2}[/tex]

Arithmetic is an area of mathematics involving the study of numbers and the different operations that can be performed on them.

The difference in the rational expression is found as;

[tex]=\frac{x+5}{x^2} -\frac{2}{5x} \\\\=\frac{5(x+5)}{x^2} - \frac{2x}{5x^2} \\\\\ = \frac{5x+25}{5x^2} -\frac{2x}{5x^2 }\\\\\ = \frac{5x+25-2x}{5x^2} \\\\ = \frac{3x+25}{5x^2}[/tex]

The difference between the rational expressions below will be,[tex]\frac{3x+25}{5x^2}[/tex].

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Answer:

-4/3

Step-by-step explanation:

If the lines are parallel, they have the same slope.

Since the red line has a slope of -4/3, the green line will have a slope of -4/3

Answer:

What parabola tool?

Step-by-step explanation:

I went ahead and graphed the quadratic function however, you should learn how to graph it yourself the way they are asking you to using the "parabola tool", because I cant really show you my steps in graphing it since I don't know what your parabola tool is.

Sorry

Answer: The percent of students have scored between 60 and 65 points is 34.13%

Step-by-step explanation:

Given : The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation of 5 points.

i.e. [tex]\mu=60\ \ \ \sigma=5[/tex]

Let x denotes the points obtained by students of a class in a test .

Now , the probability that the students have scored between 60 and 65 points :-

[tex]P(60<x<65)=P(\dfrac{60-60}{5}<\dfrac{x-\mu}{\sigma}<\dfrac{65-60}{5})\\\\= P(0<z<1)\ \ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\= P(z<1)-P(z<0.5)\ \ \ [\because\ P(z_1<Z<z_2)=P(Z<z_2)-P(Z<z_1)]\\\\=0.8413-0.5=0.3413[/tex]

[tex]=34.13\%[/tex]

Hence, the percent of students have scored between 60 and 65 points is 34.13%.

Answer:

f(n) = 2 + 3(n-1)

Step-by-step explanation:

Answer:

f(n) = 2 + 3(n-1)

Step-by-step explanation:

Answer:

The correct answer option is D. 5.

Step-by-step explanation:

We are given the following expression where 4 is to be divided by a fraction 1/5:

[tex] 4 [/tex] ÷ [tex]\frac{1}{5}[/tex]

This can also be written as:

[tex]\frac{4}{\frac{1}{5} }[/tex]

Now to find the quotient of this, we will take the reciprocal of the fraction in the denominator to change it into multiplication.

[tex]4 \times \frac{5}{1}[/tex]

Therefore, ignoring the 1 in denominator, we can simply multiply 4 by 5.

Answer:

Hi there!

The answer is last one: 5

Step-by-step explanation:

When ever you are dividing a number by a fraction you always flip the fraction and multiply it, another way of saying it is multiplying by its reciprocal.

Answer:

S>6

Step-by-step explanation:

Let us suppose the distance walked by Hanna and swati is represented by H and S.

And total distance travelled is D

D=H+S

D>14

H+S>14

Given H=8

8+S>14

S>6

Hence swati walked more than 6 miles

Answer:

B) {-5x + 4y = 8

{-x + 5y = 10

Step-by-step explanation:

Add like it said, and you will see your answer.

Answer:

Option B

[tex]-5x+4y=8[/tex]

[tex]-x+5y=10[/tex]

Step-by-step explanation:

We are given that

System of equations

[tex]-5x+4y=8[/tex]

[tex]4x+y=2[/tex]

We have to find an equivalent system of equations using sum of system and first equations

Sum of system of equations

[tex]-5x+4y+4x+y=8+2[/tex]

[tex]-x+5y=10[/tex]

Therefore, option B is true.

Answer: B. 2=3x+10x^2

Step-by-step explanation:

The expression means the quadratic function equation.

B = 10x^2 + 3x -2 = 0

the equation is [-b ±√(b^2 -4ac)]/2a

b should be +3 to become -3 when it is plugged into the equation, and 'a' should be 10, and c should be -2.

Answer:B

Step-by-step explanation:

Ye you know me keep it a buck like 123 ye 2022 baby

Answer:

-4

Step-by-step explanation:

Technically, the negative sign is treated as multiplying by -1, which is then separate from the 2.  This equation can also be rewritten as [tex]-1 * 2^2[/tex], which would be simplified to [tex]-1 * 4[/tex] and then [tex]-4[/tex].

It depends on how the parenthesis is like. -(2)^2 will equal -4 while (-2)^2 equals 4. But the answer will most likely be 4 because they tend to make sure to put parenthesis if they want the answer to be -4. (Calculators are programmed differently which is why you're getting mixed answers.)

Answer:

A

Explanation:

In image A the image becomes smaller but doesn't change shape which is what dilation is supposed to be.

Answer:

Option A

Step-by-step explanation:

[tex]\dfrac{16}{7x+4}+A=\dfrac{49x^2}{7x+4}\\\\A=\dfrac{49x^2}{7x+4}-\dfrac{16}{7x+4}\\\\A=\dfrac{49x^2-16}{7x+4}\\\\A=\dfrac{(7x-4)(7x+4)}{7x+4}\\\\A=7x-4[/tex]

[tex]\bf \stackrel{~~~~~~~~\textit{is equivalent}}{\cfrac{16}{7x+4}+A~~=~~\cfrac{49x^2}{7x+4}}\implies \stackrel{\textit{cross-multiplying}}{\cfrac{16~~\begin{matrix} (7x+4) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 7x+4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}+A(7x+4)=49x^2} \\\\\\ 16+A(7x+4)=49x^2\implies A(7x+4)=49x^2-16\implies A=\cfrac{49x^2-16}{7x+4}[/tex]

[tex]\bf A=\cfrac{7^2x^2-4^2}{7x+4}\implies A=\cfrac{\stackrel{\textit{difference of squares}}{(7x)^2-4^2}}{7x+4}\implies A=\cfrac{(7x-4)~~\begin{matrix} (7x+4) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 7x+4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A=7x-4~\hfill[/tex]

Answer:

if it was 102 when he woke

e up and lowered then it will be 99 degree fahrenheit then

Final answer:

Steve's temperature decreased by 3 degrees from the original 102 degrees F, which means his temperature two hours later was 99 degrees F.

Explanation:

The student's question involves a basic mathematical operation, specifically subtraction, used to determine a change in temperature over time. Steve originally has a temperature of 102 degrees Fahrenheit. After two hours, his temperature has decreased by 3 degrees.

To find the new temperature, we subtract the decrease from the original:
102 degrees F - 3 degrees F = 99 degrees F.

So, Steve's temperature two hours later would be 99 degrees Fahrenheit.

Answer:

0.

Step-by-step explanation:

The nonpermissible replacement of the variable in an expression is the value of x that will make the denominator of the expression zero.

This problem will therefore be written as -5/3y≠0, and it can't be 0, so 0 is your non permissible replacement.

Hope this helps!

Answer:

[tex]\frac{16x^2+48x}{8x} = 2x+6\\\frac{56x^2-14x}{7x} = 8x-2\\\frac{18x^2+15x}{3x}=6x+5\\\frac{20x^2-32x}{4x}=5x-8[/tex]

Step-by-step explanation:

We will solve the division one by one:

[tex]\frac{16x^2+48x}{8x} = \frac{8x(2x+6)}{8x} = 2x+6\\\frac{56x^2-14x}{7x}=\frac{7x(8x+2)}{7x}=8x+2\\\frac{18x^2+15x}{3x} =\frac{3x(6x+5)}{3x} = 6x+5\\\frac{20x^2-32x}{4x}=\frac{4x(5x-8)}{4x}=5x-8[/tex]

a)

[tex]\dfrac{16x^2+48x}{8x}[/tex]

Since, both the terms in the numerator have a common factor as: 8x.

Hence, we take out common 8x from the numerator term and hence it could be written as:

[tex]\dfrac{8x(2x+6)}{8x}[/tex]

i.e.

[tex]=2x+6[/tex]

b)

[tex]\dfrac{56x^2-14x}{7x}[/tex]

Since, both the terms in the numerator have a common factor as: 14x.

Hence, we take out common 14x from the numerator term and hence it could be written as:

[tex]=\dfrac{14x(4x-1)}{7x}\\\\=2(4x-1)\\\\=8x-2[/tex]

c)

[tex]\dfrac{(18x^2+15x)}{3x}[/tex]

Since, both the terms in the numerator have a common factor as: 3x.

Hence, we take out common 3x from the numerator term and hence it could be written as:

[tex]=\dfrac{3x(6x+5)}{3x}\\\\=6x+5[/tex]

d)

[tex]\dfrac{20x^2-32x}{4x}[/tex]

Since, both the terms in the numerator have a common factor as: 4x.

Hence, we take out common 4x from the numerator term and hence it could be written as:

[tex]=\dfrac{4x(5x-8)}{4x}\\\\=5x-8[/tex]

Answer:

The answer would be, both A. and B.

Answer:

both a and b

Step-by-step explanation:

Answer:

Step-by-step explanation:

When you find the sum of a number you are adding two or more numbers together. therefore the only answer that you could use to get a sum of 5 when your first term is 12 would be -7

Answer:

[tex]\large\boxed{y=-\dfrac{7}{3}x+4}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept (0, b)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points:

(0, 4) → b = 4

and (3, -3)

Substitute:

[tex]m=\dfrac{-3-4}{3-0}=\dfrac{-7}{3}\\\\y=-\dfrac{7}{3}x+4[/tex]

Answer:

a=1, b = -3, c=-2

Step-by-step explanation:

The quadratic equation is in the form

a[tex]x^{2}[/tex] + bx +c = 0

Using the given equation

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

We can see that

a=1  b=-3  c=-2

Answer:

14, 28, 42, 56, 70, 84, (etc.)

Step-by-step explanation:

14, 28, 42, 56, 70, 84, (etc.) are all multiples of 7. They're also even and have 2 digits.

Answer:     14  28  42  56  70  84

Step-by-step explanation: Hopes this helps

Answer:

C

Step-by-step explanation:

x-4 is zero when x=4

so the one that contains the factor (x-4)

C

Answer:

25 gallons.

Step-by-step explanation:

The container that holds the water for the football team is 1/2 full.

After pouring out 5 gallons of water, it is 3/10 full.

The proportion that was poured out is [tex]\frac{1}{2}[/tex] - [tex]\frac{3}{10}[/tex] = [tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex]

[tex]\frac{1}{5}[/tex] of the water in the container is equal to 5 gallons

The container therefore holds: 1 × 5 ÷ [tex]\frac{1}{5}[/tex] = 5 × 5 = 25 gallons.

Final answer:

The total capacity of the container is calculated to be 25 gallons, found by using the information that 1/2 to 3/10 of the capacity equals a 5 gallon difference.

Explanation:

We have been given that the container is initially 1/2 full and becomes 3/10 full after pouring out 5 gallons of water.

To find out the total capacity of the container, we can set up a proportion where the difference between the two fractions (1/2 and 3/10) represents the 5 gallons removed.

First, we find a common denominator for the two fractions, which is 10. Now we can say:

The difference between 5/10 and 3/10 is 2/10, which equates to the 5 gallons poured out. Thus, 2/10 of the container's capacity is 5 gallons, and we can find the full capacity (10/10) by multiplying the 5 gallons by 5 (since 2 × 5=10).

So, the container's total capacity is 5 gallons × 5 = 25 gallons.

ANSWER

The system consists of parallel lines. Both lines have the same slope.

EXPLANATION.

The first equation is

[tex]y = \frac{1}{3} x - 4[/tex]

This equation is in the slope-intercept form.

The second equation is

[tex]3y - x = - 7[/tex]

We write this one too in slope-intercept form so that we can make comparison.

[tex] \implies \: y = \frac{1}{3} x - \frac{7}{3} [/tex]

We can see that both equations have slope

[tex]m = \frac{1}{3} [/tex]

This means the two lines are parallel.

The two lines have different y-intercepts.

Two parallel lines with different y-intercepts will never meet.

The lines will never intersect.

Answer:

The true statements are:

- The system consists of parallel lines

- Both lines have the same slope

Step-by-step explanation:

* Lets talk about the solution of the linear equations

- There are three types of the solutions of the system of linear equations

# If the two lines intersect each other, then there is one solution

- The equations are ax+ by = c , dx + ey = f

# If the two lines parallel to each other, then there is no solution

- The equations are ax+ by = c , ax + by = d in its simplest form ,

  where a is the coefficient of x , b is the coefficient of y and

  c , d are the numerical terms

# If the two lines coincide (over each other), then there are infinite

   solutions

- The equations are ax+ by = c , ax + by = c in its simplest form, where

  a is the coefficient of x , b is the coefficient of y and c is the

  numerical term

* Lets solve the problem

∵ The system of equation is:

   y = 1/3 x - 4 ⇒ (1)

   3y - x = -7 ⇒ (2)

- Lets put equation (1) in the form of equation (2)

∵ y = 1/3 x - 4 ⇒ multiply both sides by 3

∴ 3y = x - 12 ⇒ subtract x from both sides

∴ 3y - x = -12

∴ Equation (1) is 3y - x = -12

∵ Equation (2) is 3y - x = -7

∵ The coefficients of x and y in the two equation are equal

∵ The numerical terms in the two equations are not equal

∴ The equations have no solution because their lines are parallel

∵ The parallel lines have same slope

* The true statements are

- The system consists of parallel lines

- Both lines have the same slope