M(-4,9) N(-5,3)

Distance formula: root of (y2-y1)^2 + (x2-x1)^2

Root of (3-9)^2 + (-5-(-4))^2

Root of (-6)^2 + (-1)^2

Root 36+1

Distance= root of 37

Root of (3-9)^2 + (-5-(-4))^2

Root of (-6)^2 + (-1)^2

Root 36+1

Distance= root of 37

How is 9.746 x 10 ^13 written in standard form?

0000000000009746

97,460,000,000,000

9.746000000000000

9,746,000,000,000,000

B. 97,460,000,000,000

hope this helps!! <33

hope this helps!! <33

12

Find the horizontal asymptote of f of x equals quantity negative 2 x squared plus 3x plus 5 end quantity over quantity x squared plus 1. (5 points)

y = −2

y = −1

y = 1

y = 2

The **horizontal asymptote** is **y = -2**

The **horizontal asymptote** is an equation of the form y = k, for some constant k, is a straight line parallel to x-axis.

**Horizontal asymptotes** are found for rational functions of polynomials when x becomes extremely large, or, as x → ∞.

The **function **given is, f(x) = (-2x²+3x+5)/(x²+1)

**Horizontal asymptote** is given by,

y = [tex]\lim_{x \to \infty} \frac{-2x^2+3x+5}{x^2+1}[/tex]

= [tex]\lim_{x \to \infty} \frac{x^2(-2+\frac{3}{x} +\frac{5}{x^2}) }{x^2(1+\frac{1}{x^2}) }[/tex]

= [tex]\lim_{x \to \infty} \frac{(-2+\frac{3}{x} +\frac{5}{x^2}) }{(1+\frac{1}{x^2}) }[/tex]

= -2

So the** horizontal asymptote** of f(x) is, **y = -2**

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**Answer:**

A) y = -2

**Step-by-step explanation:**

The rules to find the horizontal asymptote (HA) is shown below

**Y = A** if the numerator and denominator have same highest exponent for example

A^3

B^3

**Y = 0** if the numerator have lower exponent and denominator have higher exponent for example

A^1

B^2

**None HA** if the numerator have higher exponent and denominator have lower exponent for example

A^2

B^1

And the equation shown in the question have same exponent so the answer is -2

PS: please give me brainiest

Simple Interest Round answers to the nearest cent. 1. John is going to invest $100 in an account for 3 years. If the account earns 6% simple interest, how much interest can he expect to earn?

Given Data:

The initial investment is: P=$100

The total period of investment is: t=3

The annual interest is: 6%.

For the simple interest, the expression to calculate the interest in t years is,

[tex]I=(P\times\frac{r}{100})\times t[/tex]Here r is in percentage.

Substitute known values in the above expression.

[tex]\begin{gathered} I=(100\times\frac{6}{100})\times3 \\ =(6)\times3 \\ =18 \end{gathered}[/tex]Thus, the total intrest for 3 years will be $18.

need someone to answer as soon as possible!

Please please with proof too

The solutions to the **system of equations** are x=5, z=1,y=-3

What is **system of equations?**

Given **equations**:

x+y+z=3

3x+(y/3)-2z=12

-5x-6y+3z=-4

Solving by using the **substitution method**:

[tex]\begin{bmatrix}x+y+z=3\\ 3x+\left(\frac{y}{3}\right)-2z=12\\ -5x-6y+3z=-4\end{bmatrix}[/tex]

Substitute x=3-y-z

[tex]\begin{bmatrix}3\left(3-y-z\right)+\frac{y}{3}-2z=12\\ -5\left(3-y-z\right)-6y+3z=-4\end{bmatrix}[/tex]

Substitute z={8y+9}/{15}

[tex]\begin{bmatrix}-y+8\left(-\frac{8y+9}{15}\right)-15=-4\end{bmatrix}[/tex]

simplify

[tex]\begin{bmatrix}\frac{-79y-72}{15}-15=-4\end{bmatrix}[/tex]

Substitute y=-3

[tex]z=-\frac{8\left(-3\right)+9}{15}[/tex]

z=1

For x=3-y-z

Substitute z=1,y=-3

x=3-(-3)-1

x=5

The solutions to the **system of equations** are:

x=5, z=1,y=-3

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Can I have some help with the question in the attachment. I've done (a) but I think I'm doing (b) wrong

**Answer:**

8.33

**Step-by-step explanation:**

He has to be at work by 10:30, but it takes 20 mins to walk

So, 10:30-20 minutes=10:10

We then look at the arrival time closest to this, which would mean he would arrive at 10.06.

trace this back the bus would gett him at 8:38, but its a 5min walk.

8:38-5 minutes+8.33

hope this helps :)

Write the fraction 622/1000 in its simplest form

Answer:

311/55

Step-by-step explanation:

i devided each by 2 and got this then i looked it up and it said this so id k

hope this helped

Solve for s.

19.1 = s − –7.3

s =

If 7.3 is a negative, s = 11.8. If 7.3 isn’t, s = 26.4.

Make sure when you have negatives, most of the time you add parentheses. An example is (-5).

Make sure when you have negatives, most of the time you add parentheses. An example is (-5).

Is a number closer to 0 greater or less than a number more away from 0? (negatives and positives)

**Answer:**

A number closer to 0 is generally less than a number more away from 0. When it comes to negative numbers the closer the number to 0, the greater it is.

**Step-by-step explanation:**

**If you need further help please let me know.**

**Please mark brainliest!**

A Curve has the equation y=kx^2 +1 And a line has the equation y=kx where

K is a

non-zero

Constant

1)Find the Set

the value of k

for which the

curve and line have no common point.

(1) state the value for which the line is a

tangent to the Curve and for this case, find the coordinates

of the point where the line

touches the curves

The set of the value for which the curve and line have no common point are is k ∈ (0 , 4).

The value for which the line is a **tangent **is k = 4.

The coordinates of the point where the line touches the curves is point of **tangency **= ( 1/2 , 2).

**What is tangent?**

**Tangents **in geometry are lines or planes that contact curves or surfaces at points where they are closer to the curve than any other lines or planes drawn through those points.

Given equations in the question:

y = kx² + 1

y = kx

Equating y

kx² + 1 = kx

kx² -kx + 1 = 0

This is **Quadratic equation** is of the form ax²+bx+c=0 where a , b and c are real also a≠0.

D = b²-4ac is called **discriminant**.

and we know that,

D >0 roots are real and distinct

D =0 roots are real and equal

D < 0 roots are imaginary ( not real ) and different

For no common solution D < 0

For **tangent **D = 0

so,

kx² -kx + 1 = 0

D = (-k)² - 4k = k² - 4k = k(k - 4)

k(k - 4) < 0

if 0 < k < 4

Hence values of k for which the curve and the line have no common points is **k ∈ (0 , 4)**.

for **tangent**

k(k - 4) = 0

k is non zero

Hence **k = 4**

After putting the value of k, given equations are:

y = 4x² + 1

y = 4x

solving these equations to get value of x and y:

4x² + 1 = 4x

4x² - 4x + 1 = 0

(2x - 1)² = 0

x = 1/2

y = 2

**Point of tangency = ( 1/2 , 2)**

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Miranda did a survey of what time people

get to their office on Monday morning.

The table shows her results for

150 people.

Time

before 7 am

7am to 7:59 am

8am to 8:59 am

9am to 9:59 am

No of people

15

39

75

21

a) What percentage of the people surveyed arrive at their office before 7 am?

Optional working

+

Answer:

b) What percentage of the people surveyed arrive at their office after 7:59 am?

Optional working

Answer:

%

The **percentage** of the people **surveyed** that arrive at their office after 7am is 6.7%.

The **percentage** of the people surveyed that arrive at their office after 7:59 am is 64%

From the information, **Miranda** did a survey of what time people get to their office on Monday morning and the table shows her **results**.

The number of people that **arrived** before 7.59am is 15.

The total number of **people** surveyed will be:

= 15 + 39 + 75 + 21

= 150

The **percentage** of the people surveyed arrive at their office before 7 am will be:

= 10 / 150

= 6.7%

The **percentage** of the people surveyed that arrive at their office after 7:59 am will be:

= (75 + 21) / 150.

= 96/150

= 0.64

= 64%

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**Answer:**

the number of people is 15 so you would do 15/150=10percent

b) 66 percent

**Step-by-step explanation:**

A perfect score on a test with 25 questions is 100. Each question is worth 4 points. Fred got a score of 68 on the test to write a division sentence using negative numbers where the quotient represents the number of questions Fred answered incorrectly

The total number of **questions** that Fred answered incorrectly is 8.

From the information given, a perfect **score** on a test with 25 questions is 100 and each **question** is worth 4 points while Fred got a score of 68 on the test.

Therefore, let the number of **questions** that are got be x.

Based on the information given, this will be:

4 × x = 68

4x = 68

Divide

x = 68 / 4 = 17

The number of **questions** that he missed will be:

= Total questions - Correct answers.

= 25 - 17.

= 8

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I need help................

**Answer:**

D

**Step-by-step explanation:**

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (1, 7) ← 2 points on the line

m = [tex]\frac{7-1}{1-(-2)}[/tex] = [tex]\frac{6}{1+2}[/tex] = [tex]\frac{6}{3}[/tex] = 2

use either of the 2 points on the line

using (- 2, 1 ) , then

y - 1 = 2(x - (- 2) ) , that is

y - 1 = 2(x + 2) ← equation in point- slope form

MATHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH LOOK AT PHOTO

The **percentage** of** students **that use **other means** to travel school is **24%**

Percentage is the** ratio** of the **number** for which you want to find percentage to the **total number** with which you want to compare or out of and multiply this ratio with 100.

percentage = (**part** /** whole**) ×100

Given that a school has** 825 total** students.

**Percentage** of students travelling by** car** = 20%

**Percentage** of students travelling by** bus** = 48%

**Percentage** of students travelling by** bicycle** = 8%

Number of students travelling by car = 20% of 825 = (20/100)×825 = 165

Number of students travelling by bus = 48% of 825

= (48/100)×825 = 396

Number of students travelling by bus = 8% of 825 = (8/100)×825 = 66

**Number** of **students** travelling by **other means** = 825-165-396-66 = **198**

Therefore, the **Percentage** of** students** travelling by** other means** = (198/825) ×100 =** 24**%

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The measure of an angle is 78.3°. What is the measure of its complementary angle?

The **complementary **angle of the **angle **is 11.7 degrees

**Angles **are formed when two or more lines intersect. This in other words means that **angles** is the measure of space between the intersection of rays or lines

The **measure **of the **angle **is given as

Angle = 78.3 degrees

**Complementary angles **add up to 90 degrees

So, we have the other **angle** to be

Other angle = 90 - 78.3

Evaluate the difference

Other angle = 11.7

Hence, the other **angle **is 11.7

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PLEASE HELP. Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold. 1. Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work. 2. Describe how you would graph this line using the slope-intercept method. Be sure to show all your work. 3. Write the equation in function notation. Explain what the graph of the function represents. Be sure to show all your work. 4. Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology. 5. Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.

They are similar because they have the same** slope the equation** is

y = -2/3x + 531

**What is in slope-intercept form?**

changing 2x+3y=1470 to slope intercept form is solving for y

minus 2x both sides and divide by 3

y = -2/3x + 490

the slope is -2/3

the y intercept is y=490 or the point (0,490)

to graph it, I would start at the origin and go up 490 units on the y axis and put a point there

then go -2 units up (2 down) and 3 to the right and put a point there

then connect the 2 points with a line

in function notation, replace y with f(x) to get

y = -2/3x + 490

graph below

intercepts labeled

2x+3y=1593

they are similar because they have the same slope

the equation is y = -2/3x + 531

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What number is 40% of 120?

**Answer: 48**

**Step-by-step explanation:Convert 40% to a decimal = 0.4Multiply 0.4 x 120 = 48**

**Answer:**

48

**Step-by-step explanation:**

40\100×120

=48

( fourth divided by one hundred multiplied by one hundred and twenty is equal to 48)

A rectangle is 32ft by 8ft. Stephanie dilated the rectangle and the dimensions of the image were 24ft by 6ft. What was the scale factor used?

**Answer:4**

**Step-by-step explanation:**

image dimension = 24 by 6 feet

preimage dimension = 32 by 8 feet

so 24/6 = 32/8 = 4

scale factor = 4

How do you proof that sqrt(2) is irrational?

I tried this,

p/q = sqrt(2)

p^2/q^2=2

p^2=2q^2

let p = q * sqrt(2) , (equation from top one)

(q*sqrt(2))^2=2q^2

2q^2=2q^2,

q=q

Is anything wrong or does this also prove that sqrt(2) is irrational, if so how?

Assume √2 is rational, so

√2 = p/q

for some relatively prime integers p,q - meaning we can't reduce p/q any further - and q ≠ 0.

Then

p = √2 q

and squaring both sides gives

p² = 2q²

This tells us that p² is even, so 2 divides p². But if 2 divides p², it must also divide p, since p is a square number. So p = 2r for some integer r, and we have

(2r)² = 2q²

4r² = 2q²

2r² = q²

We're in the same situation as before - 2 divides q², so 2 divides q. Both p and q are thus divisible by 2, but this contradicts our assumption that p and q are relatively prime, which means √2 cannot be expressed as a rational number p/q. Therefore √2 is irrational.

What you've written in your proof is technically correct, but it doesn't help in the irrationality proof.

graph this function f(x) = 1/4(x) - 7

**Answer:**

This is your graph to the following equation f(x) = 1/4(x) - 7

This is f(x)=1/4(x)-7 when graphed

A rancher is filling a trough for her horses. The trough already contains 25 gallons of water, and the rancher is adding 11 gallons per minute. How long will it take for the trough to have 80 gallons of water?

The **equation** which is useful to find the **amount **in **gallons** of water to the number of **minutes** since **filling started **is 25 + 11x therefore, it takes 5 minutes to have 80 gallons of water.

Determine the **known** quantities and designate the **unknown **quantity as a variable while trying to **set up** or **construct** a linear equation to fit a real-world **application**.

The amount of water **initially** in the **trough **= 25 gallons.

The **rate **of **adding **water = 11 gallons per minute

Therefore, the **total amount **(A) of water in x minutes will be,

A = 25 + 11x

The **number **of **minutes **to have 80 gallons of water is,

80 = 25 + 11x

11x = 55

x = 5 minutes.

Hence "The **equation** which is useful to find the **amount **in **gallons** of water to the number of **minutes** since **filling started **is 25 + 11x therefore, it takes 5 minutes to have 80 gallons of water".

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The concession stand are the football games are 288 customers. Those customers, about 77% bought a hot dog. About how many customers buy a hotdog?

Fueron 221 clientes

288/100%= 288

2.88x77%= 221

288/100%= 288

2.88x77%= 221

I need help with this question please

**Answer:**

x=-4.5 x=-0.5

y=-1

vertex=-2

The length of a base of a rectangular prism is 12 dm and the width is 5 dm. What should be the height of the rectangular prism be so that it's volume is smaller than the volume of a cube with a side of 9 dm? (for 30 points) will give you brainlyiest or smthing title

**Answer:**

Must be less than 12.15 dm

**Step-by-step explanation:**

-3x+7=-x-1

Simplify and solve for the variable

-3x+7=-x-1

+3x +3x

7=2x-1

+1 +1

8=2x

8/2

X=4

+3x +3x

7=2x-1

+1 +1

8=2x

8/2

X=4

The points (5, r) and (10, -1) lie on a line with slope 5. Find the missing coordinate r

**Answer: r=-26**

**Step-by-step explanation:**

[tex]\displaystyle\\(5,r)\ \ \ \ (10,1)\ \ \ \ slope \ m=5\\\\\boxed {m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=5\ \ \ \ \ x_2=10\ \ \ \ \ y_1=r\ \ \ \ y_2=-1\ \ \ \ \ m=5\\\\Hence,\\\\5=\frac{-1-r}{10-5} \\\\5=\frac{-1-r}{5}[/tex]

**Multiply both parts of the equation by 5:**

[tex]5(5)=-1-r\\\\25=-1-r\\\\25+r=-1-r+r\\\\25+r=-1\\\\25+r-25=-1-25\\\\r=-26[/tex]

Given f(x) = x3 – 2x2 – x + 2, the roots of f(x) are ✔ –1, 1, 2 . Determine the end behavior of f(x).

**Answer:**

1, -1 and 2

**Step-by-step explanation:**

The zeros of the given polynomial function are 1, -1 and 2

Given the polynomial function

First, we need to assume a value of x to check if it will give us zero after substituting:

Assuming x = 1

Since f(1) =0, hence x - 1 is a factor

Dividing x - 1 by the given polynomial function, we will have:

Equating the result to zero

x + 1 = 0 and x - 2 = 0

x = -1 and 2

Hence the zeros of the given polynomial function are 1, -1 and 2

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Please Help me turn vertex form to standard form!!

**Answer:**

See below

**Step-by-step explanation:**

y = -(x-1)^2 +4 Expand R side

y = - ( x^2 -2x+1) + 4

y = -x^2 +2x -1 + 4

y = -x^2 + 2x + 3 a = -1 b = 2 c = 3

A figure is rotated 270 degrees counterclockwise about the origin. Then the image is rotated 90 degrees counterclockwise about the origin. Complete the coordinate notation that represents the series of rotations. What can you conclude about the position of the figure after the series of rotations?

If you don't mind, I need the answer ASAP

The series of **rotations** are :** **(x, y) -----> (y, -x) → (y, -x) ----> (x, y)**.**

The total **rotation** is 360 degrees. So the figure is the **original figure **itself.

First a figure is **rotated **270 degrees **counterclockwise** about the origin.

A 270 degree counterclockwise** rotation** is given by the co-ordinate **transformation**, (x, y) -----> (y, -x)

Then the figure is again **rotated **90 degrees** **counterclockwise about the origin. A 90 degree **counterclockwise** rotation is given by, (x, y) -----> (-y, x)

So combining with the above transformation, the 90 degree counterclockwise **rotation** gives, (y, -x) ----> (x, y)**.**

Thus the **total rotation** transformation is in turn, (x, y) ----> (x, y).

Thus the** total rotation** in counterclockwise direction about the origin is 360 degrees. So the **final figure** is the** original figure** itself.

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An item costs y dollars and then a 20% discount is applied. Create an expression that could represent the price of the item after the discount. Explain your reasonin

The **percentage **20% of the **costs **y is given as 0.20y thus the **expression **which represents the **price **of the item after the **discount **is P = y - 0.20y.

The **percentage** is just like the **amount** of that value but between 1 to 100 and it is very **useful **to **predict **for example if you say 678 then we have to know about the full **number **also but if you say 80% then it **becomes clear**.

It is known that x% of something y is given as,

x% of y = (x/100)y

Given that **discount **of 20% of y

20% of y = (20/100)y

20% of y = 0.20y

Now the **final** price = **initial **price - **discount **

Final price (P) = y - 0.20y

Hence"The **percentage **20% of the **costs **y is given as 0.20y thus the **expression **which represents the **price **of the item after the **discount **is P = y - 0.20y".

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Elsie is a project manager

in 2016 she earned £2100

in 2017 she was awarded a 3% increase on her monthly salary

given that in 2017 worked 42 hours a week for 45 weeks.

week out her average pay-per-hour of the year

The average **pay-per-hour** of the year for Elise will be 13.73 pounds.

From the information, in 2016 she earned £2100 and in 2017 she was awarded a 3% increase on her **monthly** salary.

Therefore, the new **salary** will be:

= 2100 + 3%(2100)

= 2100 + 63

= 2163

Now she worked for 42 **hours** per week for 45 weeks. This will be:

= 42 × 45

= 1890 hours

Therefore, the total **earnings** for the year will be:

= 2163 × 12 months

= 25956

The average **pay-per-hour** of the year will be:

= Total amount / Number of hours

= £25956 / 1890

= £13.73

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Balance the equations.MgO + HBr MgBr + HO
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