Find the midpoint of a line segment

Answer:

(a) 349.34

(b) 77.63 km/h

Step-by-step explanation:

Distance you covered before it rain S =  180 km

Speed v = 95/km

Time taken to cover 180 km = [tex]\frac{S}{v}[/tex]

                                               =  [tex]\frac{180}{95}[/tex]

                                               = 1.89473 hrs.

Total time to cover the distance between school to home T = 4.5 hrs.

Remaining time t = T - t

                             = 4.5 - 1.89473

                             = 2.60527 h.

Velocity after travel 180 km. v' = 65 km/h

Distance traveled in this velocity S' = v'(t)

                                                           = 2.60527 × 65

                                                           = 169.34 km

(a) distance of hometown from school = 169.34 + 180 = 349.34 km.

(b) Your average speed V =  [tex]\frac{S}{T}[/tex]

                                           =  [tex]\frac{349.34}{4.5}[/tex]

                                           = 77.63 km/h

Answer:

The answer to your question is: P(A) = 0.47

Step-by-step explanation:

Data

7 red flowers

3 white flowers

5 yellow flowers

Probability  that he select a red one

Formula

 P(A) = Number of favorable cases of A / total number of outcomes

Number of favorable cases = 7

Total number of outcomes = 7 + 3 + 5 = 15

Substitution

                      P(A) = 7 / 15

                      P(A) = 0.47

Answer:

  B.  3

Step-by-step explanation:

"k" represents the number of units of upward translation between f and g. Since g is translated 3 units upward from f, we must have k=3.

Answer:

  14.  61.2 mi N, 49.8 mi W

  15.  7.3 ft

Step-by-step explanation:

14. The components in the different directions are found using the sine and cosine functions. (Draw yourself a diagram to help see this.)

 north distance = (78.9 mi)cos(39°10') ≈ 61.2 mi

 west distance = (78.9 mi)sin(39°10') ≈ 49.8 mi

__

15. Let d represent the distance from the observation point to the door. Then ...

  8.8 ft = d·tan(56°)

  x = d·tan(51°)

Dividing the second of these equations by the first cancels d and gives ...

  x/(8.8 ft) = tan(51°)/tan(56°)

Multiplying by 8.8 ft, we can find x:

  x = (8.8 ft)(tan(51°)/tan(56°)) ≈ 7.3 ft

B

they have limited (3) common points where the planes meet.

Answer: 8 + 2/3 batches of brownies you can bake.

Step-by-step explanation:

6 1/2 butter  = 6 + 1/2 = (2·6 + 1)/2 = 13/2 sticks of butter, we have this

Since we have 13/2 sticks of butter and each batch of brownies needs 3/4 of a stick of butter, we have to divide the amount of butter we have between the amount of butter we use to bake a batch of brownies.

13/2 butter ÷ 3/4 butter/batch = 13·4/2·3 batches = 52/6 batches = 8 + 2/3 batches

Answer: 8 + 2/3 batches of brownies you can bake.

[tex]\textit{\textbf{Spymore}}[/tex]  

By dividing the total amount of butter (13/2 sticks) by the amount required per batch (3/4 stick), we find that it's possible to make 8 full batches of brownies with 6 1/2 sticks of butter, with some butter left over.

To determine how many batches of brownies you can bake with 6 1/2 sticks of butter, you have to divide the total amount of butter you have by the amount required for one batch. Since each batch requires 3/4 stick of butter, you calculate as follows:

Total sticks of butter: 6 1/2
Required per batch: 3/4

Now convert 6 1/2 to an improper fraction: 6 1/2 = 13/2.

Next, calculate the number of batches by dividing the total butter by the butter per batch:

Number of batches = (13/2) / (3/4) = (13/2) * (4/3) = 52/6

When you simplify 52/6, you get 8 with a remainder, meaning you can make 8 full batches of brownies, and you will have some butter left over.

Answer:

he magnitude of Sarah's displacement is less than the distance she travels

Step-by-step explanation:

Hi!

The magnitude of her displacement is just the difference between her final and initial state, however the distance she traveled is two times the distance she moved in the positive x-direction until she turned around, since she had to move back, plus her displacement.

So:

[tex]displacement = |x_{final} -x_{initial}| \\distanceTraveled = 2|x_{return}-x_{initial}| + displacement\\[/tex]

Since all the terms are positive:

[tex]x_{displacement}<x_{traveled}[/tex]

Answer:

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

Step-by-step explanation:

3x + 2y = 8

-3x - 3x

___________

2y = -3x + 8

___ _______

2 2

y = -1½x + 4

↑

rate of change [slope]

I am joyous to assist you anytime.

Answer:

The probability that the student is going to pass the test is 0.0545

Step-by-step explanation:

The variable that says the number of correct questions follows a Binomial distribution, because there are n identical and independent events with a probability p of success and a probability 1-p of fail. So, the probability of get x questions correct is:

[tex]P(x)=\frac{n!}{x!(n-x)!} *p^{x} *(1-p)^{n-x}[/tex]

Where n is equal to 10 questions and p is the probability of get a correct answers, so p is equal to 1/2

Then, if the student pass the test with at least 8 questions correct, the probability P of that is:

P = P(8) + P(9) + P(10)

[tex]P=(\frac{10!}{8!(10-8)!}*0.5^{8}*(0.5)^{10-8})+(\frac{10!}{9!(10-9)!} *0.5^{9} *(0.5)^{10-9})+(\frac{10!}{10!(10-10)!} *0.5^{10} *(0.5)^{10-10})[/tex]

P = 0.0439 + 0.0097 + 0.0009

P = 0.0545

Answer:

Parallel

Step-by-step explanation:

All of the other answers give examples of lines that intersect at some point.

Answer:

transversal

Step-by-step explanation:

The line is called transversal. A transversal is a line which intersects two or more parallel lines

Answer:

-1/32.

Step-by-step explanation:

(-1/2)^3 * (-1/2)^2

= -1/8 * 1/4

= -1/32.

The given function : [tex]f(x)=x^2+2x-3[/tex]

Using completing the squares, we have

[tex]f(x)=x^2+2x+1-1-3[/tex]        [∵ [tex](x+1)^2=x^2+2x+1[/tex]]

[tex]f(x)=(x+1)^2-4[/tex]      (1)

Comparing (1) to the standard vertex form [tex]f(x)=(x-h)^2+k[/tex] , the vertex of function is at (h,k)=(-1,-4)

For x-intercept, put f(x)=0 in (1), we get

[tex]0=(x+1)^2-4\\\\\Rightarrow\ (x+1)^2=4[/tex]    

Square root on both sides, we get

[tex]x+1=\pm2\\\\x+1=-2\ or\ \ x+1=2\\\\=x=-3\ \ or\ x=1[/tex]

∴ x intercepts : x= (-3,0) and (1,0)

For y-intercept put x=0 in (1), we get

[tex]f(1)=(1)^2-4=1-4=-3[/tex]  

∴ y intercept : (0,-3)

Axis of symmetry : [tex]\dfrac{-b}{2a}[/tex]

In [tex]f(x)=x^2+2x-3[/tex] , a=1 and b=2

Axis of symmetry=[tex]\dfrac{-2}{2(1)}=-1[/tex]

A graph of the quadratic equation [tex]f(x) = x^2 + 2x - 3[/tex] with its key features is shown on the coordinate plane in the image below.

In Mathematics and Euclidean Geometry, the standard form of a quadratic function is represented by the following equation;

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

Where:

Since the leading coefficient (value of a) in the given quadratic function [tex]f(x) = x^2 + 2x - 3[/tex] is positive one (1), we can logically deduce that the parabola would open upward and the solutions are the x-intercepts. Furthermore, the key features of this quadratic function include the following;

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Complete Question;

Graph [tex]f(x) = x^2 + 2x - 3[/tex], label the function’s x-intercepts, y-intercept and vertex with their coordinates. Also draw in and label the axis of symmetry

Answer:

#1. 408% of 568

We get two equations from this

408% = x

568 = 100%

568/x=100%/408%

Solve and you'll get

408% of 568

=2317.44

2. New - Original = % change

712500 - 950000 = -237500

3. 10 at $1, 7 at $5

4. 2.2 lb. of raisins, 7.8 lb. of nuts

As per the given conditions we have

1. Number which is 408% of 568 is equals to 2317.44 ( nearest hundredth).

2. Total decrease in percentage of the population of Detroit is equals to 25%.

3.Cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.

4. Raisins is equals to 2.2 pounds and nuts is equals to 7.8 pounds for the trail mix.

" Equation is defined as the relation between the variables using sign of equality."

" Percentage is defined as the hundredth part of the given number."

According to the question,

1. 'x' represents the number

As per given condition,

x = 408% of 568  

⇒ [tex]x= \frac{408}{100} (568)[/tex]

⇒ [tex]x = 2317.44[/tex]

Therefore, the number which is 408% of 568 is equals to 2317.44.

2. Total population of Detroit = 950,000

Population after 10 years = 712,500

Decrease in population = 950,000 - 712,500

                                       = 237,500

Total percentage decrease in population = [tex]\frac{237500}{950,000}(100)[/tex]

                                                                     = 25%

Therefore, total  decrease in percentage of the population of Detroit is equals to 25%.

3. 'x' represents the bill of $1

  'y' represents the bill of $5

As per the condition given equation we have,

$1x + $5y = $45                  ______(1)

x = y + 3                              ______(2)

Substitute the value of  equation (2) in (1) we get,

[tex]1(y + 3) + 5y = 45\\\\\implies 6y = 45-3\\\\\implies y \frac{42}{6} \\\\\implies y = 7[/tex]

Substitute the value y in (2) we get,

[tex]x= 7 + 3\\\\\implies x =10[/tex]

Therefore , cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.

4.  'x' represents the pounds of raisins

  '10- x ' represents the pounds of nuts

Cost of trail mix from raisins and nuts per pound = $6.96

Therefore,

Cost of 10 pounds of  trail mix of raisins and nuts = $(6.96 ×10)

                                                                                  = $69.6

Cost per pound of raisins = $3.45

Cost per pound of nuts = $7.95

Equation formed as per given condition we get,

[tex]3.45x + 7.95(10-x) = 69.6\\\\\implies 3.45x + 79.5 -7.95x = 69.6\\\\\implies -4.5x = 69.6 - 79.5\\\\\implies-4.5x= -9.9\\\\\implies x =\frac{9.9}{4.5}\\ \\\implies x = 2.2 pounds[/tex]

Pounds of raisins  = 2.2pounds

Pounds of nuts = 10 - 2.2

                         = 7.8 pounds

Therefore,  pounds of raisins is equals to 2.2 and pounds of nuts is equals to 7.8 for the trail mix.

Hence, As per the given conditions we have

1. Number which is 408% of 568 is equals to 2317.44 ( nearest hundredth).

2. Total decrease in percentage of the population of Detroit is equals to 25%.

3.Cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.

4. Raisins is equals to 2.2 pounds and nuts is equals to 7.8 pounds for the trail mix.

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The functions ordered from the least steep slope to the steepest slope are: logarithmic (log(x)), linear (x), quadratic (x²), exponential (eˣ), and cubic (x³).

To compare the steepness of the slopes for different types of functions, we consider the growth or decay rates of each function. The order is determined by the behavior of the functions as x increases.

1. Logarithmic function (log(x)): It grows slowly and approaches infinity as x increases, making it the least steep slope.

2. Linear function (x): It has a constant slope, making it steeper than logarithmic but less steep than quadratic, exponential, and cubic functions.

3. Quadratic function (x²): It increases faster than linear but slower than exponential and cubic functions.

4. Exponential function (eˣ): It grows at an increasing rate, making it steeper than quadratic but less steep than cubic.

5. Cubic function (x³): It has the steepest slope as x increases, making it the most rapidly increasing function.

This order is based on the general behavior of each function type and their rates of growth or decay. Understanding the characteristics of these functions helps in comparing and ordering them in terms of steepness.

Answer: here’s the correct answer

Answer:

In x: 4-1=3

In y: -2

Cartesian coordinates: (3,-2)

Step-by-step explanation:

If we move horizontally we must consider only the x axis, if we move to east it is positive, and if we move to west it is negative.

f we move vertically we must consider only the y axis, if we move to north it is positive, and if we move to south it is negative.

Answer:

The answer is: small+large.

Step-by-step explanation:

If the variable of the smaller sheetrock is stored in small:

var small.

And the variable of the larger sheetrock is stored in large:

var large.

The length of the wall will be the sum of the two pieces of sheetrock:

For example:

var small = 5;

var large = 10;

small+large = 5 + 10 = 15 is the length of the wall.

Final answer:

To calculate the total length of a wall made with two sheets of sheetrock, use the expression 'small + large'. The correct unit for measuring large objects like walls is often feet, and including units is essential for clarity in measurements.

Explanation:

The question asks for an expression to calculate the total length of a wall built with two pieces of sheetrock with lengths stored in the variables small and large. Since the total length of the wall will be the sum of the lengths of the two pieces of sheetrock, the expression you would write is small + large. This will give you the length of the entire wall when you substitute in the numerical values for the lengths represented by the two variables.

When measuring large objects like walls, the appropriate unit of measure is often feet, as inches would be too small and miles or kilometers would be excessively large. It's important to always include units in your measurements to avoid confusion and to ensure that the measurements are useful for practical applications, such as buying fabric or building materials.

Answer:

x/5

Step-by-step explanation:

To get the inverse function you need to leave the x alone and then switch variables ( f(x) = y)

f(x) = 5x

y = 5x

y/5 = x

Now that x is alone you switch the x for y and the y for x and you get:

x/5 = y

And this new y is the inverse function of f(x) ( f^-1(x))

f^-1(x) = x/5

Answer:

The answer is below

Step-by-step explanation:

Data

Winter =    234

Spring =    673

Summer = 843

Fall =         425

Total =     2175

Then

Winter                2175 -------------------------  100%

                             234 -----------------------    x

                   x = 234(100)/2175 = 10.8 %

Spring               2175 ------------------------   100%

                           673 -----------------------    x

                   x = 673(100)/2175 = 30.9 %

Summer            2175 ------------------------   100%

                          843  ------------------------     x

                    x = 843(100) /2175 = 38.8 %

Fall                   2175 ------------------------   100%

                           425 ----------------------      x

                    x = 425(100)/2175 = 19.5%

Total = 10.8 + 30.9 + 38.8 + 19.5 = 100%

Answer:

  the independent quantity is "t" (time in seconds)

Step-by-step explanation:

The problem statement tells you the function rule gives you H (the dependent quantity) as a function of t seconds. "t seconds" is the independent quantity.

Answer:

Option A is correct.

Step-by-step explanation:

From the dimensions first find the volume of the container and then find the estimate ratio of each cookie on diving the volume by number of cookies.

[tex]i.e. \\ 11 \times 6 \times 3 = 198 \\ = > \: \frac{198}{90} = 2.2 \\ \\ also \: from \: the \: second \: relation \\ 6 \times 6 \times 2 = 72 \\ = > \frac{72}{33} = 2.18 \: ( = approx \: 2.2)[/tex]

Answer:

i * i = -1

Step-by-step explanation:

W hen you multiply an imaginary number or i number by another imaginary pure number, the answer is going to be a negative number, due that i *i= -1. The joke is funny because if you do what the recording is saying there you won't have a pure imaginary number and if you dial again, the same would happen again and again.

Answer:

When we work with imaginary numbers, we have that

i = √(-1)

then, we have that i*i = √(-1)*√(-1) = -1

An imaginary number is a number of form A + B*i, where A and B are real numbers.

Now, a purely imaginary number is a number of the form B*i, where B is a real number.

Then, if we multiply this number by i, we have that:

B*i*i = B*(-1) = -B

now we have a real number.

The joke is that now you can "reach" a real number.

Answer:

HI! I'M TAKING THE TEST FOR IT! SO I HOPE THIS IS RIGHT! IF NOT, FORGIVE ME! SO THE ANSWER IS 25.094

Step-by-step explanation:

I attached the step by step, so look at it for me!

Answer:

The answer to your question is: 7 1/3 inches

Step-by-step explanation:

Data

1 inch --------- 15 miles

Distance from Richmond to Washington = 110 miles

Use a rule of three to solve it

        1 inch ----------------- 15 miles

        x    --------------------  110 miles

x = 110x 1 /15

x = 110 / 15   simplify            dividing by 5

x = 22/3

Convert it to a mix number

22/3 = 7 1/3 inches

Final answer:

On the map, 7.6 inches are between the two cities

Explanation:

To find out how many inches are between two cities on a map given the scale and the actual distance. The scale here is that 1 inch represents 15 miles. Therefore, for an actual distance of 110 miles, we simply divide the actual distance by the scale factor to obtain the distance on the map.

By setting up the proportion:
1 inch / 15 miles = x inches / 110 miles, we cross-multiply and solve for x,
which is the number of inches on the map. The calculation would be:
(1 inch / 15 miles) * 110 miles = 110 inches / 15 = 7 3/5 inches or 7.6 inches.

Answer:

y = [tex]\frac{3}{4}[/tex] x + 2

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 )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ( = (0, 2) and (x₂, y₂ ) = (4, 5) ← 2 points on the line

m = [tex]\frac{5-2}{4-0}[/tex] = [tex]\frac{3}{4}[/tex]

Note the line crosses the y- axis at (0, 2) ⇒ c = 2

y = [tex]\frac{3}{4}[/tex] x + 2 ← equation of line

Answer:

Maybe she borrowed a cookie from somone? or maybe bought a cookie?

Answer: d. 75% of the screen is occupied by the image  

Step-by-step explanation:

First we have to find a relation between image area and screen area.

Image area is the product of image dimensions.

Screen area is the product of screen dimensions.

We have to divide the major image dimension between the major screen dimension

Major image dim/Major screen dim = 20/5 = 4

Now we have to multiply this relation by the minor screen dimension

Minor screen dim x 4 = 4 x 4 = 16

Then we have found 5/4 = 20/16

Now we can calculate what percent of the screen area is occupied by the image area.

Major image dim x minor image dim/Major screen dim x minor screen dim

Since major image dim = major screen dim, we have:

Minor image dim/Minor screen dim = 12/16 = 0.75 = 75% of the screen

Answer: d. 75% of the screen is occupied by the image

[tex]\textit{\textbf{Spymore}}[/tex]  

Answer:

The coordinates of point H' are (-2 , 0) ⇒ answer B

Step-by-step explanation:

* Lets revise the vertical stretch

- A vertical stretching is the stretching of the graph away from the  

 x-axis  

- If k > 1, then the graph of y = k • f(x) is the graph of f(x) vertically

 stretched by multiplying each of its y-coordinates by k

* Lets solve the problem

- Square EFGH stretches vertically by a factor of 2.5 to create

 rectangle E′F′G′H′

∴ k = 2.5

- The square stretches with respect to the x-axis

∴ The square stretches vertically

∴ The y-coordinates of each vertex of the square EFGH are

  multiplied by 2.5 to get the vertices of the rectangle E'F'G'H'

∵ Point H located at (-2 , 0)

∵ The image of point (x , y) after stretched vertically by k is (x , ky)

∴ Point H' located at (-2 , 0 × 2.5) ⇒ (-2 , 0)

∴ The coordinates of point H' are (-2 , 0)

∴ Point H' located at (-2 , 0)

Answer:

B.   (-2, 0)

Step-by-step explanation:

Final answer:

With an expected value of −34% for the state lottery and monthly spending of $40 on tickets, a person can expect to lose $13.60 monthly or $163.20 annually.

Explanation:

If the expected value of playing the state lottery is −34%, and a person spends $40 per month on lottery tickets, we can calculate the expected annual loss as follows:

Firstly, an expected value of −34% means that on average, for every dollar spent, you would expect to lose 34 cents. So for $40 spent in one month, the expected loss would be 34% of $40, which equals $13.60.

Next, we can find the expected loss for a year by multiplying the monthly loss by the number of months in a year:

Therefore, on average, you can expect to lose $163.20 per year if you continue spending $40 on lottery tickets every month.

Answer:

h = [tex]\frac{2A}{b}[/tex]

Step-by-step explanation:

Given

A = [tex]\frac{1}{2}[/tex] bh

Multiply both sides by 2 to clear the fraction

2A = bh ( isolate h by dividing both sides by b )

h = [tex]\frac{2A}{b}[/tex]

Answer: h = 2a/b

Step-by-step explanation:

No, Jessica he will not have enough to buy the jacket. She would have saved $32, not $35.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Lets x represent the number of weeks it will take to save enough money. If she saves $11 each week, then in x weeks she will save 11x dollars.

Also, Add this to the 107 she has already saved, and at the end of 11 weeks she will have 11x + 107 dollars.

We want the amount saved to be equal to the price of the bike, so our equation;

11x + 107 = 173

Now we solve the equation.

Subtract 107 from both sides ;

11x = 66

Divide both sides by 11;

x = 6

No, Jessica he will not have enough to buy the jacket. She would have saved $32, not $35.

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