Four friends went on vacation with their family over the summer. Harlin’s family drove 363 miles in 6 hours, Kevin went 435 miles in 7 hours, Shanna drove 500 miles in 8 hours, Hector drove 215 miles in 5 hours. Which family drove the fastest?

Answer:

I have provided two solutions both concluding the same thing.

There is no solution.

Simplest solution says this is a parabola opened up at vertex (-2,5) which means it never crosses the x-axis.  There is no solution because thee curve does not touch the x-axis.

Step-by-step explanation:

Harder solution (algebraic solution):

The vertex form a parabola is [tex]y=a(x-h)^2+k[/tex]

We are given the vertex (h,k) is (-2,5)

So we have [tex]y=a(x+2)^2+5[/tex]

Now we also know [tex]a>0[/tex] since the parabola opens up.

That is all we know about a.

Let's see what [tex]y=a(x+2)^2+5[/tex] is in standard form

[tex]y=a(x+2)(x+2)+5\\y=a(x^2+4x+4)+5\\y=ax^2+4ax+4a+5\\\\[/tex]

So we are asked to solve for the solution set of

[tex]0=ax^2+4ax+4a+5\\A=a\\B=4a\\C=4a+5\\\\[/tex]

Plug into quadratic formula

I'm going to write the quadratic formula with the capital letters to be less confusing:

[tex]x=\frac{-B \pm \sqrt{B^2-4AC}}{2A}\\x=\frac{-4a \pm \sqrt{16a^2-4(a)(4a+5)}}{2a}\\x=\frac{-4a \pm \sqrt{16a^2-16a^2-20a}}{2a}\\x=\frac{-4a \pm \sqrt{-20a}}{2a}\\x=\frac{-4a \pm \sqrt{4} \sqrt{-5a}}{2a}\\x=\frac{-4a \pm 2 \sqrt{-5a}}{2a}\\x=\frac{-4a}{2a} \pm \frac{\sqrt{-5a}}{a}\\[/tex]

This says [tex]a[/tex] has to be negative... The inside of the square root... So there was no real solution.\\

\\

Simpler solution (graph/visual)

You could have also drawn a parabola open up with vertex at (-2,5) and we should have seen that it was impossible it cross the x-axis.

Answer:

The answer is impossible so is Ф

Answer:

The farmer would need 80 posts.

Step-by-step explanation:

If one side of the garden is 10m long, and the garden is a square, we can assume that all 4 sides will be 10m. That makes it 40m in total. Times 40×2 and you get 80.

=====================================================

Explanation:

The angle EQD is an inscribed angle that cuts off the arc from E to D (the shortest path). Note how central angle ECD also cuts off this same arc. By the inscribed angle theorem, we know that

inscribed angle = (1/2)*(central angle)

angle EQD = (1/2)*(angle ECD)

We can multiply both sides by 2 and flip the equation to get

angle ECD = 2*(angle EQD)

Now replace "angle EQD" with 5x+2

angle ECD = 2*(5x+2)

2*(5x+2) = angle ECD

Next, replace "angle ECD" with 104 as this is the measure of this central angle.

2*(5x+2) = angle ECD

2*(5x+2) = 104

From here, we solve for x

2*(5x+2) = 104

2*5x + 2*2 = 104

10x + 4 = 104

10x+4-4 = 104-4 ..... subtracting 4 from both sides

10x = 100

10x/10 = 100/10 ...... dividing both sides by 10

x = 10

Answer:

Look to the attached file

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

Step 1 : Simplify the equation

3(x-5) + 7x = 65

3x - 15 + 7x = 65

Step 2 : Make x the subject

3x + 7x = 65 + 15

10x = 80

x = 80/10

x = 8

!!

Answer:

The answer is B

Step-by-step explanation:

The reasoning behind this is because in the second step, if you were to add all of the numbers you would get the solution of -5x or something like that.

Hope this helps!

Answer:

Step-by-step explanation:

Put x = -7 to the equation -4x - 9y = -26, and solve it for y:

-4(-7) - 9y = -26

28 - 9y = -26            subtract 28 from both sides

-9y = -54           divide both sides by (-9)

y = 6

Answer: cubic meters : m³

Step-by-step explanation:

Cylinder volume is the product of area of the base by height.

Area of the base is the product of π·radius² = square meters : m²

Volume = square meters·meters =  m²·m = cubic meters : m³

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

The simultaneous Equations for both total costs are;

Company A: y = 45x + 150

Company B: y = 50x + 125

Thus, both companies charge the same amount of money for food truck permits for 5 months

How to find the equation of the total charges?

We are told that;

Company A charges a one time fee of $150 and $45 per month.

Company B charges a one time fee of $125 and $50 per month.

Thus, using the concept of the equatiom of a line In slope intercept form, we have:

Company A: y = 45x + 150

Company B: y = 50x + 125

let's use the number 5 for x as an example

45(5) + 150 = 375

50(5) + 125 = 375

So both companies charge the same amount of money for food truck permits for 5 months.

Complete question is;

Two companies allow you to pay monthly for your food truck permits. Company A charges a one time fee of $150 and $45 per month. Company B charges a one time fee of $125 and $50 per month. Write an equation or a system of equations and explain what each solution tells you about the situation

Answer:

90

Step-by-step explanation:

There are 9 options for the first choice and 10 options for the second. Multiply them together to get the full number of combinations, which is 90.

Answer:

130 degrees

Step-by-step explanation:

let the angle be x

2x+45+55=360(Sum of angles in quad)

2x=260

x=130

The measure of <Q is 130 degree.

There are four angles in a quadrilateral. Its inner angles add up to 360 degrees.

The angle sum property of a Quadrilateral states that the sum of all four inner angles is 360 degrees.

We have

<T = 55

<R= 45

let us consider the two angles are Equal.

Using angle sum Property

<T + <R + Q + <S = 360

45+ 55 + x + x = 360

100 + 2x = 360

2x = 260

x = 130

Thus, the measure of <Q is 130 degree.

Learn more about Angle sum Property here:

https://brainly.com/question/21364160

#SPJ7

Answer:

Option C. Graph C

Step-by-step explanation:

we have

[tex]y=(x-3)^{2}-25[/tex]

This is the equation of a vertical parabola open upward (vertex is a minimum)

The vertex is the point (3,-25)

therefore

The graph is C

The graph in the attached figure

Answer:c

Step-by-step explanation:

Answer: D. Horizontal stretch by a factor of 3.

Step-by-step explanation:

Below are some transformations for a function [tex]f(x)[/tex]:

If [tex]f(x)-k[/tex], then it is shifted "k" units down.

If [tex]f(x-k)[/tex], then it is shifted rigth"k" units.

If [tex]-f(x)[/tex], then it is reflected across the x-axis.

If [tex]cf(x)[/tex] and [tex]c>1[/tex], then it is stretched vertically by a factor of "c".

If [tex]f(cx)[/tex] and [tex]0<c<1[/tex], then it is stretched horizontally by a factor of [tex]\frac{1}{c}[/tex].

Based on this, the transformations done to the function [tex]f(x)=x[/tex]  to get the function [tex]g(x)=-3(x-4)-7[/tex] are:

- It is shifted 7 units down.

- It is shifted rigth 4 units.

- It is reflected over the x-axis.

- It is vertically stretched by a factor of 3.

Therefore, the transformations that was not done to the function [tex]f(x)=x[/tex]  to get the function [tex]g(x)=-3(x-4)-7[/tex] is:

Horizontal stretch by a factor of 3.

Answer:

Let j = amount Jasmine spent, k = amount Karen spent, and m = amount Maggie spent.

m = 3k, k = (1/2)j

j + k + m = $60

2k + k + 3k = $60

6k = $60

k = $10, m = $30, j = $20

Jasmine spent $20, Karen spent $10, and Maggie spent $30.

1box = 1400/7 = 200

200×3=600

1400+600=2000

Answer:

2000

Step-by-step explanation:

Given :Workers have packed 1,400 glasses in 7 boxes.

To Find :If they pack 3 more boxes, how many glasses will they have packed in all?

Solution:

Workers packed no. of glasses in 7 boxes = 1400

Workers packed no. of glasses in 1 box = [tex]\frac{1400}{7}[/tex]

Workers packed no. of glasses in 3 boxes = [tex]\frac{1400}{7} \times 3[/tex]

                                                                      = [tex]600[/tex]

So, initially they packed 1400 glasses

If they pack 3 more boxes so, the pack 600 glasses more

So, The total no. of glasses have packed by workers = 1400+600 = 2000

Hence they have packed 2000 glasses in all.

Answer:

[tex]\large\boxed{\dfrac{1}{2}}[/tex]

Step-by-step explanation:

[tex]\text{The average rate of change of function}\ f(x)\\\text{over the interval}\ a\leq x\leq b\ \text{is given by this expression:}\\\dfrac{f(b)-f(a)}{b-a}.\\\\\text{Read from graph the values of function for}\ x=3\ \text{and}\ x=5.\\(look\ at\ the\ picture)\\\\f(3)=1,\ f(5)=2\\\\\text{Substitute:}\\\\\dfrac{f(5)-f(3)}{5-3}=\dfrac{2-1}{2}=\dfrac{1}{2}[/tex]

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

here m = [tex]\frac{1}{2}[/tex] and (a, b) = (- 7, 2), hence

y - 2 = [tex]\frac{1}{2}[/tex] (x - (- 7)) → D

y - 2 = [tex]\frac{1}{2}[/tex](x + 7)

The point-slope form of the equation will be [tex]y-2 = \dfrac{1}{2}(x-(-7))[/tex]. The correct option is D.

In mathematics, slope refers to the measure of the steepness or inclination of a line or a curve. It quantifies the rate at which one variable changes with respect to another variable. The slope is commonly denoted by the letter "m."

Given that the slope of the line is 1/2. The point through which the line is passing is (-7,2).

The general form of the equation of the line passing through the point (-7,2) and the slope is 1/2 can be written as,

[tex]y-y_1 = m(x-x_1)[/tex]

The equation of the line in point-slope form can be written as,

[tex]y - y_1 = m(x-x_1)\\y-2=\dfrac{1}{2}(x-(-7))[/tex]

To know more about slope follow

https://brainly.com/question/29421841

#SPJ2

Answer:

Is an acute triangle

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

G(7,3), H(9, 0), I(5, -1)

step 1

Find the distance GH

substitute in the formula

[tex]d=\sqrt{(0-3)^{2}+(9-7)^{2}}[/tex]

[tex]d=\sqrt{(-3)^{2}+(2)^{2}}[/tex]

[tex]GH=\sqrt{13}\ units[/tex]

step 2

Find the distance IH

substitute in the formula

[tex]d=\sqrt{(0+1)^{2}+(9-5)^{2}}[/tex]

[tex]d=\sqrt{(1)^{2}+(4)^{2}}[/tex]

[tex]IH=\sqrt{17}\ units[/tex]

step 3

Find the distance GI

substitute in the formula

[tex]d=\sqrt{(-1-3)^{2}+(5-7)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(-2)^{2}}[/tex]

[tex]GI=\sqrt{20}\ units[/tex]

step 4

Verify what type of triangle is the polygon

we know that

If applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+b^{2}[/tex] ----> is a right triangle

[tex]c^{2}> a^{2}+b^{2}[/tex] ----> is an obtuse triangle

[tex]c^{2}< a^{2}+b^{2}[/tex] ----> is an acute triangle

where

c is the greater side

we have

[tex]c=\sqrt{20}\ units[/tex]

[tex]a=\sqrt{17}\ units[/tex]

[tex]b=\sqrt{13}\ units[/tex]

substitute

[tex]c^{2}= (\sqrt{20})^{2}=20[/tex]

[tex]a^{2}+b^{2}=(\sqrt{17})^{2}+(\sqrt{13})^{2}=30[/tex]

therefore

[tex]c^{2}< a^{2}+b^{2}[/tex]

Is an acute triangle

Answer:

ACUTE !!!!!!!!

Step-by-step explanation:

Answer:

[tex]-(4x^2)+6(x^4)y[/tex]

Step-by-step explanation:

Here apply the law of indices where ;

[tex]A^x*A^y=A^{x+y}[/tex]

Given;

[tex]\frac{48x^4y-72x^6y^2}{-12x^2y} \\\\\\\frac{-12x^2y(4x^2-6x^4y^2)}{-12x^2y} \\\\\\=-4x^2+6x^4y\\\\\\=-(4x^2)+6(x^4)y[/tex]

[tex]x^2<49\\x<7 \wedge x>-7\\x\in(-7,7)[/tex]

i think its a

hope that helps

Answer:

A.

Step-by-step explanation:

Vertex form for a absolute value function is f(x)=a|x-h|+k

The vertex is (h,k)

If a is positive it is open up

If a is negative it is open down

So looking at the a part we can rule out 2 choices B and D

Finding the vertex is enough because A and C different in that slightly

The vertex is (-2,3)

So the absolute value function should look like this f(x)=a|x+2|+3

So the answer is A.

Answer:

d

Step-by-step explanation:

i jut did it in google calculator (trust me)

Hello There!

First, our formula for finding the volume of a cylinder is Pi*radius^2*height

Now, let'd get into solving for the volume. First, we need to find the radius so in this problem, we are given the diameter so to find the radius, we just divid the diameter by 2. Once we divide, our radius comes out to 6.5.

Next, in our formula it says we have to square our radius so we would multiply 6.5 by 6.5 to get a product of 42.25.

Lastly, we need to multiply 42.25 by our height which is our last step in our formula. Once we multiply 42.25 by the height of the cylinder which is 11, we get a product of 464.75.

464.75 rounded to the nearest tenth is 464.8

Your answer is the first one

Answer:

7p^15 / q^12

Step-by-step explanation:

7p^9+6 q^-5-7 / 3         #28 is divided by 12

7p^15 / q^12       #Answer

Answer:

7p^15/3q^12 is equivalent to 28p^9 q^-5/12p^-6 q^7

Step-by-step explanation:

Given Parameter:

28p^9 q^-5/12p^-6 q^7

Required; To simplify.

To simplify the above expression, we'll apply 2nd law of indices.

But first, let's rewrite the expression.

28p^9 q^-5/12p^-6 q^7 becomes

(28 * p^9 * q^-5) / (12 * p^-6 * q^7)

Then we collect similar indices. This is done as follows

(28/12) * (p^9/p^-6) * (q^-5/q^7)

From second law of indices (law of division);

If the two terms have the same base () and are to be divided their indices are subtracted.

For instance x^a/x^b = x^(a - b).

Applying this law; we have

(28/12) * (p^9/p^-6) * (q^-5/q^7) becomes

(28/12) * (p^(9 - (-6))) * (q^(-5-7))

(28/12) * (p^(9+6)) * (q^-12)

(28/12) * p^15 * q^-12

Simplify 28/12

(4*7)/(4*3) *p^15 * q^-12

(7/3) * p^15 * q^-12

(7/3) * p^15 * 1/q^12

7p^15/3q^12

Hence, 7p^15/3q^12 is equivalent to 28p^9 q^-5/12p^-6 q^7

Answer:

D. x + 5

Step-by-step explanation:

2x^4 + 20x^3 + 50x^2

= 2x^2 (x^2 + 10x + 25)

= 2x^2 (x + 5)^2

= 2x^2 (x + 5) (x + 5)

Answer

D. x + 5

For this case we have the following expression:

[tex]2x ^ 4 + 20x ^ 3 + 50x ^ 2[/tex]

It is observed that we can extract common factor [tex]2x ^ 2[/tex], since it is common in the three terms:

[tex]2x ^ 2 (x ^ 2 + 10x + 25) =[/tex]

If we factor the expression into parentheses, we must look for two numbers that add 10 and multiply 25. These are: 5 and 5.

Rewriting the expression we have:

[tex]2x ^ 2 ((x + 5) (x + 5))[/tex]

Thus, one of the factors of the original expression is[tex]x + 5[/tex].

Answer:

Option D

Answer:

Answer:  

$6 *53 = $318  

Step-by-step explanation:

Answer: $318

Step-by-step explanation:

Given : A grocer takes delivery of beverages from your truck at $6 per case.

If you  unloaded 53 cases for the grocer today.

Then the amount of money the grocer owes you will be the product of 53 and 6 .

Thus,  the amount of money the grocer owes you= [tex]53\times6=\$318[/tex]

Hence, the  grocer owes you $318 .

Answer:

y = [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

Given

- 3y = - [tex]\frac{6}{5}[/tex]

Multiply both sides by 5 to eliminate the fraction

- 15y = - 6 ( divide both sides by - 15 )

y = [tex]\frac{-6}{-15}[/tex] = [tex]\frac{6}{15}[/tex] = [tex]\frac{2}{5}[/tex]

Answer:

19

Step-by-step explanation:

g(x)=x^2+3

g(x)=(4^2)+3

g(x)=16+3=19

if g of x = x squared + 3, then 4 squared = 16, plus 3 = 19

Answer:

option(B)  g(4) =19.

Step-by-step explanation:

Given:If g(x) = [tex]x^{2}[/tex] + 3.

To find: g(4).

Solution: We have given that  

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

for x=4.

g(4) = [tex]4^{2}[/tex] + 3.

g(4) = 16+3

g(4) =19.

Therefore, option(B)  g(4) =19.

Answer: The 3rd from the left.

Step-by-step explanation: