Danielle walked from her house to several locations in her town. The graph represents her distance from home after x hours.


a.How far from home was Danielle after 1/2 hour?

b.What was Danielle's speed between 0 and 1 hour?

c.What was Danielle's speed between 1 and 2 hours?

d.What is the domain when the function is increasing?

e.What is the domain when the function is decreasing?

f.What is the domain when the function is constant?

Graph down below

PLEASE HELP ASAP!!!

The expression is equivalent to −78x − 198.

To simplify the expression −13(6x + 15) − 3, you can start by distributing the −13 across the terms inside the parentheses:

−13 * 6x = −78x

−13 * 15 = −195

So, the expression becomes:

−78x − 195 − 3

Next, combine the constant terms:

−195 − 3 = −198

The simplified expression is now:

−78x − 198

This expression is equivalent to the original expression −13(6x + 15) − 3. It cannot be further simplified as the terms are not like terms and cannot be combined further. So, the answer is −78x − 198.

The expression represents a linear equation where x is the variable. It can be used to find the value of the expression for specific values of x.

To know more about expression:

https://brainly.com/question/34132400

#SPJ6

Answer:

3/8

Step-by-step explanation:

You'd first want to count all the triangles (possibilities) which is 8 total numbers

Then find the even numbers. There is 2, 2, and 4 which is a total of 3 even numbers

The fraction would be 3/8 and it can't be simplified any further

Answer:

3/8

Step-by-step explanation:

This is because, out of 8 results, only 3 of them are even numbers. That is the biggest chance you have at getting an even number.

Answer:

Differentiation of both the term is [tex]2x+3[/tex]

Step-by-step explanation:

As we have to use first principle of derivatives lets recall the formula.

[tex]f(x)= \lim_{h\to 0}\frac{(x+h)-f(x)}{h}[/tex]

Solving our eqaution.

[tex]y=x^2+3x[/tex]

We will work with [tex]f(x+h)[/tex] then [tex]-f(x)[/tex] separately then put in the above formula.

1.

[tex]f(x+h)=(x+h)^2+3(x+h)[/tex]

[tex](x^2+h^2+2hx+3x+3h)[/tex]

Now [tex]-f(x)[/tex]

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

Plugging the values of both.

[tex]f(x)= \lim_{h\to 0}\frac{(x+h)-f(x)}{h}[/tex]

[tex]f(x)= \lim_{h\to 0}\frac{(x^2+h^2+2hx+3h+3x)- x^2-3x}{h}=\frac{h^2+2hx+3h}{h}[/tex]

Taking [tex]h[/tex] as common.

[tex]f(x)= \lim_{h\to 0}\frac{h^2+2hx+3h}{h}=h+2x+3[/tex]

Putting [tex]h=0[/tex]

Then

[tex]f(x)=2x+3[/tex] is the final derivative.

This will be same for [tex]y= x^2 + 3x + 8[/tex] as we have to put [tex]8[/tex] only.

2.

[tex]f(x+h)=(x+h)^2+3(x+h)+8[/tex]

[tex](x^2+h^2+2hx+3x+3h)[/tex]

Then [tex]-f(x)=-x^2-3x-8[/tex]

Plugging the values of both.

[tex]f(x)= \lim_{h\to 0}\frac{(x+h)-f(x)}{h}[/tex]

[tex]f(x)= \lim_{h\to 0}\frac{(x^2+h^2+2hx+3h+3x+8)- x^2-3x-8}{h}=\frac{h^2+2hx+3h}{h}[/tex]

Taking [tex]h[/tex] as common.

[tex]f(x)= \lim_{h\to 0}\frac{h^2+2hx+3h}{h}=h+2x+3[/tex]

Putting [tex]h=0[/tex]

Then

[tex]f(x)=2x+3[/tex] is the final derivative.

So both the derivatives are same.

The transformation on the figure is a reflection over the y-axis.

In the image, we can see that we have an original figure in the left side of the y-axis, and then it is reflected over it.

We can see that it is a reflection and not a translation, because the orientation of the figure changes (you can see that in both figures, the 90° is in the side farthest away from the axis).

So the correct option is B, reflection over the y-axis.

If you want to learn more about reflections, you can read:

https://brainly.com/question/4289712

Answer:  2b/3 (second answer choice)

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

Explanation:

The work shown on the screenshot basically shows plugging x = 2(a+c)/3 into the y(x) function and then simplifying. Step 5 isnt fully simplified, so let's combine like terms, factor, and then divide out a pair of (a-2c) terms to get the following:

y = (2ab+2bc-6bc)/(3(a-2c))

y = (2ab-4bc)/(3(a-2c))

y = (2b*a-2b*2c)/(3(a-2c))

y = 2b(a-2c)/(3(a-2c))

y = 2b/3

Answer:Bob Owes $186 to the store he purchased an item at

Step-by-step explanation:

1. It's True. Since it's 485 gallons every 6.5 minutes, then to find 1 minute you would do 485/6.5 which is approximately 74 gallons.

2. It's False. 85% of 33500 is 28475 gallons. If you divide that by 74, since that's the number of gallons per minute, you get approximately around 384 minutes. Since you want the time in hours, you divide 384 by 60, and you get the decimal 6.4. Since 6 hours is greater than 4 hours, it's false.

3. It's False. 64% of 33500 is 21440 gallons. 48% of 33500 is 16080 gallons. 21440-16080 is 5360 gallons, not 3360 gallons.

4. It's False. To find the percent of change, you first need to subtract 19800 from 33500, which gives you a result of 13700. Then you divide 13700/33500, which gives you a quotient of approximately 0.41. You multiply that by 100 to find the percent, which is 41%. 41% is not equal to 12%.

5. It's False. Since the unit rate is 74 gallons per minute, you divide 33500 by 74 to see how many minutes it takes. That gives you a quotient of approximately 453 minutes. You divide that by 60 since you want the time in hours, and the quotient of that is 7.55. 7 hours is greater than 5, so it's false.

I'm not too sure about some of them, so you might want to check my math. :)

Answer: All four runners ran .96 seconds

Step-by-step explanation: The total time of the four runners, divided by the amount of runners.

3.86/4= .965

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=2(4^x)[/tex]

This is a exponential function of the form

[tex]f(x)=a(b^x)[/tex]

where

a is the initial value

b is the base

r is the rate

b=(1+r)

In this problem we have

[tex]a=2\\b=4\\r=b-1=4-1=3=300\%[/tex]

For x=0

[tex]f(0)=2(4^0)[/tex] -----> [tex]f(0)=2[/tex] ---> y-intercept or initial value

For x=1

[tex]f(1)=2(4^1)[/tex] -----> [tex]f(1)=8[/tex]

Identify the graph

using a graphing tool

The graph in the attached figure

The height of the observer can be taken negligible in case of big measurements. The height of the kite from the ground is 40 meters approximately.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Referring to the figure attached below, we have the vertical distance of the kite from the ground as the length of the side BC.

(assume that the height of the observer flying kite is negligible and that kite's string is straight, and some more basic assumptions)

Using the Pythagoras theorem as the triangle ABC is a right angled triangle as vertical distance means line perpendicular to the ground, we get the length of the line segment BC as:

[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\|BC|^2 = |AC|^2 - |AB|^2\\\\|BC| = \sqrt{|AC|^2 - |AB|^2}\\[/tex]

(positive root since length is a non-negative quantity).

We have |AC| = length of the kite's string = 50 meters

|AB|  = distance of the observer from the point directly above which the kite is flying = 30 meters

Thus, we get the height of the kite from the ground as:

[tex]|BC| = \sqrt{|AC|^2 - |AB|^2}\\|BC| = \sqrt{50^2 - 30^2} = \sqrt{1600} = 40\: \rm \text{(in meters)}[/tex]

Thus,  the height of the kite from the ground is 40 meters approximately.

Learn more about Pythagoras theorem here:

https://brainly.com/question/12105522

Answer:

6r+24

Step-by-step explanation:

2(r+3)=2r+6

2(2r+9)=4r+18

(2r+6)+(4r+18)=6r+24

Answer:

0.0042%

Step-by-step explanation:

We know that 1 pound is equivalent to 16 ounces.

So, 3 pounds of a product is equivalent to (16 × 3) = 48 ounces of the product.

Now, it is given that I add 0.002 ounces of coloring to 3 lbs of product.

So, the required percentage of coloring I used to product is [tex]\frac{0.002 \times 100}{48 + 0.002} = 0.0042[/tex]% (Answer)

4 divided by 3/5

pretend that 4 has a denominator which is 1

4/1 divided by 3/5

when dividing always flip over the second fraction

4/1*5/3

multiply the numerators together

4*5=20

multiply the denominators together

1*3=3

answer:

20/3 or 6 2/3

Answer:

Step-by-step explanation:

Hello

Area triangle DCE :

10 x (8/2) / 2 = 10 x 4 / 2 = 20 cm^2

Area triangle ABE = Area triangle DCE

Area ABCD :

10 x 8 = 80 cm^2

Area triangle AED :

Area ABCD - 2 area DCE

= 80 - 2 x 20

= 80 - 40

= 40 cm^2

Answer:

the value of x is 7cm.

Step-by-step explanation:

i looked it up on the Internet next u could try n do tht

Answer:

x=65 degrees

Step-by-step explanation:

in a triangle all angles will have to add up to 180 adding the two given you can find the third one.

Answer:

The greatest number is A. 1.3 * 10⁵

Step-by-step explanation:

Let's find the greatest number:

Option A : 1.3 * 10⁵ = 1.3 * 100,000 = 130,000

Option B : 9.8 * 10² = 9.8 * 100 = 980

Option C : 9.6 * 10⁴ = 9.6 * 10,000 = 96,000

Option D : 4.6 * 10⁻⁵ = 4.6 * 0.00001 = 0.000046

130,000 > 96,000 > 980 > 0.000046

The greatest number is A. 1.3 * 10⁵

Answer:

-1/2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(3-9)/(7-(-5))

m=-6/(7+5)

m=-6/12

m=-1/2

Answer:

im pretty sure its c

Step-by-step explanation:

The number is 1

Step-by-step explanation:

Let x be the required number

Then according to given statement

Five times the difference of twice a number and seven is negative twenty-five.

[tex]5(2x-7) = -25[/tex]

Simplifying

[tex]10x-35 = -25\\[/tex]

Adding 35 on both sides

[tex]10x-35+35 = -25+35\\10x = 10[/tex]

Dividing both sides by 10

[tex]\frac{10x}{10} = \frac{10}{10}\\x = 1[/tex]

Verification:

[tex]5[2(1)-7] = -25\\5(2-7) = -25\\5(-5) = -25\\-25=-25[/tex]

Hence,

1 is the number

Keywords: Linear equation

Learn more about linear equation at:

#LearnwithBrainly

Answer:

Option 2. [tex]x > 11[/tex]

Step-by-step explanation:

we have

[tex]72 < 7x-5[/tex]

Solve the inequality for x

Adds 5 both sides

[tex]72+5 < 7x-5+5[/tex]

[tex]77 < 7x[/tex]

Divide by 7 both sides

[tex]77/7 < 7x/7[/tex]

[tex]11 < x[/tex]

Rewrite

[tex]x > 11[/tex]

Answer:24.5

Step-by-step explanation:

Formula:

H=KV²

8=K×20²(400)

=8/400

=0.02

H=0.02×35²

=24.5

Answer:

The maximum height reached by the golf ball when v = 35 is 24.5 meters.

Step-by-step explanation:

Given : A golf ball, thrown upwards, rises at a speed of v metres per second. The ball reaches a maximum height of h metres.  h is proportional to the square of v.  When v = 20, h = 8.

To find : Work out the maximum height reached by the golf ball when v = 35 ?

Solution :

h is proportional to the square of v i.e. [tex]h\propto v^2[/tex]

[tex]h=kv^2[/tex]

Where, k is the constant of proportionality

When v = 20, h = 8,

[tex]8=k(20)^2[/tex]

[tex]8=400k[/tex]

[tex]k=\frac{8}{400}[/tex]

[tex]k=0.02[/tex]

The equation became [tex]h=0.02v^2[/tex].

Now, when v = 35 the value of h is

[tex]h=0.02(35)^2[/tex]

[tex]h=0.02\times 1225[/tex]

[tex]h=24.5[/tex]

Therefore, the maximum height reached by the golf ball when v = 35 is 24.5 meters.

Answer:

linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants)

Step-by-step explanation:

Answer:

[tex]x < 18[/tex]

Step-by-step explanation:

We are given the following information in the question:

"Citizens less than 18 years old are not allowed to vote"

We define a variable x such that x represents the age of citizens.

We have to write a relationship with the help of an inequality for the ages of citizens who are not allowed to vote.

Citizens less than 18 are not allowed to vote.

So x should be less than 18.

This can be written as:

[tex]x < 18[/tex]

is the required  inequality for the ages of citizens who are not allowed to vote.

Answer:

[tex]S'(4,6)[/tex]

Step-by-step explanation:

Dilation rules :

For a pre-image point [tex](x,y)[/tex] which is dilated by a scalar factor of [tex]k[/tex] about the origin, the corresponding point of the image can be given by [tex](kx,ky)[/tex]

Pre-image point [tex](x,y)\rightarrow (kx,ky)[/tex] Image point

Given points of quadrilateral PQRS.

P(2,10)

Q(6,8)

R(6,3)

S(2,3)

The quadrilateral is dilated about the origin by a scalar factor of 2.

The co-ordinates of point S' after dilation can be given by:

[tex]S(2,3)\rightarrow S'((2\times2),(2\times3))[/tex]

Thus [tex]S'(4,6)[/tex] (Answer)

Answer:

As jitumahi456 states B).(4, 6) is the correct answer.

Step-by-step explanation:

I took the test on edg.

Answer:

7k

Step-by-step explanation:

Note that - (- 8k) = + 8k

Given

- k - (- 8k)

= - k + 8k

= 7k

Answer:

The positive real number is 26

Step-by-step explanation:

Let

x ----> the number

we know that

The algebraic expression that represent this problem is

[tex]x^{2} =15x+286[/tex]

so

[tex]x^{2}-15x-286=0[/tex]

The formula to solve a quadratic equation of the form

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

is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2}-15x-286=0[/tex]

so

[tex]a=1\\b=-15\\c=-286[/tex]

substitute in the formula

[tex]x=\frac{-(-15)(+/-)\sqrt{-15^{2}-4(1)(-286)}} {2(1)}[/tex]

[tex]x=\frac{15(+/-)\sqrt{1,369}} {2}[/tex]

[tex]x=\frac{15(+/-)37}{2}[/tex]

[tex]x_1=\frac{15(+)37}{2}=26[/tex]

[tex]x_2=\frac{15(-)37}{2}=-11[/tex]  ---> the solution cannot be negative

therefore

The positive real number is 26

Answer:

77.  [tex]\cot^{6} x = \cot^{4} x \csc^{2}x - \cot^{4} x[/tex]Proved

78.  [tex]\sec^{4}x \tan^{2} x = \sec^{2}x [\tan^{2}x + \tan^{4}x ][/tex] Proved

79. [tex]\cos^{3} x\sin^{2} x = [\sin^{2}x - \sin^{4}x] \cos x[/tex] Proved.

80. [tex]\sin^{4}x - \cos^{4}x = 1 - 2\cos^{2}x + 2 \cos^{4} x[/tex] Proved.

Step-by-step explanation:

77. Left hand side

= [tex]\cot^{6} x[/tex]

= [tex]\cot^{4} x \times \cot^{2} x[/tex]

= [tex]\cot^{4}x [\csc^{2}x - 1][/tex]  

{Since we know, [tex]\csc^{2} x - \cot^{2}x = 1[/tex]}

= [tex]\cot^{4} x \csc^{2}x - \cot^{4} x[/tex]  

= Right hand side (Proved)

78. Left hand side

= [tex]\sec^{4}x \tan^{2} x[/tex]

= [tex]\sec^{2} x [1 + \tan^{2}x] \tan^{2} x[/tex]  

{Since [tex]\sec^{2}x - \tan^{2}x = 1[/tex]}

= [tex]\sec^{2}x [\tan^{2}x + \tan^{4}x ][/tex]

= Right hand side (Proved)

79. Left hand side  

= [tex]\cos^{3} x\sin^{2} x[/tex]

= [tex]\cos x[1 - \sin^{2} x] \sin^{2} x[/tex]

{Since [tex]\sin^{2}x + \cos^{2} x = 1[/tex]}

= [tex][\sin^{2}x - \sin^{4}x] \cos x[/tex]

= Right hand side

80. Left hand side  

= [tex]\sin^{4}x - \cos^{4}x[/tex]

= [tex][\sin^{2}x + \cos^{2}x]^{2} - 2\sin^{2} x \cos^{2}x[/tex]

{Since [tex]\sin^{2}x + \cos^{2} x = 1[/tex]}

= [tex]1 - 2\cos^{2} x[1 - \cos^{2}x ][/tex]

= [tex]1 - 2\cos^{2}x + 2 \cos^{4} x[/tex]

= Right hand side. (Proved)

Answer:

the answer is 194

Step-by-step explanation:

Answer:4/5

Step-by-step explanation:

2/15 + 10/15=12/15=4/5

easy right?