To find the slope, Jackie makes right triangle P by using the graph of the line as the hypotenuse of the triangle as shown in the figure. To check her work, she repeats the process and makes a right triangle Q as shown. Which statement explains why the slope of the line should be the same when calculated with either triangle?

A
The two triangles are similar.

B
The two triangles are congruent.

C
One triangle is a translation of the other triangle.

D
The lengths of the hypotenuse of each triangle are equal.

Answer:

50000 times

Step-by-step explanation:

Since these are given in scientific notation, we can convert them to have the same powers of 10. Converting 4*10^12 to something times 10^7, we can get 4*10^5*10^7. So we divide 400000 by 8 to see how many times larger it is than 8. So we get 50000 times as our answer.

Final answer:

To determine how many times larger [tex]4 * 10^{12}[/tex] is than [tex]8 * 10^7[/tex], divide the two numbers to get [tex]0.5 * 10^5[/tex], which simplifies to [tex]5 * 10^4[/tex] or 50,000 times larger.

Explanation:

To find out how many times larger [tex]4 * 10^{12}[/tex] is than [tex]8 * 10^7[/tex], we can divide the first number by the second:

[tex]4 * 10^{12}[/tex] ÷ [tex]8 * 10^7[/tex] = (4/8) x [tex]10^{(12-7)}[/tex]

Now, simplify:

First, simplify the division of the coefficients (4/8) which equals 0.5.

Then, subtract the exponents of 10, which is 12 - 7 = 5.

So, the final answer is:

[tex]0.5 * 10^5 = 5 * 10^4[/tex]

This means that [tex]4 * 10^{12}[/tex] is 50,000 times larger than [tex]8 * 10^7[/tex].

well, the assumption is that is a rectangle, namely it has two equal pairs, so we can just find the length of one of the pairs to get the dimensions.

hmmmm let's say let's get the length of the segment at (-1,-3), (1,3) for its length

and

the length of the segment at (-1, -3), (-4, -2) for its width

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{length}{L}=\sqrt{[1-(-1)]^2+[3-(-3)]^2}\implies L=\sqrt{(1+1)^2+(3+3)^2} \\\\\\ L=\sqrt{4+36}\implies L=\sqrt{40} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{width}{w}=\sqrt{[-4-(-1)]^2+[-2-(-3)]^2}\implies w=\sqrt{(-4+1)^2+(-2+3)^2} \\\\\\ w=\sqrt{9+1}\implies w=\sqrt{10} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the rectangle}}{A=Lw}\implies \sqrt{40}\cdot \sqrt{10}\implies \sqrt{400}\implies \boxed{20}[/tex]

Answer:

1000 years

Step-by-step explanation:

1x10^11 is basically 100 billion

1x10^8 is basically 100 million

so 100 billion divided by 100 milllion is basically 1000

so 1000 years

Answer:

D=.56 g/cm^3

Explanation:

Density= mass/volume

D=4.49/8

D=.56 g/cm^3

Hope you get it!

An 8 cm³ block of confectioners sugar that weigh 4.49 grams would have a density of 0.56 g/cm³. Thus, the density of powdered sugar is 0.56 g/cm³

From the question, we are to determine the density of the powdered sugar

Density can be calculated by using the formula,

[tex]Density = \frac{Mass}{Volume}[/tex]

From the given information,

Volume = 8 cm³

and Mass = 4.49 g

Putting the parameters into the equation,

[tex]Density = \frac{4.49}{8}[/tex]

Density = 0.56125 g/cm³

Density ≅ 0.56 g/cm³

Hence, the density of powdered sugar is 0.56 g/cm³

Learn more on Calculating density here: https://brainly.com/question/11258429

Answer:

v=3i+8j

Step-by-step explanation:

The given the vector v has an initial point (-2,-6) and a terminal point of (1,2).

To find the components of vector v, we subtract the terminal points from the initial point to obtain.

v=<1,2>-<-2,-6>

v=<1--2,2--6>

v=<1+2,2+6>

v=<3,8>

As a linear combination of the standard unit vectors.

v=3i+8j

Answer: 10

a=27-5-12=10

A= (27-5)=22-12=10

A=10

Answer:

one A has a diameter of 10 inches and Cone B has a diameter of 50 inches. If the cones are similar, find the volume ratio of Cone A to Cone B.

Step-by-step explanation:

The surface area of Cone A when  the surface area of Cone B is 725 ft² for the case when Cone A is similar to Cone B with a scale factor of 3:5 is 2013.89 ft²

Similar figure are zoomed in or zoomed out (or just no zoom) version of each other. They are scaled version of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.

So, if a side of a figure is of length L units, and that of its similar figure is of M units, then:

[tex]L = k \times M[/tex]

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by [tex]k^2[/tex]

to get each other corresponding quantity from their similar figures' quantities.

Similarly, increasing product derived quantities will need increased power of 'k' to get the corresponding quantity. Thus, for volume, it is k cubed. or

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

For this case, we're given that:

The scale factor between cone A and cone B is 3:5

That can be taken as: [tex]3/5 = 0.6[/tex] scale factor.

It means,

side length of cone A = [tex]0.6 \times[/tex] corresponding side length of cone B

Also, as given, we have:

Surface area of cone B = 725 ft²

Assume that cone A's surface area is S, then we get:

surface area of cone A = [tex]0.6^2 \times[/tex] surface area of cone B

[tex]725 = 0.6^2 \times S\\S =\dfrac{725}{0.6^2} \approx 2013.89 \: \rm ft^2[/tex]

Thus, the surface area of Cone A when  the surface area of Cone B is 725 ft² for the case when Cone A is similar to Cone B with a scale factor of 3:5 is 2013.89 ft²

Learn more about scale factor here:

https://brainly.com/question/11178083

#SPJ2

Answer:

2(5+7)

Step-by-step explanation:

2 times any equation is 2(equation) and our equation is the sum of 5 and 7 which means 5 plus 7, therefore our equation is 2(5+7)

Answer

(5 + 7) · 2

Step-by-step explanation

If we take a look at PEMDAS or BEDMAS whichever one you were taught, multiplication comes before addition. (And unless you are in 2nd grade, you will know that "times" means multiplication, and sum is the result of an addition problem.)

P = Parentheses {|} B = Brackets/Parentheses

That means that anything in parentheses or brackets comes first, no matter what type of problem it is. So, if we add 5 and 7 and then multiply it by two and just rephrase that, we get 2 times the sum of 5 and 7.

Answer:

C

Step-by-step explanation:

The answer is C.

Hope this helps :)

Answer:

1. y=0.25x+9

2. The graph that starts at 9 and the highest number is 11.

NOT THE ONE WITH THE HIGHEST NUMBER 15

Step-by-step explanation:

I got it right on edmentum

The equation that correctly models this situation y=0.25x+9.

solving this we will get the valve of Y if x is given.

calculation:-

⇒pickup charges of the cap company= $9

⇒charge for per mile = $0.25

⇒let the total distance traveled is X

⇒total amount George pays (y)=  0.25x+9.

Learn more about linear equations here:-https://brainly.com/question/14323743

#SPJ2

Answer:

The maximum possible area of the triangle is 36 units²

Step-by-step explanation:

Let

x, y the legs of the right triangle

Applying the Pythagoras Theorem

[tex]12^{2}=x^{2}+y^{2}\\\\144=x^{2}+y^{2}[/tex]

[tex]y=\sqrt{144-x^{2}}[/tex] ----> equation A

The area of the right triangle is equal to

[tex]A=\frac{1}{2}xy[/tex] ----> equation B

substitute equation A in equation B

[tex]A=\frac{1}{2}x(\sqrt{144-x^{2}})[/tex]

Using a graphing tool

The vertex of the graph is a maximum

That means

The x-coordinate of the vertex is the value of x for the maximum possible area of the triangle

The y-coordinate of the vertex is the maximum possible area of the triangle

The vertex is the point (8.485,36)

see the attached figure

therefore

The maximum possible area of the triangle is 36 units²

Answer:

b 1/8 inch

Step by step

just got right on ed

The height of each individual cracker in the vertical column is 1/8 inches.

The height of each individual cracker can be determined by dividing the volume of the column by 40 and the area of each cracker.

Area of each cracker = 2 x 1 1/2

= 2 x 3/2 = 3 inches

Height of each individual cracker = 15/40 x 3 = 1/8 inches

To learn more about the volume, please check: https://brainly.com/question/26406747

Answer:

8 units

Step-by-step explanation:

mid point of hypotenuse of right angled isosceles triangle is equidistant from three vertices.

length of altitude=16/2=8

The question is incomplete, here is a complete question.

Triangle FGH is an isosceles right triangle with a hypotenuse that measures 16 units. An altitude, GJ, is drawn from the right angle to the hypotenuse.

What is the length of GJ?

A. 2 units

B. 4 units

C. 6 units

D. 8 units

Answer : The correct option is, (D) 8 units

Step-by-step explanation :

Given:

Length FH = 16 unit

As we know that a altitude between the two equal legs of an isosceles triangle creates right angles is a angle and opposite side bisector.

Thus,

Length FJ = Length HJ = [tex]\frac{16}{2}[/tex] = 8 units

As, the triangle is an isosceles. So, length GF = length GH = x unit

First we have to determine the value of 'x'.

Using Pythagoras theorem in ΔFGH :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](FH)^2=(GF)^2+(GH)^2[/tex]

Now put all the values in the above expression, we get :

[tex](16)^2=(x)^2+(x)^2[/tex]

[tex]256=2x^2[/tex]

[tex]x^2=128[/tex]

[tex]x=8\sqrt{2}[/tex]

Thus, length GF = length GH = x unit = [tex]8\sqrt{2}[/tex]

Now we have to determine the length GJ.

Using Pythagoras theorem in ΔGJH :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](GH)^2=(GJ)^2+(HJ)^2[/tex]

Now put all the values in the above expression, we get :

[tex](8\sqrt{2})^2=(GJ)^2+(8)^2[/tex]

[tex]128=(GJ)^2+64[/tex]

[tex](GJ)^2=128-64[/tex]

[tex](GJ)^2=64[/tex]

[tex]GJ=\sqrt{64}[/tex]

[tex]GJ=8[/tex]

Thus, the length of GJ is, 8 units.

Answer:

Acceleration = 2 meters /second^2.

Step-by-step explanation:

Use Newton's Second Law of Motion:

Force = mass * acceleration.

0.5 = 0.25 * a

a = 0.5 / 0.25

a = 2 meters /second^2.

Answer:

A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple steps: Step 1: Work out the missing lengths around the edge of the compound shape.

Step-by-step explanation:

Answer:

16cm

Step-by-step explanation:

To find the diameter we must first find the radius and multiply by 2.

The isosceles triangle that has the length of a leg to be 8cm and a vertex angle of [tex]120\degree[/tex] that has been circumscribed is shown in the attachment.

We draw a line from the vertex of the isosceles triangle that bisects the base through the center O of the circle.

This implies that [tex]m\angle OAC=60\degree[/tex].

Based on this [tex]m\angle ACO=60\degree[/tex] because the two radii are equal.

It follows that:[tex]m\angle AOC=60\degree[/tex] because sum of angles in a triangle must be 180 degrees.

This means that, triangle AOC is an equilateral triangle, hence all sides are equal.

One side of this equilateral triangle happens to be the side of the leg of the isosceles triangle which is 8cm.

It follows that, the radius of the circle is 8cm.

Therefore the diameter of the circle is 16cm

Answer:

[tex]29\sqrt{5}[/tex]

Step-by-step explanation:

We want to simplify:

[tex]11\sqrt{45}-4\sqrt{5}[/tex]

We need to simplify the first radical before we can subtract

[tex]11\sqrt{9\times5}-4\sqrt{5}[/tex]

[tex]11\sqrt{9} \times\sqrt{5}-4\sqrt{5}[/tex]

This implies that:

[tex]11\times 3\times\sqrt{5}-4\sqrt{5}[/tex]

[tex]33\sqrt{5}-4\sqrt{5}[/tex]

We have now obtained like surds.

We simplify to get:

[tex]29\sqrt{5}[/tex]

Answer: The answer to your question is C. (7*5) - (7*3)

Step-by-step explanation: because when you have an expression or equation in parentheses, you apply the distributive property to get rid of the parentheses:

The problem will now look like this:

[tex]7(5-3)= (7*5) - (7*3)[/tex]

And if they asked you for the answer in a whole number, it would be 14 because

7*5=35 and 7*3=21

35-21=14

So, therefore, the expanded form would be (7*5) - (7*3)

[tex]\bf \sqrt{1764}~~ \begin{cases} 1764=&2\cdot 2\cdot 3\cdot 3\cdot 7\cdot 7\\ &2^2\cdot 3^2\cdot 7^2\\ &(2\cdot 3\cdot 7)^2\\ &42^2 \end{cases}\implies \sqrt{42^2}\implies 42[/tex]

Answer:

D (5,7.4)

Step-by-step explanation:

This is because all of the other (x,y) vales are close together in number and this is an outlier because it stands out from the group.

The answer is D. (5, 7.4)

Answer:

[tex]\large\boxed{\text{The slope}\ m=-\dfrac{1}{2}}[/tex]

Step-by-step explanation:

The formula of a slope:

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

We have the points (-3, 5) and (-1, 4). Substitute:

[tex]m=\dfrac{4-5}{-1-(-3)}=\dfrac{-1}{2}=-\dfrac{1}{2}[/tex]

Answer:

[tex]y=\pm i \sqrt{7}[/tex]

Step-by-step explanation:

Given equation is [tex]\frac{y}{\left(y-4\right)}-\frac{4}{\left(y+4\right)}=\frac{3^2}{(y^2-16)}[/tex]

Factor denominators then solve by making denominators equal

[tex]\frac{y}{\left(y-4\right)}-\frac{4}{\left(y+4\right)}=\frac{3^2}{(y^2-16)}[/tex]

[tex]\frac{y}{\left(y-4\right)}-\frac{4}{\left(y+4\right)}=\frac{9}{(y+4)\left(y-4\right)}[/tex]

[tex]\frac{y\left(y+4\right)-4\left(y-4\right)}{\left(y-4\right)\left(y+4\right)}=\frac{9}{(y+4)\left(y-4\right)}[/tex]

[tex]y\left(y+4\right)-4\left(y-4\right)=9[/tex]

[tex]y^2+4y-4y+16=9[/tex]

[tex]y^2=9-16[/tex]

[tex]y^2=-7[/tex]

take squar root of both sides

[tex]y=\pm \sqrt{-7}[/tex]

[tex]y=\pm i \sqrt{7}[/tex]

Hence final answer is [tex]y=\pm i \sqrt{7}[/tex].

Answer:

D. $1257.71

Step-by-step explanation:

Used my calculator. lol

Answer:

$1257.71.

Step-by-step explanation:

8.25% = 0.0825.

So the sales tax on $15,245

= $15,245 * 0.0825

= $1257.71.

Answer:

[tex]\large\boxed{\dfrac{1}{45}}[/tex]

Step-by-step explanation:

1.

2 yellow marables of 10 all marables

[tex]P(A_1)=\dfrac{2}{10}=\dfrac{1}{5}[/tex]

2.

1 yellow marable of 9 all marables

[tex]P(A_2)=\dfrac{1}{9}[/tex]

[tex]P(A)=P(A_1)\cdot P(A_2)\\\\P(A)=\dfrac{1}{5}\cdot\dfrac{1}{9}=\dfrac{1}{45}[/tex]

Answer:−8x8y9z7

Step-by-step explanation:

-5(3)+13

=-15+13

=-2

Answer: g(3)= -2

ANSWER

g(3)=-2

EXPLANATION

The given function is

[tex]g(r) = - 5r + 13[/tex]

We want to find g(3).

We substitute r=3 into the given function to obtain:

[tex]g(3) = - 5 \times 3 + 13[/tex]

Multiply out the first term

[tex]g(3) = - 15 + 13[/tex]

Simplify the result to obtain:

[tex]g(3) = -2[/tex]

Multiply her pay by the FICA tax rate:

325 x 0.0625 = $20.31

Now look in the table for her pay and then find her number of deductions ( 2) and find what the corresponding number is, then add that to her tax.

See picture:

20.31 + 2 = $22.31

Answer:

The length of the arc shown in red is [tex]\frac{22}{9}\pi\ in[/tex]

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=4\ in[/tex]

substitute

[tex]C=2\pi (4)[/tex]

[tex]C=8\pi\ in[/tex]

step 2

Find the length of the arc in red

Remember that the length of the circumference subtends a central angle of 360 degrees

so

by proportion find the length of the arc by a central angle of 110 degrees

[tex]\frac{8\pi}{360}=\frac{x}{110}\\ \\x=8\pi*110/360\\ \\x=\frac{880}{360}\pi\ in[/tex]

Simplify

[tex]\frac{880}{360}\pi=\frac{22}{9}\pi\ in[/tex]

Answer:

y = -2

Step-by-step explanation:

We have a point (-1,y) on the graph of y = 3x + 1

When x = -1 then,

y = 3(-1) + 1

y = -3 + 1 = -2

Answer:

If the question is  "If (-1, y) lies on the graph of y = 3^x+1, then y = 1"

So the answer is 1

Step-by-step explanation:

Answer: [tex](2g+h)[/tex] and [tex](2g-h)[/tex]

Step-by-step explanation:

The area of a rectangle is obtained by multiplying its lenght by its width.

You know that the area of this rectangle is [tex]4g^2- h^2[/tex], then you need to apply the Difference of squares to find the dimensions of this rectangle.

Remember that the Difference of squares is:

[tex]a^2-b^2=(a+b)(a-b)[/tex]

Then, applying this, you get:

 [tex]4g^2- h^2=(2g+h)(2g-h)[/tex]

Therefore, now you know that the dimensions are:

[tex](2g+h)[/tex] and [tex](2g-h)[/tex]

the length and breadth of rectangle are [tex]2g - h[/tex] and [tex]2g + h[/tex] respectively

The given expression for the area of the rectangle is [tex]4g^2 - h^2[/tex]

This expression is a difference of squares, which can be factored using the formula: [tex]a^2 - b^2 = (a - b)(a + b)[/tex]

Now by comparing both equations we can factor as follows:

[tex]4g^2 - h^2 = (2g)^2 - h^2\\\\4g^2 - h^2 = (2g+h)(2g-h)[/tex]

We know that area of a rectangle is a product of its length and breadth so we can say that:

Length: 2g - h

Breadth: 2g + h

So, the length and breadth of rectangle are [tex]2g - h[/tex] and [tex]2g + h[/tex] respectively