What is the distance between the points (2, 8) and (-7, -4) in the coordinate plane?​

Answer:

$176

Step-by-step explanation:

The function[tex]p(x) = 5x^4-3x^3 + 2x^2 + 24[/tex] represents how much money each girl spent based on the number of hours they were shopping.

Janelle goes shopping for 2 hours, then x=2 and

[tex]p(x)=5\cdot 2^4-3\cdot 2^3+2\cdot 2^2+24=5\cdot 16-3\cdot 8+2\cdot 4+24=80-24+8+24=88[/tex]

Thus, Janelle spent $88.

Carmen goes shopping for 2 hours, then x=2 and

[tex]p(x)=5\cdot 2^4-3\cdot 2^3+2\cdot 2^2+24=5\cdot 16-3\cdot 8+2\cdot 4+24=80-24+8+24=88[/tex]

Thus, Carmen spent $88 too.

Together they spent

$88+$88=$176

Answer:

176

Step-by-step explanation:

well, the difference is 21330 - 19700 = 1630.

now, if we take 21330 as the 100%, what is 1630 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 21330&100\\ 1630&x \end{array}\implies \cfrac{21330}{1630}=\cfrac{100}{x}\implies \cfrac{2133}{163}=\cfrac{100}{x} \\\\\\ 2133x = 16300\implies x=\cfrac{16300}{2133}\implies x \approx 7.64[/tex]

Answer:

Change in the price of the car was 7.64%

Step-by-step explanation:

Cindy bought a car for $21330.

After few years she sold the car for $19700.

Net loss she suffered = Selling price - Cost price

= 21330 - 19700

= $1630

Now the percent change in the value will be = [tex]\frac{\text{Difference in the price}}{\text{Cost price of the car}}\times 100[/tex]

= [tex]\frac{1630}{21330}\times 100[/tex]

= 7.64%

Therefore, change in the price of the car was 7.64%

Answer:

Two Angles are Supplementary when they add up to 180 degrees.

Step-by-step explanation:

Notice that together they make a straight angle.

Answer:

The surface area of the structure is [tex]SA=2,500\pi\ m^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of a sphere is equal to

[tex]SA=4\pi r^{2}[/tex]

In this problem we have

[tex]r=50/2=25\ m[/tex] -----The radius is half the diameter

substitute

[tex]SA=4\pi (25)^{2}[/tex]

[tex]SA=2,500\pi\ m^{2}[/tex]

Answer:

A:(1,-3/4)

Step-by-step explanation:

Use substitution to solve the system

y= 1/4x-1

y= -1/2x-1/4

1/4x-1 = -1/2x-1/4, Solve for x

3/4x= 3/4, x = 1, Next solve for y by plugging the x-value into either equation.

y=1/4(1)-1

y=-3/4

Answer:

1,-3/4

Step-by-step explanation:

For this case we have that by definition, the volume of a rectangular solid is given by the product of its length (l), its width (w) and its height (h).

Then, according to the data, it is not specified to which side each measurement corresponds. So, we multiply:

[tex]V = 10.5 * 6.5 * 8.5\\V = 580.125[/tex]

Rounding:

[tex]V = 580.1cm ^ 3[/tex]

Answer:[tex]V = 580.1cm ^ 3[/tex]

Answer:

y = 2x + 14

Step-by-step explanation:

As we move from  (-8, - 2) to (-4, 6)​, x increases by 4 and y increases by 8.

Thus, the slope, m, equal to rise / run, is m = 8/4, or m = 2.

Use the slope-intercept form of the equatino of a straight line:

y = mx + b.  This becomes 6 = 2(-4) + b, or 6 = -8 + b.  Thus, b = 14, and the desired equation is y = 2x + 14.

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years \end{cases} \\\\\\ A=500\left(1+\frac{0.03}{1}\right)^{1\cdot 5}\implies A=500(1.03)^t[/tex]

Answer:

b

Step-by-step explanation:

Answer:

The length of the wire is 22.42 feet

The distance from the base of the pole to the spot where the wire touches the ground is 16.66 feet

Step-by-step explanation:

* Lets explain the situation in the problem

- The telephone pole , the wire and the ground formed a right triangle

- The wire is the hypotenuse of the triangle

- The height of the telephone pole and the distance from the base of

 the pole to the spot where the wire touches the ground are the legs

 of the triangle

- The angle between the wire and the ground is 42°

- The angle 42° is opposite to the height of the telephone pole

- The height of the telephone pole is 15 feet

* Lets use the trigonometry functions to find the length of the wire

 (hypotenuse) and the distance from the base of the pole to the spot

 where the wire touches the ground

∵ sin Ф = opposite/hypotenuse

∵ Ф = 42° and its opposite side = 15 feet

∴ sin 42 = 15/hypotenuse ⇒ by using cross multiplication

∴ sin 42° (hypotenuse) = 15 ⇒ divide both sides by sin 42

∴ hypotenuse = 15/sin 42° = 22.42 feet

∵ The length of the wire is the hypotenuse

∴ The length of the wire is 22.42 feet

∵ The distance from the base of the pole to the spot where the wire

   touches the ground is the adjacent side to the angle 42°

∵ tan Ф = opposite/adjacent

∴ tan 42° = 15/adjacent ⇒ by using cross multiplication

∴ tan 42° (adjacent) = 15 ⇒ divide both sides by sin 42

∴ adjacent = 15/tan 42° = 16.66 feet

∵ The adjacent side is the distance from the base of the pole to the

  spot where the wire touches the ground

∴ The distance from the base of the pole to the spot where the wire

   touches the ground is 16.66 feet

Answer:

The perimeter of the square in the projection is [tex]224\ cm[/tex]

Step-by-step explanation:

we know that

1 cm of the image on the monitor represents 8 cm on the screen

so

using proportion

Find out how much represent on the screen  7 cm on a computer monitor

Let

x ----> the length side of the square image on the screen

[tex]\frac{1}{8}\frac{monitor}{screen} =\frac{7}{x}\frac{monitor}{screen} \\ \\x=8*7\\ \\x=56\ cm[/tex]

Find the perimeter of the image on the screen

the perimeter of a square is equal to

[tex]P=4b[/tex]

[tex]b=56\ cm[/tex]

substitute

[tex]P=4(56)=224\ cm[/tex]

Answer:

224cm

Step-by-step explanation:

The scale factor of the dilation is 8, so a 1 cm by 1 cm square on the monitor represents a 8 cm by 8 cm

square on the screen.

The figure shows two squares. The larger square has a side of 56 centimeters. The smaller square has a side of 7 centimeters. The sides of the larger square are parallel to the sides of the smaller one.

The side length of the square in the projection is the product of the side length of the preimage and the scale factor.

h=7(8)

cm

Simplify.

h=56

cm

The perimeter of the square is

P=4(56)

cm

Simplify.

P=224

cm

Therefore, the perimeter of the square in the projection is 224

cm.

Answer:

When you graph all the equations into a graphing calculator, you find the answer is:

C. x-2y=1 and 3x-y=-1

The system of equations has a solution of approximately (0.6, –0.8) are;

x + 2 y = - 1 and 3 x + y = 1

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.

From this information, it is clear that the green line and the Purple line intersect each other at an approximate point (0.6, -0.8).

Since, the green line passes through the x-intercept (-1,0) and y-intercept (0,-0.5).

Therefore, the equation of the green line will be;

⇒ x + 2y = - 1

Again, the purple line passes through the point (0,1) and has a negative slope thus, the equation of purple line will be;

3x + y = 1 {Since it has negative slope}

Therefore, the first option will be the answer.

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ6

[tex]\bf \begin{array}{ccll} \stackrel{teaspoons}{pepper}&potatoes\\ \cline{1-2} \frac{1}{4}&3\\ x&9 \end{array}\implies \cfrac{~~\frac{1}{4}~~}{x}=\cfrac{3}{9}\implies \cfrac{~~\frac{1}{4}~~}{\frac{x}{1}}=\cfrac{1}{3}\implies \cfrac{1}{4}\cdot \cfrac{1}{x}=\cfrac{1}{3} \\\\\\ \cfrac{1}{4x}=\cfrac{1}{3}\implies 3=4x\implies \cfrac{3}{4}=x[/tex]

Answer:

Since 9 is 3 times the denominator of the first ratio, multiply the numerator of the first ratio by 3 to get the numerator of the second ratio. The amount of pepper is 3/4 teaspoon.

Step-by-step explanation:

Rectangular prism: 6 faces (4 lateral, 2 bases), 8 vertices, 12 edges, meeting all criteria specified.

let's break down the characteristics of each of the options provided:

1. **Square Pyramid**:

  - Faces: A square pyramid has five faces. It has a square base and four triangular faces.

  - Vertices: A square pyramid has five vertices.

  - Edges: A square pyramid has eight edges (the base square has four edges, and each triangular face has one edge).

2. **Triangular Prism**:

  - Faces: A triangular prism has five faces. It has two triangular bases and three rectangular lateral faces.

  - Vertices: A triangular prism has six vertices.

  - Edges: A triangular prism has nine edges (three on each base triangle and three connecting the lateral faces).

3. **Rectangular Prism**:

  - Faces: A rectangular prism has six faces. It has two rectangular bases and four rectangular lateral faces.

  - Vertices: A rectangular prism has eight vertices.

  - Edges: A rectangular prism has 12 edges (four on each base rectangle and four connecting the lateral faces).

4. **Triangular Pyramid**:

  - Faces: A triangular pyramid has four faces. It has a triangular base and three triangular lateral faces.

  - Vertices: A triangular pyramid has four vertices.

  - Edges: A triangular pyramid has six edges (three on the base triangle and three connecting the lateral faces).

Given the characteristics you provided: six faces, four lateral faces, two bases, eight vertices, and 12 edges, we can eliminate the options of square pyramid and triangular pyramid because they don't fit all the criteria.

Now let's look at the remaining options:

- **Triangular Prism** has five faces, six vertices, and nine edges. It doesn't match the given criteria.

- **Rectangular Prism** has six faces (two bases and four lateral faces), eight vertices, and 12 edges, which perfectly matches all the provided characteristics.

Therefore, the correct answer is the **Rectangular Prism**.

Answer:

False

Step-by-step explanation:

A counterexample goes against what you said in the conjecture. An example of a counterexample in this case would be that your dog ate a burger, which is not dog food, last night.

Answer:

Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3 ⇒ 3rd answer

Step-by-step explanation:

* Lets explain how to solve the problem

- To prove that all circles are similar, a translation and a scale factor

  from a dilation will be found to map one circle onto another

- So we can translate the circles to share the same center and dilated

 one of them by the scale factor of the dilation and the center of

 dilation is the common center of the circles

* Lets solve the problem

∵ Circle X has a radius 6 units

∵ Circle Y has a radius 2 units

- At first we translate the circles to share the same center

∴ Use translation to put the centers of the circles at the same point

- Find the scale factor of the dilation from the radii of the two circles

∵ The radius of circle X is 6 units

∵ The radius of circle Y is 2 units

∴ The scale factor = 6/2 = 3

∴ Dilate circle y by scale factor 3

* The steps would prove the circles are similar are;

  Translate the circles so they share a common center point, and

  dilate circle Y by a scale factor of 3.

Answer: 398

Step-by-step explanation:

200^2 - 199^2 = 399

Answer:

397

Step-by-step explanation:

200^2 - 1 = 40000 - 1 =   39999

199^2 + 1 = 39601+ 1 =    39602

Difference =                         397

A couple of things you should keep in mind.

Step-by-step explanation:

Definition:

A pyramid is a polyhedron formed by connecting a one polygonal base and a point, called the apex. Each base edge and apex form a triangle.

A) A pyramid has only one base.   TRUE   (definition)

(look at any photo with the pyramid)

B) The base of a pyramid is a polygon.   TRUE    (definition)

(look at any photo with the pyramid)

C) If the altitude of a right pyramid and the apothem of the base are known, then the Pythagorean theorem can be used to find its slant height.   TRUE

(look at the picture)

D) The slant height is always the same length as the base of the pyramid.

FALSE

E) The lateral faces of a pyramid are rectangles.   FALSE   (definition)

(the lateral faces of a pyramid always are triangles)

F) The slant height is used to calculate the lateral area.   TRUE

(the lateral faces of a pyramid are triangles. The formula of an area of a triangle is A = (bh)/2. Where b - base of triangle, h - height of triangle)

Answer:

A: pyramid has only one base.

B: The base of a pyramid is a polygon.

C: If the altitude of a right pyramid and the apothem of the base are known, then the Pythagorean theorem can be used to find its slant height.

F: The slant height is used to calculate the lateral area.

Answer:

x = 3, plus or minus, radical 5 all over 2

Step-by-step explanation:

Answer:

96 mm

Step-by-step explanation:

A square has 4 equal lengths. If you cut through with a diagonal, then you have form a right isosceles triangle.

So we have the diagonal, the hypotenuse, is [tex]24\sqrt{2}[/tex] mm.

We need to find the side measurement of the square, one of the leg measurements of the right isosceles triangle.

Let's assume it's leg measurement is x.

So by Pythagorean Theorem we have:

[tex]x^2+x^2=(24\sqrt{2})^2[/tex]

Combine like terms and simplify:

[tex]2x^2=24^2(\sqrt{2})^2[/tex]

The square and square root cancel there.

[tex]2x^2=24^2(2)[/tex]

I'm going to stick 24^2 * 2 in my calculator:

[tex]2x^2=1152[/tex]

Divide both sides by 2:

[tex]x^2=576[/tex]

Take the square root of both sides:

[tex]x=24[/tex]

So each side of the square is 24 mm long.

To find the perimeter I add up add all the side measurements of the square or multiply 24 by 4 since all sides of square are congruent.

24(4)=96

Answer is 96 mm

Given the diagonal of a square is 24 Square root two millimeters, the perimeter is calculated by first finding the side length using the diagonal, which is 24mm, and then multiplying it by 4 to get the perimeter, resulting in 96 millimeters.

The question asks to find the perimeter of a square given that the length of a diagonal is 24 Square root two millimeters. To solve this, we use the property that the diagonal of a square is √2 times longer than its side (a). This stems from the Pythagorean theorem applied in a square, where the diagonal acts as the hypotenuse, leading to the equation a² + a² = d² (where a is the side length and d is the diagonal).

Therefore, a = d / √2. Substituting the given diagonal length, we get a = 24mm. Since the perimeter (P) of a square is 4 times the side length, P = 4a. Thus, the perimeter is 96 millimeters.

Answer:

The answer is D.

Step-by-step explanation:

AQRT is a 30-60-90 triangle.

Answer:

The answer id D. AQRT is a 30-60-90 triangle.

Hope this Helps!

Answer:

Step-by-step explanation:

[tex](g-f)(x)=g(x)-f(x)\\\\f(x)=4-x,\ g(x)=6x\\\\(g-f)(x)=6x-(4-x)=6x-4-(-x)=6x-4+x=7x-4\\\\(g-f)(3)-\text{put}\ x=3\ \text{to the expression}\\\\(g-f)(3)=7(3)-4=21-4=17[/tex]

as you may already know, to get the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".

[tex]\bf \stackrel{f(x)}{y}=x^3-9\implies \stackrel{\textit{quick switcheroo}}{\underline{x}=\underline{y}^3-9}\implies x+9=y^3\implies \sqrt[3]{x+9}=\stackrel{f^{-1}(x)}{y}[/tex]

Answer:

Option a) dodecahedron

Step-by-step explanation:

we know that

case a) Dodecahedron

it is a polyhedron that has 12 faces (from Greek dodeca- meaning 12). Each face has 5 edges (a pentagon)

case b) Octahedron

it is a polyhedron that has 8 faces (from Greek okto- meaning eight).

case c) Icosahedron

it is a polyhedron that has 20 faces (from Greek icos- meaning twenty).

case d) Terrahedron

it is a polyhedron composed of four triangular faces (from Greek tetra- meaning four).

therefore

The answer is dodecahedron

To find the surface area of a right triangular prism, we have to calculate the area of all its faces, which include the two triangular bases and the three rectangular faces.
1. **Triangular Bases:** If the right triangle base has sides of lengths `a`, `b`, where `b` is the base and `a` is the height of the triangle, then the area of one triangular base will be given by the formula:
  \[\text{Area of one triangular base} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times a \times b.\]
  Since there are two identical triangular bases, we multiply this area by 2:
  \[\text{Total area of triangular bases} = 2 \times \left( \frac{1}{2} \times a \times b \right) = a \times b.\]
2. **Rectangular Faces:** The three rectangular sides include two rectangles that are formed by the sides of the triangle (`a` and `b`) with the height (`h`) of the prism and one rectangle that is the width of the base `b` and the height of the prism. The areas of these rectangles will be:
  - Rectangle with side `a` and height `h`: \[a \times h.\]
  - Rectangle with base `b` and height `h`: \[b \times h.\]
  - Rectangle with the side corresponding to the hypotenuse `c` of the base triangle and height `h`: \[c \times h.\]
  Therefore, the total area of the three rectangles is the sum of the areas:
  \[\text{Total area of rectangular faces} = a \times h + b \times h + c \times h = h \times (a + b + c).\]
Putting it all together, the formula for the total surface area (SA) of the right triangular prism is:
\[ SA = a \times b + h \times (a + b + c).\]
So, the expression that will help you find the surface area of a right triangular prism is the sum of the areas of the two triangles and the three rectangles as given by this formula.

Answer:

  250

Step-by-step explanation:

If we let p represent the 1975 population, we have ...

  p + 140%×p = 600

  p(1 +1.40) = 600

  p = 600/2.4 = 250

There were 250 grizzly bears living in the wild in 1975.

Answer:

60 inches squared

Step-by-step explanation:

The formula for the area of a triangle is as follows:

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

Where A=area, b=base, and h=height.

Plug in 15 for your base and 8 for your height and solve.

[tex]A=\frac{1}{2} (15)(8)\\A=7.5(8)\\A=60[/tex]

Answer:

B) 60 squared inches

Step-by-step explanation:

To find the area of a triangle you have to use this equation:

A = 1/2 b*h

Now plug in the numbers,

A = 1/2 15*8

15*8 = 120

1/2 of 120 = 60

A = 60

The area of this triangle is 60 squared inches.

a = hours worked by the first mechanic

b = hours worked by the second mechanic.

since the first mechanic charges $55 per hour, then for "a" hours that'd be a total of 55*a or 55a, likewise, for the second mechanic that'd be a total charge of 80*b or 80b.

we know all hours combined are 15, so then a + b = 15.

we also know that all charges combined are $950, so 55a + 80b = 950.

[tex]\bf \begin{cases} a+b=15\\ \boxed{b}=15-a\\ \cline{1-1} 55a+80b=950 \end{cases}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{55a+80\left( \boxed{15-a} \right)=950} \\\\\\ 55a+1200-80a=950\implies -25a+1200=950\implies -25a=-250 \\\\\\ a=\cfrac{-250}{-25}\implies \blacktriangleright a = 10\blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{b=15-a\implies }b=15-10\implies \blacktriangleright b=5 \blacktriangleleft[/tex]

Answer:

see explanation

Step-by-step explanation:

If A +B = 45° then tan(A+B) = tan45° = 1

Expanding (1 + tanA)(1 + tanB)

= 1 + tanA + tanB + tanAtanB → (1)

Using the Addition formula for tan(A + B)

tan(A+B) = [tex]\frac{tanA+tanB}{1-tanAtanB}[/tex] = 1 ← from above

Hence

tanA + tanB = 1 - tanAtanB ( add tanAtanB to both sides )

tanA + tanB + tanAtanB = 1 ( add 1 to both sides )

1 + tanA + tanB + tanAtanB = 2

Then from (1)

(1 + tanA)(1 + tanB) = 2 ⇒ proven

Answer:

y is 90

Step-by-step explanation:

The y/x is proportional per point (x,y) since this is a direct variation.

That is ,

[tex]\frac{30}{-3}=\frac{y}{-9}[/tex].

Cross multiply:

[tex]30(-9)=y(-3)[/tex]

Simplify:

[tex]-270=-3y[/tex]

Divide both sides by -3

[tex]\frac{-270}{-3}=y[/tex]

[tex]90=y[/tex]

Answer:

x = 6 and x = -5

Step-by-step explanation:

The zeros are what 2 x-values makes this function equal to zero.

So we need to find  [tex]x^2-x-30=0[/tex]

Now we need 2 numbers multiplied that gives us -30 (constant) and added gives us -1 (coefficient in front of x).

The two numbers are : -6, and 5

Now we can write:

[tex]x^2-x-30=0\\(x-6)(x+5)=0\\x=6, -5[/tex]

Hence the zeroes are x = 6 and x = -5

Final answer:

The zeros of the function f(x) = x^2 - x - 30 are found by factoring the quadratic equation. They are x = 6 and x = -5.

Explanation:

To find the zeros of the function f(x) = x2 - x - 30, we need to solve the equation for when f(x) equals zero. This means we have to solve x2 - x - 30 = 0. This is a quadratic equation, and we can attempt to factor it to find the solutions.

The factors of -30 that add up to -1 (the coefficient of x) are -6 and +5. Thus, we can rewrite the quadratic as (x - 6)(x + 5) = 0. Now, we can set each factor equal to zero to find the zeros of the function:

x - 6 = 0, which gives x = 6

x + 5 = 0, which gives x = -5

Therefore, the zeros of the function are x = 6 and x = -5.