in set builder notation Write a compound inequality to represent all of the numbers between -4 and 6.

Answer:

The width of the original rectangle on the left is [tex]5\ m[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

so

Let

z -----> the scale factor

a ----> perimeter of the reduced rectangle on the right

b ----> perimeter of the original rectangle on the left

[tex]z=\frac{a}{b}[/tex]

we have

[tex]a=24\ m[/tex]

[tex]b=30\ m[/tex]

substitute

[tex]z=\frac{24}{30}=0.8[/tex]

step 2

Find the width of the reduced rectangle on the right

we know that

The perimeter of rectangle is equal to

[tex]P=2(L+W)[/tex]

we have

[tex]L=8\ m[/tex]

[tex]P=24\ m[/tex]

substitute and solve for W

[tex]24=2(8+W)[/tex]

[tex]12=(8+W)[/tex]

[tex]W=12-8=4\ m[/tex]

step 3

Find the width of the original rectangle on the left

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

so

Let

z -----> the scale factor

y ----> the width of the reduced rectangle on the right

x ----> the width of the original rectangle on the left

[tex]z=\frac{y}{x}[/tex]

we have

[tex]y=4\ m[/tex]

[tex]z=0.8[/tex]

substitute and solve for x

[tex]0.8=\frac{4}{x}[/tex]

[tex]x=\frac{4}{0.8}[/tex]

[tex]x=5\ m[/tex]

Answer:

Step-by-step explanation:

Look at the picture.

We have the triangles 30° - 60° - 90° and 45° - 45° - 90°.

The sides are in proportions:

30° - 60° - 90° ⇒ 1 : √3 : 2

45° - 45° - 90° ⇒ 1 : 1 : √2

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

[tex]SR=ST\sqrt3\to ST\sqrt3=2\sqrt3\qquad\text{divide both sides by}\ \sqrt3\\\\ST=2\\\\TR=2ST\to TR=2(2)=4\\\\RQ=TR\to RQ=4\to x=4[/tex]

Answer:

x ≈ 11.7

Step-by-step explanation:

When 2 secants are drawn from an external point to a circle then

The products of the measures of one secant's external part and the entire secant is equal to the product of the measures of the other secant's external part and that entire secant, that is

3(3 + x) = 4(4 + 7)

9 + 3x = 4 × 11 = 44 (subtract 9 from both sides )

3x = 35 ( divide both sides by 3 )

x ≈ 11.7

Ad+ae+bd+be so that is your solution

Answer:2, 2

2 factors

2 terms

This expression consist of 2 factors, each factor contains 2 terms

Step-by-step explanation:

Terms are single numbers, variables, or the product of a number and variable.

A factor is one part of a product.

The expression (a+b) (d+e) consists of two parts of a product, and each part is a factor. The first factor is (a+b) and the second is (d+e).

Each of the factors contains the sum of two variables. Variables connected by addition are separate terms. The expression (a + b) contains two terms: a and b. The expression (d + e) also contains tow terms.

The expressions (a+b) (d+e) consists of 2 factors, and each of there factors has 2 terms.

Answer:

From the information we can conclude that the triangle is a isosceles triangle.

First, we can calculate the hypotenuse by using pythagorean theorem:

√(6² + 6²) = √(36 + 36) =√64 = 8 (cm)

To calculate the area of the triangle, we first need to know the height of it.

Since this is a isosceles triangle, the altitude (which is also the height) will also  be the median of that triangle.

Then we also have a 90° angle, this triangle is also a right triangle, and in right triangle, the median will equal half of the hypotenuse.

From the reasoning above, we can now calculate the height of the triangle:

8/2 = 4(cm)

The area of the triangle should be:

S = hb/2 = (4 . 6)/2 = 12 (cm²)

Answer:

the rule is add 7 i thinso it would be m+7

Step-by-step explanation:

Answer:

? = 7

Step-by-step explanation:

We know it's 7 because,

2 + 7 = 9

4 + 7 = 11

8 + 15 = 7

11 + 7 + 18

Hey, this is easy! Why not ask your parents?

Answer: b 11.9

Step-by-step explanation:

the chord and the line to the center can be used to create a triangle

the radius is the hypotenuse of this triangle

4.5squared + 11 squared= 11.9

Answer: Mika walks 16 days and 26.5 total miles.

Step-by-step explanation: You count each x to figure out the days and and them all together like so: 1 1/2 x 5 = 7 1/2. 7 1/2 + 1 5/8 = 12.1875, and so forth and so on.

Answer:

A - f

Step-by-step explanation:

Break each term down into its prime factors

7f^2 = 7 *f*f

12f = 2*2*3*f

The common term is f

Factor out the f

f(7f-12)

Answer:

π/90 or 0.0035 units

Step-by-step explanation:

equation: length of the arc = ∠of the angle/360 * circumference

Substitute: S = 0.4/360 * 10π --> C = 2πr

Simplify: S = 1/900 * 10π

Simplify: S = π/90 ≈ 0.003489 units

Polygon D'E'F'G' is larger than polygon DEFG, because the scale factor is greater than 1.

An equation is an expression that shows the relationship between two or more numbers and variables.

Polygon DEFG is dilated with the origin as the center of dilation using the rule (x, y) → (2x, 2y) to create polygon D'E'F'G'. Therefore:

Polygon D'E'F'G' is larger than polygon DEFG, because the scale factor is greater than 1.

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The dilation doubles the distances between corresponding vertices, indicating an enlargement.

Therefore, choice A is correct: Polygon D'E'F'G' is larger due to the scale factor exceeding 1.

To determine whether polygon D'E'F'G' is larger or smaller than polygon DEFG after dilation with the origin as the center and using the rule (x, y) → (2x, 2y), we need to understand the effect of the dilation on the coordinates of the vertices.

Let's assume the coordinates of the vertices of polygon DEFG are as follows:

D(x₁, y₁)

E(x₂, y₂)

F(x₃, y₃)

G(x₄, y₄)

Now, applying the dilation rule (x, y) → (2x, 2y) to each vertex, we get the coordinates of the corresponding vertices of polygon D'E'F'G':

D'(2x₁, 2y₁)

E'(2x₂, 2y₂)

F'(2x₃, 2y₃)

G'(2x₄, 2y₄)

Now, let's compare the distances between the vertices of the original and dilated polygons to determine if the dilation resulted in enlargement or reduction.

1. Distance between D and E:

  Original: √((x₂ - x₁)² + (y₂ - y₁)²)

  Dilated: √((2x₂ - 2x₁)² + (2y₂ - 2y₁)²) = √(4(x₂ - x₁)² + 4(y₂ - y₁)²)

  The distance between D' and E' is twice the distance between D and E. So, the scale factor is indeed 2, indicating an enlargement.

2. Similarly, for the other sides (DE, EF, FG), we'll find the same result.

Since the scale factor is greater than 1, we can conclude that polygon D'E'F'G' is larger than polygon DEFG.

So, the correct answer is:

A) Polygon D'E'F'G' is larger than polygon DEFG, because the scale factor is greater than 1.

The answer is:

We will have to fill 226.194 cubic inches.

To solve the problem, we need to find the volume of the flower vase, and then, calculate the two third parts of its volume. Also, from the statement we know that the shape of the flower vase is a right cylinder, since the only given information about it, is its diameter and height.

We can calculate the volume of a right cylinder using the following equation:

[tex]V_{Cylinder}=\pi radius^{2}*height[/tex]

So, we are given the following information:

[tex]diameter=6in\\radius=\frac{diameter}{2}=\frac{6in}{2}=3in\\height=12in[/tex]

Then,

Substituting the given information, and calculating, we have:

[tex]V_{Cylinder}=\pi *(3in)^{2}*12in=108\pi=339.292in^{3}[/tex]

Now, calculating how many cubic inches are [tex]\frac{2}{3}[/tex] of the flower vase volume, we have:

[tex]VolumeToFill=CubicInchesToFill=\frac{2}{3}*Volume\\\\CubicInchesToFill=\frac{2}{3}*339.292in^{3} =226.194in^{3}[/tex]

Hence, we have that we will have to fill 226.194 cubic inches.

Have a nice day!

Answer:

[tex]72\pi\ in^{3}[/tex]

Step-by-step explanation:

step 1

Calculate the volume of the cylinder (flower vase)

The volume is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]r=6/2=3\ in[/tex] -----> the radius is half the diameter

[tex]h=12\ in[/tex]

substitute the values

[tex]V=\pi (3)^{2}(12)=108\pi\ in^{3}[/tex] ------> exact value

step 2

Calculate  2/3 of the volume

[tex]V=(2/3)108\pi=72\pi\ in^{3}[/tex]

Answer:

Step-by-step explanation:

a=12, b=10, c=?

a²+b²=c²

Using pythagorean theorem you can find that c= 2√61

Final answer:

The distance along the hypotenuse of the right triangle with 12 feet vertical height and 10 feet horizontal length is found using the Pythagorean Theorem. The calculated distance is approximately 15.62 feet.

Explanation:

To find the distance along the hypotenuse of a right triangle formed by five people with a total vertical height of 12 feet and a total horizontal length of 10 feet, we use the Pythagorean Theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Thus, the formula is a² + b² = c².

In this case, we have:

Plugging these values into the Pythagorean Theorem gives:

12² + 10² = c²
144 + 100 = c²
244 = c²

Now, find the square root of 244 to get the length of the hypotenuse:

c = √244

c ≈ 15.62 feet (using three significant figures)

Therefore, the distance along the hypotenuse of the human triangle is approximately 15.62 feet.

2 units.

Since a triangle is basically a rectangle split in half, we just use the dimensions of the triangle without dividing by 2.

Answer:

its 12 units long and unit c is 5 units long good luck! :D

Step-by-step explanation:

ANSWER

[tex]\left[ { \begin {array} {cc} 10&0& | 10\\-5&-8& | 9\\ \end {array}} \right] [/tex]

EXPLANATION

The given system of equations is

10x=10

-5x-8y=9

We can rewrite this as:

10x+0y=10

-5x-8y=9

The augmented matrix is the combination of the coefficient matrix and the constant matrix.

The coefficient matrix is

[tex] \left[ { \begin {array} {cc} 10&0\\ - 5& - 8\\ \end {array}} \right] [/tex]

The constant matrix is

[tex] \binom{10}{9} [/tex]

The augmented matrix is

[tex]\left[ { \begin {array} {cc} 10&0& | 10\\-5&-8& | 9\\ \end {array}} \right] [/tex]

The augmented matrix is:

         [tex]\begin{bmatrix}10 & 0| & 10\\ -5 &-8| & 9\end{bmatrix}[/tex]

The steps of an augmented matrix are as follows:

The system of equation is:

[tex]10x=10\\and\\-5x-8y=9[/tex]

Hence, the system could be written in the form:

[tex]AX=b[/tex]

where:

[tex]A=\left[\begin{array}{ccc}10&0\\-5&-8\end{array}\right][/tex]

[tex]X=\left[\begin{array}{ccc}x\\y\end{array}\right][/tex]

and

[tex]b=\left[\begin{array}{ccc}10\\9\end{array}\right][/tex]

Hence, the augmented matrix  is:

    [tex]\begin{bmatrix}10 & 0| & 10\\ -5 &-8| & 9\end{bmatrix}[/tex]

hence the answer is 16units

hope helps you!!!!!!

The equation of diagonals of kite are x = 0 and y = 0 and their point of intersection is (0,0)

A straight line is a one-dimensional figure that never ends and has no breadth.

Equation of line : y = mx + c

m - slope of the line

c - y intercept

Let the vertices of the Kite ABCD be A(-4 , 0), B(0 , 4), C(4 , 0), D(0 , -4)

The equation of Diagonal AC is y = 0

The equation of Diagonal BD is x = 0

The point of intersection of diagonals will be ( 0 , 0)

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Answer:

360 or D.

Step-by-step explanation:

Answer:

Required inequality is [tex]4800+183x>8000[/tex].

Step-by-step explanation:

Given that Mrs. Robinson, an insurance agent, earns a salary of $4,800 per year plus a 3% commission on her sales. The average price of a policy she sells is $6,100. Write an inequality to find how many policies Mrs. Robinson must sell to make an annual income of at least $8,000.

Calculation is given by:

Salary per year = $4,800

Average price of a policy = $6,100.

commission on her sales = 3%

Then commission on $6,100 = 3% of $6,100 = 0.03 ($6,100) = $183

Let number of policies Mrs. Robinson must sell to make an annual income of at least $8,000 = x

then total commission on x policies = 183x

Total income using x policies = 4800+183x

Since she wants to make an annual income of at least $8,000. so we can write inequality as:

[tex]4800+183x>8000[/tex]

Hence required inequality is [tex]4800+183x>8000[/tex].

This answer should be found using the distance formula. Steps are attached. Answer is 7.

Simple! All you need to do is graph the coordinates and then count the spaces in between, and the answer should be seven! Or, try -5 + 7, which would equal 2.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x=3y&\text{subtract}\ 3y\ \text{from both sides}\\3x-2y=14\end{array}\right\\\\\left\{\begin{array}{ccc}x-3y=0&\text{multiply both sides by (-3)}\\3x-2y=14\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-3x+9y=0\\3x-2y=14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad7y=14\qquad\text{divide both sides by 7}\\.\qquad\qquad y=2\\\\\text{put the value of y to the first equation:}\\x=3(2)=6[/tex]

The geometric sequence is B: 32

Final answer:

To find the 6th term in the given geometric sequence, the common ratio is calculated and the nth term formula is applied. However, the calculated value doesn't match any of the provided options, indicating a possible error in calculation or the sequence itself.

Explanation:

To find the 6th term of the geometric sequence 1024, 528, 256, we first need to determine the common ratio. We get this by dividing the second term by the first term:

Common ratio (r) = 528 / 1024 = 0.515625

Now, using the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term and n is the term number:

a6 = 1024 × 0.515625(6-1) = 1024 × (0.515625)5

Calculating this, we get:

a6 = 1024 × 0.1184844970703125 = 121.234375

This value does not match any of the options provided (64, 32, 16, or 8), suggesting that there may have been a miscalculation or misunderstanding of the sequence. Please double-check the sequence or provide additional information.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3x+4y=-23&(1)\\x=3y+1&(2)\end{array}\right\\\\\text{Substitute (2) to (1):}\\\\3(3y+1)+4y=-23\qquad\text{use the distributive property}\\\\(3)(3y)+(3)(1)+4y=-23\\\\9y+3+4y=-23\qquad\text{subtract 3 from both sides}\\\\13y=-26\qquad\text{divide both sides by 13}\\\\\boxed{y=-2}\\\\\text{Put the value of }\ y\ \text{to (2)}:\\\\x=3(-2)+1\\\\x=-6+1\\\\\boxed{x=-5}[/tex]

Answer:

x = -5

y = -2

Step-by-step explanation:

Answer: 91,445,760 ft³

Step-by-step explanation:

You know that the base of this pyramid is a square, then you can use the following formula to calculate its volume:

[tex]V=\frac{s^2h}{3}[/tex]

Where "s" is the lenght of any side of the base of the pyramid and "h" is the height of the pyramid.

You know that:

[tex]h=480ft\\s=756ft[/tex]

Then, you can substitute these values into the formula. So, you get that the volume of The Great Pyramid is:

[tex]V=\frac{(756ft)^2(480ft)}{3}=91,445,760ft^3[/tex]

it has infinitely many solutions

Answer:it has many solutions

8-2x = 10x+3 Subtract 3 from both sides

5-2x = 10x Add 2x to both sides

5 = 12x Divide 12 to both sides

Final answer X=5/12

The solution to the algebraic expression 8-2x=10x+3 is: x = 12/5

An algebraic expression in mathematics is defined as an expression which is made up of variables and constants, along with algebraic operations

We are given the algebraic expression as:

8 - 2x = 10x + 3

Using addition property of equality, add 2x - 3 to both sides to get:

8 - 2x + 2x - 3 = 10x + 3 + 2x - 3

5 = 12x

x = 12/5

x = 2.4

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Answer:

put the united states population over the world population you will get a simplified fraction to the ratio between them which is 1/23   easily you can multiply 23 by the USA population to get the world population so it is more than USA population 23 times  

3*10^8 / 6.9*10^9 = 1/23

then   23  *  3*10^8  = 6.9*10^9  

The world population is approximately 23 times larger than the population of the United States.

The question is asking us to determine how many times larger the world's population is compared to the population of the United States. It gives us the population of the United States as 3 x 108 and the world's population as 6.9 x 109. To solve this, we'll divide the world population by the US population.

The calculation is as follows: (6.9 x 109) / (3 x 108) which equals to 23

This means that the world population is approximately 23 times larger than the United States population.

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Answer:

y= |x|-2.5

Step-by-step explanation:

The attached picture is the graph for the function y=|x|

The picture you asked differs in the origin of the graph, which resides in the point (0, -2.5).

So our equation should look like the following

y=a|x|+b

From the first point you have (0, -2.5), This means 0=a*|0|+b, we have obtained that b=-2.5

Now 'a' is the slope, we need to find another point in the graph. that would be (2.5, 0) (obtained from the given graph)

the slope is obtained using the equation

[tex]a=\frac{x_{2}-x_{1} }{y_{2}-y_{1}  }[/tex]

Where (x1, y1)= (0, -2.5), (x2,y2)=(2.5,0)

thus we have that a=1

So our equation is y=|x|-2.5

The answer is 9424.78

Reason:

Answer:

52$

Step-by-step explanation:

ok so 2 pins cost 4$ so if you buy one pin its 2$ correct? take 12 and multiply it by 2 and take 14 and multiply by 2,

12×2=24$

14×2=28$

add those two together and you get 52$

Answer:

Step-by-step explanation:

We know: the sum of the measures of triangle angles is 180°.

Therefore we have the equation:

[tex]2x+(3x-10)+50=180\\\\(2x+3x)+(-10+50)=180\\\\5x+40=180\qquad\text{subtract 40 from both sides}\\\\5x+40-40=180-40\\\\5x=140\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}=\dfrac{140}{5}\\\\x=28[/tex]

The sum of all the angles of a triangle is 180°

This means you have to add all the angles together and set it equal to 180. Here is the formula:

50 + 2x + 3x - 10 = 180

Now you solve for x

Step 1: Combine like terms

(50 + (-10) ) + (2x + 3x) = 180

40 + 5x = 180

Step 2: Subtract 40 to both sides

(40-40) + 5x = 180 - 40

5x = 140

Step 3: Isolate x by dividing 5 to both sides

[tex]\frac{5x}{5}  = \frac{140}{5}[/tex]

x = 28

Check: 50 + 2(28) + 3(28) - 10 = 180

50 + 56 + 84 - 10 = 180

180 = 180

Therefore your value of x is 28!

Hope this helped!