[tex]-6 + 3x - 9x^{2}=-16[/tex]

Reason:

Refer to the diagram below. The tiny square angle markers tell us we have a 90 degree angle, meaning those lines are perpendicular.

You can think of the parallel lines being the metal part of train tracks, while the perpendicular line connecting the metal rails is the wooden part of the train tracks.

6 / 2 =  3

Every 3 feet of shadow would be 1 foot of height of the tower.

171 feet/ 3 = 57

Answer: The tower is 57 feet tall.

Answer:

[tex]31.8\%[/tex]

Step-by-step explanation:

The area of the circle is [tex]A=\pi r^2=\pi(4)^2=16\pi[/tex]

The area of the triangle is [tex]A=\frac{bh}{2}=\frac{8*4}{2}=\frac{32}{2}=16[/tex]

Hence, the probability of a randomly selected point within the circle falls in the red shaded area is [tex]\frac{16}{16\pi}=\frac{1}{\pi}\approx0.318\approx31.8\%[/tex]

When the converted costs are compared, the earlier edition of the history book is more expensive.

The consumer price index measures the changes in price of a basket of good. It is used to measure inflation.

Converted price of the earlier edition = (CPI in 1992 / CPI in 1999) x later edition of the book

(140.3 / 166.3) x $43 = $36.28

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Answer:  Choice A

f(x) = (x + 2)^2 - 11

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

Work Shown:

y = x^2 + 4x - 7

y+7 = x^2 + 4x

y+7+4 = x^2 + 4x + 4

y+11 = x^2 + 4x + 4

y+11 = (x + 2)^2

y = (x + 2)^2 - 11

f(x) = (x + 2)^2 - 11

In the third step, I added 4 to both sides to complete the square for the x^2+4x portion. Notice that (x+2)^2 = x^2+4x+4. So I added 4 to fill in the missing piece needed to complete the square.

Put another way the '4' added to both sides is because we first divided the x coefficient 4 in half to get 4/2 = 2. Then you square it to get 2^2 = 4.

--------------------

Alternative Method (optional)

y = x^2 + 4x - 7 is in the form of y = ax^2+bx+c

where: a = 1, b = 4, c = -7

Plug those a,b values into the formula below

h = -b/(2a)

h = -4/(2(1))

h = -2

This is the x coordinate of the vertex.

Use it to find the y coordinate of the vertex.

y = x^2 + 4x - 7

y = (-2)^2 + 4(-2) - 7

y = -11

The vertex is located at (h,k) = (-2,-11)

We have the template y = a(x-h)^2 + k update to y = (x + 2)^2 - 11 after plugging in a = 1, h = -2, and k = -11.

Answer: Both diagonals bisect each other.

Answer:

130 degrees

Step-by-step explanation:

3:40, it has traveled 6 * 40 = 240 degrees  which is 110 degrees from vertical The difference is 240 - 110 = 130 degrees, which is the final answer.

Hope This Helped

Answer:

5

Step-by-step explanation:

2 negatives will make a positive so 3-(-2) is equal to 3+2 and the answer is 5.

hope it helps

[tex]|a+bi|=\sqrt{a^2+b^2}[/tex]

[tex]|6-8i|=\sqrt{6^2+(-8)^2}=\sqrt{36+64}=\sqrt{100}=10[/tex]

Answer:

5/2 13/6 80/21

Step-by-step explanation:

the reciprocal is just flipping the fraction over, if they asked you to simplify its

4 1/2, 2 1/6, and 3 4/5  

Answer: x = 4

Step-by-step explanation:

(√x + 2)(√x - 2) = 0

√x*√x - 2√x + 2√x -4 = 0

x - 0 - 4 = 0

x = 4

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

(√x + 2)(√x - 2) = 0

√x × √x - √x · 2 + 2 · √x - 2 · 2 = 0

√xx - 2 × √x + 2 · √x - 4 = 0

√x^1+1 - 2 · √x + 2 × √x - 4= 0

√x² - 2 · √x + 2· √x - 4 = 0

x^2/2 - 2 × √x + 2 · √x - 4 = 0

x - 2· √x + 2 · √x - 4 = 0

x - 4 = 0

(x - 4) + 4 =  0

x - 4 + 4 = 0

x = 4

The incenter of a triangle is the point at which the triangle's three internal angle bisectors connect. The correct options are A, B, and, C.

The incenter of a triangle is the point at which the triangle's three internal angle bisectors connect. In other words, it is the point at which the internal angle bisectors of the triangle intersect.

The properties that are true about the incenter of a triangle are:

A. The incenter is equidistant from each side of the triangle.

B. The incenter of a triangle is always inside it.

C. The incenter is where all of the bisectors of the angles of the triangle meet.

Hence, the correct options are A, B, and, C.

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The relation that describes the graph {(-1, 3), (-2, 1), (-3, -3), (-4, -5)}

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The coordinates of given graph:

Hence, the relation is {(-1, 3), (-2, 1), (-3, -3), (-4, 5)}.

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Step-by-step explanation:

so, this sounds like the blimp is located between the stadium and the planetarium.

we have a triangle :

the ground distance between the stadium and the planetarium is the baseline.

and the 2 lines of sight from the blimp on one side to the stadium and on the other side to the planetarium are the 2 legs.

we know the height of this triangle is 600 ft.

the angle of depression down to the stadium is 37°. which makes the inner triangle angle at the ground point at the stadium also 37°.

and the angle of depression down to the planetarium is 29°. which makes the inner triangle angle at the ground point at the planetarium also 29°.

and because the sum of all angles in a triangle is always 180°, we know the angle at the blimp is

180 - 37 - 29 = 114°

in order to solve this triangle, we need to split it into 2 right-angled triangles by using the height of the main triangle as delimiter.

we get a stadium side and a planetarium side triangle.

the baselines (Hypotenuses) of the 2 triangles are the corresponding lines of sight from the blimp.

the height of the large triangle is also a height and a leg in each small triangle.

and the stadium side part of the large baseline (between ground point and intersection with the height) is the second leg for the stadium side triangle.

and correspondingly, the planetarium side part of the large baseline (between ground point and intersection with the height) is the second leg for the planetarium side triangle.

the inner blimp angle of the stadium side triangle is

180 - 37 - 90 = 53°

and the inner blimp angle of the planetarium side triangle is

180 - 29 - 90 = 61°

now we can use the law of sine to get the lengths of the 2 parts of the baseline of the large triangle.

and when we add these 2 numbers we get the distance between stadium and planetarium.

law of sine is

a/sin(A) = b/sin(B) = c/sin(C)

with the sides being opposite of the associated angles.

for the stadium side triangle we get

part1/sin(53) = 600/sin(37)

part1 = 600×sin(53)/sin(37) = 796.226893... ft

for the planetarium side triangle we get

part2/sin(61) = 600/sin(29)

part2 = 600×sin(61)/sin(29) = 1,082.428653... ft

the distance between the stadium and the planetarium is

part1 + part2 = 1,878.655546... ft

Answer:

62 degree

Step-by-step explanation:

A triangle has 180 degree

180 - (43 + 75) = 62

The true statements about the triangles RST and DEF are: (a), (d) and (e)

The statement ΔRST ≅ ΔDEF means that the triangles RST and DEF are congruent.

This above implies that:

The above means that the possible true statements are: (a), (d) and (e)

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Answer:

4 and 11

Step-by-step explanation:

See attached image

The quadrilateral that matches the characteristics is a square.

A quadrilateral is a 2 dimensional figure with 4 sides. Example of quadrilaterals are rectangle, rhombuses, square, parallelograms and many more.

Therefore, the quadrilateral that matches the characteristics is a square.

Properties of a square

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Squares are the results of multiplying a value by itself.  The value of 2.4494897… is equivalent to √6.

Squares are the results of multiplying a value by itself. Whereas the square root of a number is a value that when multiplied by itself yields the original value. As a result, both are vice versa approaches. For example, the square of 2 is 4 and the square root of 4 is 2.

The value of 2.4494897… is equivalent to √6.

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Answer:

a. [tex]x^{-2}[/tex]

b. [tex]x^{-6}[/tex]

c. 1

d. 1

e. [tex]x^{-6}[/tex]

f. [tex]x^{15}[/tex]

Step-by-step explanation:

Answer:

deviation is 10

this will help you

The correct expansion of (4x-2)(2x² + 3) is 4x 2x² + 4x 3+ (-2) 2x² + (-2) 3.

The correct option is (C).

An expression is a set of terms combined using the operations +, – , x or ,/.

Given expression: (4x-2)(2x² + 3)

= 4x (2x² + 3) -2 (2x² + 3)

= 4x* 2x² + 4x * 3- 2* 2x² - 2*3

= 4x* 2x² + 4x *3+ (-2) *2x² + (-2)* 3

Hence, the correct expansion is 4x 2x² + 4x 3+ (-2) 2x² + (-2) 3.

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Hi Student!

Looking at this problem, it's fairly simple and just asks us to determine whether x = 1 is a solution to the expression that was provided.  The first step that we must take to solving this is to plug in the value 1 for each of the places that we have x.  Then we simplify and look at the final expression and if it evaluates to true than x = 1 is a solution to the expression.

Plug in the values

Simplify both sides

Looking at the final expression that is shown, we can see that it states that 4 is greater than or equal to 4 which evaluates to true since 4 is equal to 4.  Therefore, x = 1 would be considered a solution of the expression that was provided in this problem.

Answer:

is it 1:4 or am I missing something

Step-by-step explanation:

Answer:

Pythagorean theorem is mainly used for finding the length of the third side of a right angled triangle if the lengths of other two sides are known.

For this, it is more useful if the theorem is stated in terms of the length of the sides of the triangle.

Consider a right angled triangle with sides of lengths p,b and h, where p,b and h are the lengths of perpendicular,base and hypotenuse respectively.

Draw squares on each of these sides.These squares have areas p²,b² and h².

For any right angled triangle with sides of length p,b and h;

[tex] \: \: \: \: \: \: \: {h}^{2} = {p}^{2} + {b}^{2} ....................(i)[/tex]

[tex] \therefore \: h = \sqrt{ {p}^{2} + {b}^{2} } [/tex]

From (i); p²=h²-b²

[tex] \therefore \: p = \sqrt{ {h}^{2} - {b}^{2} } [/tex]

Similarly,

[tex]b = \sqrt{ {h}^{2} - {p}^{2} } [/tex]

Step-by-step explanation:

[tex] \blue{ \frak{seolle_{aphr.odite} }}[/tex]