A radio tower is located on a coordinate system measured in miles. The range of a signal in a particular direction is modeled by a quadratic function where the boundary of the signal starts at the vertex at (4, 2). It passes through the point (5, 4). A linear road connects points (–3, 7) and (8, 2). Which system of equations can be used to determine whether the road intersects the boundary of the tower’s signal?

Answer:

C

Step-by-step explanation:

Given

sinR = [tex]\frac{5}{13}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]

This is a 5- 12- 13 triangle with legs PQ = 5, QR = 12, hypotenuse PR = 13

cosR = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{QR}{PR}[/tex] = [tex]\frac{12}{13}[/tex]

Answer:

First answer choice: [tex]y=\sqrt{x}[/tex] shifted right 6 units and down 2 units.

Step-by-step explanation:

Graph

Answer:

(3x + 7y)^2 =  9 x^2 + 42xy + 49y^2

Step-by-step explanation:

Answer:

I attached pictures of the two graphs, I hope they help!

Step-by-step explanation:

Answer:

x = 2 is a vertical line going through 2 on the x-axis. It has an undefined slope.

y = 4 is a horizontal line going through 4 on the y-axis. It has a slope of zero

They are perpendicular.

Step-by-step explanation:

Observe that

5/12 = 1/4 + 1/6

so that

tan(5π/12) = tan(π/4 + π/6)

Then

tan(5π/12) = sin(π/4 + π/6) / cos(π/4 + π/6)

… = (sin(π/4) cos(π/6) + cos(π/4) sin(π/6)) / (cos(π/4) cos(π/6) - sin(π/4) sin(π/6))

… = (cos(π/6) + sin(π/6)) / (cos(π/6) - sin(π/6))

(since sin(π/4) = cos(π/4) = 1/√2)

… = (√3/2 + 1/2) / (√3/2 - 1/2)

… = (√3 + 1) / (√3 - 1)

… = (√3 + 1) / (√3 - 1) × (√3 + 1) / (√3 + 1)

… = (√3 + 1)² / ((√3)² - 1²)

… = ((√3)² + 2√3 + 1²) / (3 - 1)

… = (3 + 2√3 + 1) / 2

… = (4 + 2√3) / 2

… = 2 + √3 … … … (C)

If you insist on using the half-angle identity, recall that

sin²(x) = (1 - cos(2x))/2

cos²(x) = (1 + cos(2x))/2

==>   tan²(x) = (1 - cos(2x)) / (1 + cos(2x))

Let x = 5π/12. The angle x lies in the first quadrant, so we know tan(x) is positive.

==>   tan(x) = +√[(1 - cos(2x)) / (1 + cos(2x))]

We also know

cos(2x) = cos(5π/6) = -√3/2

which means

tan(x) = tan(5π/12) = √[(1 - (-√3/2)) / (1 + (-√3/2))]

… = √[(1 + √3/2) / (1 - √3/2)]

… = √[(2 + √3) / (2 - √3)]

… = √[(2 + √3) / (2 - √3) × (2 + √3) / (2 + √3)]

… = √[(2 + √3)² / (2² - (√3)²)]

… = √[(2 + √3)² / (4 - 3)]

… = √[(2 + √3)²]

… = 2 + √3

Answer:

All real numbers

Step-by-step explanation:

The range is whatever the output can be. In this case, the output is y. Because the line is going through all numbers vertically, and arrows are going up and down, we can say that the line is going through all y values. Therefore, the range is all real numbers

Answer:

y=[tex]\frac{-3x}{2}[/tex]

Step-by-step explanation:

Hi there!

We need to find the equation of the line that passes through the origin (the point (0,0)) and (-2,3)

There are 3 ways to write the equation of the line, although the most common way is slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

So we need to find the slope of the line first

The formula for the slope (m) calculated from two points [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) are points

We have the needed information to calculate the slope, but let's label the values of the points to avoid any confusion

[tex]x_{1}[/tex]=0

[tex]y_{1}[/tex]=0

[tex]x_{2}[/tex]=-2

[tex]y_{2}[/tex]=3

Now substitute their values into the equation and find m

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

m=[tex]\frac{3-0}{-2-0}[/tex]

subtract

m=[tex]\frac{3}{-2}[/tex]

so the slope of the line is [tex]\frac{3}{-2}[/tex]. It can also be rewritten as [tex]\frac{-3}{2}[/tex]

Here is the equation of the line so far:

y=[tex]\frac{-3x}{2}[/tex]+b

we need to find b

As the equation passes through both (0,0) and (-2,3), we can use either one of them to solve for b

Let's take (0,0) for this case

Substitute 0 as x and 0 as y

0=-[tex]\frac{3}{2}[/tex](0)+b

multiply

0=0+b

add 0 to both sides

0=b

So b is 0

The equation of the line therefore is y=[tex]\frac{-3x}{2}[/tex]

Hope this helps!

Answer:

t > 28

Step-by-step explanation:

Answer:

Enlargement

k =[tex]\frac{18}{4}[/tex] =  [tex]\frac{9}{2}[/tex]

Step-by-step explanation:

k = [tex]\frac{new}{old}[/tex]

If k > 1 then its an enlargement.

If k < 1 then its a reduction

Answer:

Solution given:

Cos X=Adjacent/hypotenuse

Cos X=6.5/8.4

x=Cos-¹(6.5/8.4)

x=39.3°

Answer:

R = (-3, 8).

Step-by-step explanation:

Recall the midpoint formula:

[tex]\displaystyle M=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)[/tex]

Where M is the midpoint, (x₁, y₁) is one point and (x₂, y₂) is another.

We are given that Q is the midpoint of PR, where P = (11, -2) and Q = (4, 3) and we want to find the coordinates of R.

Substitute Q for M and let P(11, -2) be (x₁, y₁). Hence:

[tex]\displaystyle (4, 3)=\left(\frac{11+x_2}{2}, \frac{-2+y_2}{2}\right)[/tex]

Split into two separate equations:

[tex]\displaystyle \frac{11+x_2}{2}=4\text{ and } \frac{-2+y_2}{2}=3[/tex]

Solve for each case:

[tex]\displaystyle 11+x_2=8\Rightarrow x_2=-3[/tex]

[tex]\displaystyle -2+y_2=6\Rightarrow y_2=8[/tex]

Therefore, our second point (x₂, y₂) is (-3, 8).

Hence, R = (-3, 8).

Answer:

(15/2),(1/2)

Step-by-step explanation:

(x1 + x2 / 2)  ,   (y1 + y2) / 2)

(11 + 4 / 2) , (-2 + 3 / 2)

(15/2) , (1/2)

4 x minus four-fifths = 2 and one-fifth; x = three-fourths of a pound

Answer:

sin o = opposite/hypotenuse

sin o= 7/12

Answer:

41.34

Step-by-step explanation:

80/1.94

= 41.34

Answer:

Estimating the economic impact of climate change from weather variation

Step-by-step explanation:

Estimating the economic impact of climate change from weather variation:If economists are going to be able to offer clear guidance about the appropriate ambition of climate change policy, we need firmer damage estimates.This column introduces a new model that prices farmers’ ex-post and ex-ante adaptations to weather changes and forecasts. #accelerationism

Answer:

the first row in the table has x = -2 and f(x) = 1

therefore,

f(-2) = 1

f(x) = -2

when x = 4 as in 3rd row.

Answer:

the answer is 6803

Step-by-step explanation:

the first clock want to go next number and this number is 6 according to clockwise and second go 8 third go 0 and fourth go 3

Answer:

6803

Step-by-step explanation:

Answer:

10/3

Step-by-step explanation:

31/8= 3.8

10/3= 3.3

Answer:

<A = <B

=> 8x - 8 = 5x + 25

<=> 3x = 33

<=> x = 11

with x = 11 => mB = 5.11 + 25 = 55 + 25 = 80⁰

Answer:

x=11

B=80

Step-by-step explanation:

8x-8=5x+25

3x=33

x=11

B=5(11)+25

B=80

Answer:

Marcela tardó 6 horas y Roberto tardó 8 horas.

Step-by-step explanation:

Dado que Marcela tardó dos horas menos que Roberto en recorrer una distancia en bicicleta, y sabiendo que el producto de los dos tiempos es de 48 horas, para determinar cuánto tardó cada uno se debe realizar el siguiente cálculo:

M = X

R = X + 2

X x (X + 2) = 48

8 x 6 = 48

Por lo tanto, Marcela tardó 6 horas y Roberto tardó 8 horas.

Answer:

I dont know the answer for this question

Answer:

$49 hours

Step-by-step explanation:

12*40=$480

642-480= $162

$162/18= 9 hours more than 40

40+9=49 hours

Answer:

C

Step-by-step explanation:

use Pythagorean theorem

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

c is the longest side

if [tex]a^{2}[/tex] + [tex]b^{2}[/tex] > [tex]c^{2}[/tex] then it's acute (greater than)

if [tex]a^{2}[/tex] + [tex]b^{2}[/tex] < [tex]c^{2}[/tex] then it's obtuse   (less than)

if they are equal, then its a right triangle

[tex]6^{2}[/tex] + [tex]10^{2}[/tex] = [tex]12^{2}[/tex]

36 + 100 = 144

136 = 144

136 < 144   obtuse

The correct classification for this triangle is:

obtuse, because 6² + 10² < 12²

Option C is the correct answer.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

To determine the classification of a triangle based on its side lengths, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, we have a triangle with side lengths of 6 cm, 10 cm, and 12 cm. Checking the sum of the lengths of each pair of sides, we have:

6 + 10 = 16 > 12

6 + 12 = 18 > 10

10 + 12 = 22 > 6

Since all three pairs satisfy the triangle inequality theorem, the given side lengths do form a valid triangle.

Next, we can use the law of cosines to determine the measure of the largest angle in the triangle, which will allow us to classify it.

The law of cosines states that, for a triangle with side lengths a, b, and c, and the angle opposite c denoted as C, we have:

[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]

In this case, the side lengths are a = 6 cm, b = 10 cm, and c = 12 cm. Substituting these values into the formula and solving for cos(C), we get:

cos(C) = (6² + 10² - 12²) / (2 x 6 x 10)

cos(C) = -1/5

Since the cosine function is negative for angles between 90 and 180 degrees, we know that angle C is obtuse.

Therefore,

The correct classification for this triangle is:

obtuse, because 6² + 10² < 12²

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ7

Answer:

Amount Dan has = $17

Amount Ann has = $27

Amount Pablo has = $34

Step-by-step explanation:

Total amount they have = $78

Let

Amount Dan has = x

Amount Ann has = x + 10

Amount Pablo has = 2x

Total = Dan + Ann + Pablo

78 = x + (x + 10) + 2x

78 = x + x + 10 + 2x

78 = 4x + 10

78 - 10 = 4x

68 = 4x

x = 68/4

x = 17

Amount Dan has = x = $17

Amount Ann has = x + 10

= 17 + 10

= $27

Amount Pablo has = 2x

= 2(17)

= $34

Answer:

A

Step-by-step explanation: