Imagine that this graph represents the distance Brianna travels to get to her babysitting job with respect to time. Describe a relation that the graph may represent.

Answer:

a) [tex]cos(\alpha)=-\frac{3}{5}\\[/tex]

b)  [tex]\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]

c) [tex]\frac{4+3\sqrt{3} }{10}\\[/tex]

d)  [tex]\alpha\approx 53.1^o[/tex]

Step-by-step explanation:

a) The problem tells us that angle [tex]\alpha[/tex] is in the second quadrant. We know that in that quadrant the cosine is negative.

We can use the Pythagorean identity:

[tex]tan^2(\alpha)+1=sec^2(\alpha)\\(-\frac{4}{3})^2 +1=sec^2(\alpha)\\sec^2(\alpha)=\frac{16}{9} +1\\sec^2(\alpha)=\frac{25}{9} \\sec(\alpha) =+/- \frac{5}{3}\\cos(\alpha)=+/- \frac{3}{5}[/tex]

Where we have used that the secant of an angle is the reciprocal of the cos of the angle.

Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:

[tex]cos(\alpha)=-\frac{3}{5}[/tex]

b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:

[tex]cos (\beta)=\frac{1}{2} \\\\sin^2(\beta)=1-cos^2(\beta)\\sin^2(\beta)=1-\frac{1}{4} \\\\sin^2(\beta)=\frac{3}{4} \\sin(\beta)=+/- \frac{\sqrt{3} }{2} \\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]

where we took the positive value, since we know that the angle is in the first quadrant.

c) We can now find [tex]sin(\alpha -\beta)[/tex] by using the identity:

[tex]sin(\alpha -\beta)=sin(\alpha)\,cos(\beta)-cos(\alpha)\,sin(\beta)\\[/tex]

Notice that we need to find [tex]sin(\alpha)[/tex], which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:

[tex]sin(\alpha)=\sqrt{1-cos^2(\alpha)} \\sin(\alpha)=\sqrt{1-\frac{9}{25} )} \\sin(\alpha)=\sqrt{\frac{16}{25} )} \\sin(\alpha)=\frac{4}{5}[/tex]

Then:

[tex]sin(\alpha -\beta)=\frac{4}{5}\,\frac{1}{2} -(-\frac{3}{5}) \,\frac{\sqrt{3} }{2} \\sin(\alpha -\beta)=\frac{2}{5}+\frac{3\sqrt{3} }{10}=\frac{4+3\sqrt{3} }{10}[/tex]

d)

Since [tex]sin(\alpha)=\frac{4}{5}[/tex]

then  [tex]\alpha=arcsin(\frac{4}{5} )\approx 53.1^o[/tex]

Answer:

H = 0.95 feet

Step-by-step explanation:

The circumference of Earth = 2πR

My belt = 2πR    (Where R is the radius of the Earth)

Peter's belt = 2πR+6

We have to find the Height "h" so the radius of the circle for Peter's belt becomes R+h So the expression becomes 2π(R+h)

But we already know,

Peter's belt = 2πR+6

So,

2πR+6 = 2π(R+H)

2πR + 6 = 2πR + 2πH

Subtracting 2πR to both sides

=> 6 = 2πH

OR

=> H = 6/2π

=> H = 3/π

Where π = 3.14

=> H = 0.95 feet

Answer: 0.00016 miles

Step-by-step explanation:

According to Google, the circumference of the Earth is 24,901.461 miles. Using the formula 2*pi*r = circumference, the radius of your belt is around 3963.19061 miles. Now, 6 feet is 0.001 miles. So his belt is 24,901.461+0.001 = 24,901.462 miles. Use 2*pi*r to get 3963.19077 miles, a full 0.00016 miles above the surface!

Answer:

the answer is 12

Step-by-step explanation:

because (6, 12) x axis is 6, and the 12 is the y axis. Meaning that you would go 12 along the y axis.

Answer:

I believe the answer is 12

Hey there! :)

Answer:

56.7 kg.

Step-by-step explanation:

Use the density formula to solve for the mass:

D = m/V.

Rearrange in terms of mass, or 'm':

DV = m.

Solve for the volume:

0.06 × 0.9 × 1.5 = 0.081 m³.

Plug this into the equation along with the density:

700 × 0.081 = 56.7 kg.

Answer:

Length = (x^2-6x-7)m²/ (x-7)m

Step-by-step explanation:

let L =length

let W= width

let A = area of the rectangle.

if A = L × W

making L the subject, divide both side by W

A/W= L×W/W

therefore, L =A/W

L= (x²-6x-7)m²/(x-7)m

Answer:

x = 5, -6

Step-by-step explanation:

Step 1: Write out equation

x² + 2x - 25 = x + 5

Step 2: Move everything to one side

x² + x - 30 = 0

Step 3: Factor

(x - 5)(x + 6) = 0

Step 4: Find roots

x - 5 = 0

x = 5

x + 6 = 0

x = -6

Answer:

[tex]\frac{13}{3}[/tex] ÷ [tex](-\frac{5}{6})[/tex]

Step-by-step explanation:

[tex]4\frac{1}{3}/(-\frac{5}{6})=\\\\\frac{13}{3}/(-\frac{5}{6})[/tex]

Answer:

13/3  ÷ - 5/6

Step-by-step explanation:

4 1/3 ÷ - 5/6

Change the mixed number to an improper fraction

4 1/3 = (3*4 +1)/3 = 13/3

13/3  ÷ - 5/6

Answer:

A: There is only one solution since the two lines meet up. If it was parallel or the two lines where on top of each other there would be either an infinite amount of solutions or zero.

B:(3,5)

Step-by-step explanation:

Answer:

336 cm3

Step-by-step explanation:

Using Cavalieri’s principle, this volume is the same as for a right rectangular prism with these dimensions. Apply the formula for volume of a rectangular prism:

V = lwh

V = (6)(4)(14)

V = 336 cm3

Answer:

13

Step-by-step explanation:

Evaluate 3² then add and subtract, that is

10 + 3² - 6

= 10 + 9 - 6

= 19 - 6

= 13

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

12x + 3y = 15

Express it in the form y = mx + c

3y = -12x + 15

Divide all terms by 3

y = - 4x + 5

From the equation m = - 4

Since the lines are parallel their slope are also the same

So the slope of the parallel line is also - 4

Hope this helps you

Answer:

The answer would be A. because AB/EF=BC/DE

Step-by-step explanation:

AB = 2

EF = 5

BC = 1

DE = 2.5

2/5 = 0.4

1/2.5 = 0.4

The equation AB/EF=BC/DE is correct. All of the others are not.

The slope of line segment AC the same as the slope of line segment DF in the figure below because AB/EF = BC/DE.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

We need to find the proportionality statement for the ratio of the sides of the triangles.

If two triangles are similar, then the corresponding sides are proportional.

ABC ≈ DEF,

Here AB, BC, and AC are corresponding sides of DE, EF, and DF respectively.

Using the definition of similarity we ge

AB = 2

EF = 5

BC = 1

DE = 2.5

2/5 = 0.4

1/2.5 = 0.4

The equation AB/EF = BC/DE is correct. All of the others are not.

Learn more about a triangle;

https://brainly.com/question/7116550

#SPJ2

Answer:

0.16 P(Yellow or Brown)=0.16

Answer: 0.44

Step-by-step explanation:

0.4 + 0.28 = 0.68

1.00 - 0.68 = 0.32

0.32 divided by 2.0 = 0.16

Total answer is 0.44

GLAD TO HELP:)

HAVE A NICE DAY!

BTW: I WAS DOING A TEST, BUT TOOK MY TIME TO HELP YOU! :)

PLEASE BRAINLEST ME!

Hey there! :)

Answer:

5.

Step-by-step explanation:

The pattern of this puzzle is to take the bottom two numbers of the triangle, find the sum, then divide by the top number. For example:

8 + 4 = 12 --> 12/3 = 4.

5 + 13 = 18 --> 18/6 = 3.

9 + 5 = 14 --> 14/2 = 7.

Therefore:

14 + 6 = 20 --> 20/4 = 5. The missing number is 5.

Answer: 5

Step-by-step explanation:

Answer:

See the explanation

Step-by-step explanation:

The function given to us is:

f(x) = (1/3)⁻ˣ

We can convert the negative power into positive one by interchanging the numerator and denominator.

f(x) = (3/1)ˣ

f(x) = 3ˣ

Substitute value for x= -3 , -2, -1, 0, 1, 2, 3

f(-3) = 3⁻³ = 0.037

f(-2) = 3⁻² = 0.111

f(-1) = 3⁻¹ = 0.333

f(0) = 3⁰ = 1

f(1) = 3¹ = 3

f(2) = 3² = 9

f(3) = 3³ = 27

f(4) = 3⁴ = 81

and so on

The table of the found values of f(x) or y for the corresponding values of x, along with their graph is given below.

Answer:  A

Since you already have an equation just put in how many stickers and erasers she wants to get: 0.35(2)+0.99(2)+0.59≤4.

Then you multiply: .35(2)=.70. .99(2)=1.98.

Then add: .70+1.98+.59=3.27, so yes she can since 3.27 is less than 4 so the answer is A

Answer:

A. yes, because the total will be $3.27

Step-by-step explanation:

0.35x + 0.99y + 0.59 ≤ 4

0.35(2) + 0.99(2) + 0.59 ≤ 4

0.70 + 1.98 + 0.59 ≤ 4

3.27 ≤ 4

Answer:

The number is 5250

Step-by-step explanation:

5/6 * x = 4375

Multiply each side by 6/5 to isolate x

6/5 * 5/6 x = 4375 * 6/5

x =5250

Answer:

5250

Step-by-step explanation:

5/6x= 4375

x= 4375*6/5

x= 5250

Answer:

The answer is option c.

There are no x-intercepts

Hope this helps

Answer:

(a) y = -3/5 x + 13/5

(b) y = 5/3 x + 1/3

Step-by-step explanation:

(a) The slope of the tangent line is dy/dx.  Use implicit differentiation:

x² + y² + 4x + 6y − 21 = 0

2x + 2y dy/dx + 4 + 6 dy/x = 0

2x + 4 + (2y + 6) dy/dx = 0

x + 2 + (y + 3) dy/dx = 0

(y + 3) dy/dx = -(x + 2)

dy/dx = -(x + 2) / (y + 3)

At the point (1, 2), the slope is:

dy/dx = -(1 + 2) / (2 + 3)

dy/dx = -3/5

Using point-slope form of a line:

y − 2 = -3/5 (x − 1)

Simplifying to slope-intercept form:

y − 2 = -3/5 x + 3/5

y = -3/5 x + 13/5

(b) The normal line is perpendicular to the tangent line, so its slope is 5/3.  It also passes through the point (1, 2), so point-slope form of the line is:

y − 2 = 5/3 (x − 1)

Simplifying to slope-intercept form:

y − 2 = 5/3 x − 5/3

y = 5/3 x + 1/3

Answer:

1. equilateral triangle

2. rectangle

3. circle area

4. trapezoid

5. circle circumference

6. parallelogram

7. regular polygon

8. triangle

Hope that helps.

Answer:

x >5

Step-by-step explanation:

-4(3-X) > 8

Divide by -4, remembering to flip the inequality

-4/-4(3-X) < 8/-4

3-x < -2

Subtract 3 from each side

3-x-3 < -2-3

-x <-5

Divide by -1, remembering to flip the inequality

x >5

Answer:

[tex]c.[/tex] [tex]5<x[/tex]

Step-by-step explanation:

[tex]-4(3-x)>8\\3-x>-2\\-x>-5\\x>5[/tex]

Answer:

(a,c) ∪ (f, g)

Step-by-step explanation:

The function is:

Draw the slope of the tangent lines of several points on the curve,

Answer:

The height of the tree is about 30 feet.

Step-by-step explanation:

tan(55) = h/21

*21          *21

21*tan(55)=h

29.99=h

h=29.99=30 feet

The height of the tree will be 30 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Given; A tree casts a shadow 21 m long.

The angle of elevation of the sun is 55°.

Let h be the height of tree.

Then the height of the tree will be;

tan(55) = h/21

21*tan(55)=h

29.99=h

h = 29.99 = 30 feet

Therefore, The height of the tree will be 30 feet.

More about the right-angle triangle link is given below;

brainly.com/question/3770177

#SPJ2

Answer: 5x + 1

Step-by-step explanation:

f(x) - g(x)

(3x + 2) - (-2x + 1)       Here you distribute the negative sign to (-2x + 1)

3x + 2 + 2x - 1            Here you combine like terms

5x + 1                         This is the answer.

Answer:

1. The train is will cross the tunnel in 2 minutes.

The train is traveling at 30 km every hour or 60 minutes, so it will move 1 km every 60/30 minutes, or every 2 minutes.

2. Explanation here first: 22 free throws means 22 points and 22 field goals.

184-22=162 points they still needed to get, and

85-22=63 goals they still needed to score

We can now use a system of equations, (where x is 3-point goals, and y is 2-point goals) to solve the problem:

3x+2y=162

x+y=63 (-2)

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

3x+2y=162

-2x-2y= -126

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

x=36, and y=27 so the NBA players got 36 3-point goals, and 27 2-point goals

We can check this:

(36*3) + (27*2) + 22 = 108+54+22 = 184 total points

Step-by-step explanation:

Hope this helps!

Answer:

30.25

Step-by-step explanation:

Answer:     2.345

Step-by-step explanation:

The square root of 5.5 is 2.345.

Answer:

what is the answer?

Step-by-step explanation:

Answer:

C. $6/hour

Step-by-step explanation:

AP3X

Answer:

Option A.

Step-by-step explanation:

Note: The given function should be [tex]f(x)=\dfrac{2}{5}(10)^x[/tex] instead of [tex]f(x)=(10)^x[/tex].

Consider the given function is  

[tex]f(x)=\dfrac{2}{5}(10)^x[/tex]

We need to find the function which represents a reflection of f(x) across the x-axis.

If a function f(x) is reflected across the x-axis, then the new function is

[tex]g(x)=-f(x)[/tex]

Using this rule, we get

[tex]g(x)=-\dfrac{2}{5}(10)^x[/tex]        [tex][\because f(x)=\dfrac{2}{5}(10)^x][/tex]

Therefore, the correct option is A.

Answer:

The probability that the combined sample tests positive  for the virus is 0.083

Since the probability that combined sample test positive for the virus is greater than 0.05, it is not likely for such a combined  sample to test positive.

The probability that the combined sample will test positive is 0.083

Step-by-step explanation:

Given that:

The probability of a randomly selected adult in one country being infected with a certain virus is 0.003.

P = 0.003

number of blood sample size n = 29

The probability mass function of X is as follows;

[tex]P(X=x) = \left[\begin{array}{c}{29}&x\\\end{array}\right] (0.003)^x (1-0.003)^{29-x}[/tex]

Thus; the required probability is;

[tex]P(X \geq 1) = 1 - P ( X < 1)[/tex]

[tex]P(X \geq 1) = 1 - P ( X =0)[/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} \dfrac{29!}{0!(29-0)!} \ \ \times 0.003)^0 \times (1-0.003)^{29-0}}\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} 1 \times 1 \times ( 0.9166)\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - 0.9166[/tex]

[tex]P(X \geq 1) = 0.0834[/tex]

Therefore; the probability that the combined sample tests positive  for the virus is 0.083

Is it unlikely for such a combined  sample to test positive?

P(combined  sample test positive  for the virus ) = 0.0834

Since the probability that combined sample test positive for the virus is greater than 0.05, it is not likely for such a combined  sample to test positive.

The probability of a randomly selected adult in one country being infected with a certain virus is 0.003.

P = 0.003

number of blood sample size n = 29

The probability mass function of X is as follows;

[tex]P(X=x) = \left[\begin{array}{c}{29}&x\\\end{array}\right] (0.003)^x (1-0.003)^{29-x}[/tex]

Thus; the required probability is;

[tex]P(X \geq 1) = 1 - P ( X < 1)[/tex]

[tex]P(X \geq 1) = 1 - P ( X =0)[/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} \dfrac{29!}{0!(29-0)!} \ \ \times 0.003)^0 \times (1-0.003)^{29-0}}\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} 1 \times 1 \times ( 0.9166)\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - 0.9166[/tex]

[tex]P(X \geq 1) = 0.0834[/tex]

The probability that the combined sample will test positive is 0.083

Answer:

12 rational

Step-by-step explanation:

2√3×√12 =

= 2√3×√2²·3

= 2√3×2√3

= 2×2×√3×√3

= 4×3

= 12