In the figure below, lines A and B are parallel. Find the m∠5 if m∠1 = 75° and m∠3 = 40°

Answer:

x = 4cos(t) – 1 and y = 4sin(t) + 3

Step-by-step explanation:

Equation of a circle:

The equation of a circle has the following format:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

In which:

The centre is is [tex](x_0,y_0)[/tex] and r is the radius. The parametric equations are given by:

[tex]x(t) = r\cos{(t)} + x_0[/tex]

[tex]y(t) = r\sin{(t)} + y_0[/tex]

In this question:

[tex](x + 1)^2 + (y - 3)^2 = 4^2[/tex]

This means that the centre is [tex](-1,3)[/tex] and the radius is 4. So, the answer is:

x = 4cos(t) – 1 and y = 4sin(t) + 3

Answer: A = 28 B = 47 C = 105 in degrees

Step-by-step explanation:

OKAY JUST A DISCLAIMER:

I did Geometry last year and the concepts are basically gone but I think I remember how to do this one

So I think one of the theorems stated that the inner angle is half of the outer arc.

So.. angle a would be 56/2 = 28

Angle b would be 94/2 = 47

Angle C is a vertical angle to the angle in the triangle, so it would be 180-47-28=105

Answer:

3 busses and 5 vans

Step-by-step explanation:

3 x 51 = 153

193 - 153 = 40

40 / 8 = 5

Answer:

angle bisectors and opposite side perpendiculars

Step-by-step explanation:

Answer:

8 miles

Step-by-step explanation:

24 miles/6 hours = 4 miles per hour

4 miles per hour x 2 hours = 8 miles

Answer:

8 miles

Step-by-step explanation:

24/6 is your ratio. He runs 4 miles an hour, but we need 2 hours. 4x2=8 miles in 2 hours.

Step-by-step explanation:

6 customers per hour [tex]=1[tex] customer per 10 minutes

[tex]X \sim \operatorname{Exp}(\beta=10) \quad[/tex] (given mean)

Pdf is given by: [tex]f(x)=\frac{1}{\beta} e^{-x / \beta}, 0<x[/tex]

Pdf: [tex]f(x)=\frac{1}{10} e^{-x / 10}, \quad 0<x,[tex] and zero otherwise.

Cdf: [tex]P(X \leq x)=1-e^{-x / \beta}[/tex]

[tex]P(X \leq x)=1-e^{(-x / 10)} \quad[/tex] for [tex]x>0 \Longrightarrow P(X>x)=e^{-x / 10}[/tex]

a)[tex] \begin{array}{c}

P(X<12)=1-\exp (-12 / \beta)=1-e^{-1.2}=1-0.301194=0.698806 \approx 0.699 \\

P(X<12)=0.699 \end{array}[/tex]

[tex]\begin{aligned}

&\begin{array}{c}

P(X>20)=\exp (-20 / \beta)=e^{-2} \approx 0.135335 \approx 0.1353 \\

P(X>20)=0.1353

\end{array}\\[/tex]

&\text { c) }\\

&P(8<X<15)\\

&\begin{array}{l}

=P(X<15)-P(X<8) \\

=(1-\exp (-15 / \beta))-(1-\exp (-8 / \beta)) \\

=\exp (-8 / \beta)-\exp (-15 / \beta) \\

=e^{-0.8}-e^{-1.5} \\

=0.449329-0.22313 \approx 0.226199 \approx 0.2262 \\

\quad P(8<X<15)=0.2262

\end{array}

\end{aligned}

\begin{aligned}

&\text { d) }\\

&\begin{array}{l}

P(14<X<22) \\

=P(X<22)-P(X<14) \\

=(1-\exp (-22 / \beta))-(1-\exp (-14 / \beta)) \\

=\exp (-14 / \beta)-\exp (-22 / \beta) \\

=e^{-1.4}-e^{-2.2} \\

=0.246597-0.110803 \approx 0.135794 \approx 0.1358 \\

P(X<14 \cup X>22)=1-P(14<X<22)=1-0.1358=0.8642 \\

P(X<14 \cup X>22)=0.8642

\end{array}

\end{aligned}

Answer:

Step-by-step explanation:

100(133-380)/380=-65%

So the discount was 65%

Answer:

I think the answer is 672 please be right

Answer:

Amount = Initial value × (1 + rate of interest)^years and 374

Step-by-step explanation:

The formula to determine the student population and the estimated student population is given below:

As we know that

Amount = Initial value × (1 + rate of interest)^years

= 284 × (1 + 0.04)^7

= 284 × 1.04^7

= 373.72

= 374

Answer:

P≈28068.32

Step-by-step explanation:

Grace needs to invest, to the nearest cent, for the value of the account to reach $46,000 in 13 years is 27705.78944.

We have given that,

Grace is going to invest in an account paying an interest rate of 3.8% compounded continuously.

We have to determine how much would Grace need to invest, to the nearest cent, for the value of the account to reach $46,000 in 13 years.

[tex]A=Pe^{rt}[/tex]

A=46000, t=13  ,r=0.038

[tex]Pe^{0.039\left(13\right)}=46000[/tex]

[tex]Pe^{0.039\left(13\right)}=46000[/tex]

[tex]\frac{Pe^{0.039\cdot \:13}}{e^{0.507}}=\frac{46000}{e^{0.507}}[/tex]

[tex]P=\frac{46000}{e^{0.507}}[/tex]

[tex]\quad P=27705.78944[/tex]

Therefore, Grace needs to invest, to the nearest cent, for the value of the account to reach $46,000 in 13 years is 27705.78944.

To learn more about the account balance visit:

https://brainly.com/question/2151013

#SPJ2

Answer:

Volume of cuboid = 2000 m³

Step-by-step explanation:

Given the following data;

Base area = 500 m²

Height = 4m

To find the volume of a cuboid;

The volume of a cuboid is given by the formula;

Volume of cuboid = length * breadth * height

But remember, base area = length * breadth

Therefore, the volume of the cuboid becomes;

Volume of cuboid = base area * height

Substituting into the equation, we have;

Volume of cuboid = 500 * 4

Volume of cuboid = 2000 m³

Answer:

y = 15.75x + 25 is the linear equation

$88 would be the total cost

Step-by-step explanation:

First, create the equation using y = mx + b, where x is the number of hours:

y = 15.75x + 25 will be the equation, since the charge is $15.75 per hour and the flat fee is $25

There are 4 hours in between 8:30 AM and 12:30 PM, so to find the cost, plug in 4 as x and simplify:

y = 15.75x + 25

Plug in 4 as x:

y = 15.75(4) + 25

y = 63 + 25

y = 88

So, the total cost would be $88

Answer:

4ft

Step-by-step explanation:

Answer:

B. 12 in.

Step-by-step explanation:

Diameter = 5 in.

Diagonal = 13 in.

Apply Pythagorean theorem to find the height of the cylinder.

Thus:

13² - 5² = height²

144 = height²

√144 = height

12 in. = height

Answer:

B. 12 in.

Step-by-step explanation:

Answer:

B: y= 3(1/3)^x

Step-by-step explanation:

I graphed it on Desmos

Answer:

222 ft

Step-by-step explanation:

add 15 ft to each side of the length and width

L = 28 + 30 = 58

W = 23 + 30 = 53

perimeter = 2(L + W) = 2(58 + 53) = 222 ft

Answer:

222 ft

Step-by-step explanation:

The fence must be 15x2 (30) feet wider and 15x2 (30) feet longer, since the fence must be 15ft away at all points. Take 23+30 to find width, and take 28+30 to find length. You get that the fence is 53 ft. wide and 58 ft long. Feet of fencing is the same as asking for perimeter, so 53+53+58+58=222 feet of fencing

Answer:

Step-by-step explanation:

Answer:

V = J = 92

Step-by-step explanation:

The angles are the same on both shapes.

Answer:

C = dπ

37.68 = d(3.14)

d = 12 inches

2r = d

2r = 12

radius = 6 inches

Answer:

4

Step-by-step explanation:

because

8÷2=4

16÷4=4

24÷6=4

32÷8=4

Answer:

(x - 3)² + (y + 4)² = 49

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + *y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (3, - 4) and r = 7 , then

(x - 3)² + (y - (- 4) )² = 7² , that is

(x - 3)² + (y + 4)² = 49 ← equation of circle

Answer:

Answer:

50°

Step-by-step explanation:

Given that a triangle measures 180°.

∠U =40°

∠W=90°

Sum:130°

180°-130°=50°

Answer:

[tex]Fence = 41.408ft[/tex]

Step-by-step explanation:

Given

[tex]d = 24ft[/tex]

Required

Determine the length of the wall

First, we calculate the circumference (C) of the semi-circle

[tex]C =\pi d[/tex]

[tex]C = 3.142 * 24[/tex]

[tex]C = 75.408[/tex]

The length of the fence is calculated by subtracting the diameter from the circumference:

[tex]Fence = C - d[/tex]

[tex]Fence = 75.408ft - 24ft[/tex]

[tex]Fence = 41.408ft[/tex]

Answer:

-3

Step-by-step explanation:

Slopes of a perpendicular line are the opposite reciprocal.

So, the opposite of 1/3 is -1/3.

Then the reciprocal of -1/3 is -3 (since -3 is -3/1).

Answer:

your answer will be C. The function has an inverse because it passes the horizontal line test.

bye have a nice day ^_^

C. The function has an inverse because it passes the horizontal line test.

A function is a rule or a relation that associates each element of a non-empty set A, to at least a single element of another non-empty set B.

The relation f from a domain set to co-domain set is called function.

Example : f = {(x, y) | for all x∈X & y∈Y}

A relation becomes function when every element of domain has one and only one image in co-domain.

If f is a function which is one-one as well as on-to, i.e, if the function is bijective, then the inverse of this function exists and the inverse is then denoted by [tex]f^{-1\\}[/tex]

Inverse function of a function always undoes the operations of the function f.

f(a) = b if and only if f⁻¹ (b) = a , where a is from domain & b is from co-domain set.

From the above descriptions, we can see that, since the function passes through the horizontal line, so it has an inverse.

Hence the option C is the correct one.

C. The function has an inverse because it passes the horizontal line test.

Learn more about inverse function here :

https://brainly.com/question/11735394

#SPJ2

Answer:

A, C, and D are the exponential functions that have been simplified correctly

Answer:

Step-by-step explanation:

f(x) = 65536(b)^x

Find b by substituting a point. (1, 16384)

16384 = 65536(b)^1

b=0.25

Thus,

f(x) = 65536(1/4)^x

Plug in 6,

f(8) = 1