Look at the figure. Complete the statement and justify your answer. line VT ≅ _____
line TX ; Reflexive Property of Congruence

line VX ; Reflexive Property of Congruence

line VX ; Converse of the Isosceles Triangle Theorem
line TX ; Converse of the Isosceles Triangle Theorem

Answer:

B. 1 1/7

Step-by-step explanation:

-9 2/7-(-10 3/7)

=-9 2/7+10 3/7

=1 1/7

Therefore, B. 1 1/7

Answer:

The answer is B

Step-by-step explanation:

B. 1 1/7

Answer: the Smaller number is 3

The larger number is 60

Step-by-step explanation:

Let x represent the smaller of the numbers.

Let y represent the larger number.

One number is 20 times another number. This means that

y = 20x

The product of the two numbers is 180. This means that

xy = 180- - - - - - - - - -1

Substituting y = 2x into equation 1, it becomes.

x × 20x = 180

20x² = 180

x² = 180/20 = 9

x = √9

x = 3

y = 20x = 20 × 3

y = 60

Answer:

i need more context

Step-by-step explanation:

Answer:

Tara bought a total of 160 treats.

Step-by-step explanation:

We are given the following in the question:

Number of boxes of dog treats = 3

Number of treats in each dog box = 40

Total number of treats in dog box =

[tex]40 \times 3 = 120[/tex]

Number of boxes of cat treats = 2

Number of treats in each cat box = 20

Total number of treats in cat box =

[tex]20\times 2 = 40[/tex]

Total number of treats Tara brought =

Total number of treats in dog box + Total number of treats in cat box

[tex](40\times 3)+(20\times 2)\\= 120 + 40\\=160[/tex]

Thus, Tara bought a total of 160 treats.

Answer:

8pi feet per second

Or, 25.1 feet per second (3 sf)

Step-by-step explanation:

C = 2pi×r

dC/dr = 2pi

dC/dt = dC/dr × dr/dt

= 2pi × 4 = 8pi feet per second

dC/dt = 25.1327412287

Answer: the height of the melted candies in the pot is 12.2 mm

Step-by-step explanation:

The formula for determining the volume of a square base pyramid is expressed as

Volume = area of base × height

Area of the square base = 12² = 144 mm²

Volume of each pyramid = 15 × 144 = 2160 mm³

The volume of 100 pyramid shaped chocolate candies is

2160 × 100 = 216000 mm³

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Since the pyramids was melted in the cylindrical pot whose radius is 75 mm, it means that

216000 = 3.14 × 75² × h

17662.5h = 216000

h = 216000/17662.5

h = 12.2 mm

Answer:

The height of the melted candies in the pot is 4.07mm

Step-by-step explanation:

H= 100*1/3(12)^2(15)/π(75)^2=64/5π=4.07

Answer:

There would be

13 x 8 x 4 x 3 = 3,276 different cheeseburger combinations

If the taste tester takes 10 minutes to eat a cheeseburger, then it would take him

3276 x 10 = 32760 minutes

Eating round the clock, it would take him

32760 / 60 = 546 hours

546 / 24 = 22 days 18 hours

Now these are the numbers I'm seeing

1313 buns

88 cheese

44 lettuces

33 tomatoes

There would be

1313 x 88 x 44 x 33 = 167,769,888 different cheeseburger combinations

If the taste tester takes 10 minutes to eat a cheeseburger, then it would take him

167769888 x 10 = 1,677,698,880 minutes

1677698880 / 60 = 27,961,647 hours

27961647 / 24 = 1,165,068.62 days

1165068.62 / 365 = 3,191.97 years

Step-by-step explanation:

cos (a - b) is 56/65

Step-by-step explanation:

Given sin a = 5/13, find cos a.

sin a = opposite side/hypotenuse = 5/13

The adjacent side can be found using Pythagoras Theorem.

Hypotenuse² = Opposite Side² + Adjacent Side²

⇒ Adjacent side² = Hypotenuse² - Opposite Side²

                             = 13² - 5² = 169 - 25 = 144

∴ Adjacent Side = 12

⇒ cos a = adjacent side/hypotenuse = 12/13

Given cos b = 3/5, find sin b.

cos b = adjacent side/hypotenuse = 3/5

The opposite side can be found using Pythagoras Theorem.

Hypotenuse² = Opposite Side² + Adjacent Side²

⇒ Opposite side² = Hypotenuse² - Adjacent Side²

                             = 5² - 3² = 25 - 9 = 16

∴ Opposite Side = 4

⇒ sin b = opposite side/hypotenuse = 4/5

Find cos(a - b).

cos(a - b) = cos a cos b + sin a sin b

               = 12/13 × 3/5 + 5/13 × 4/5

               = 36/65 + 20/65 = 56/65

Answer:

Answer in explanation

Step-by-step explanation:

The two laws are mathematical laws which are used in navigating problems which involves triangles. While the Pythagorean theorem is used primarily and exclusively for right angled triangle, the cosine rule is used for any type of triangle.

So, why is the cosine rule a stronger statement? The reason is not far fetched. As said earlier, the cosine rule can be used to resolve any triangle type while the Pythagorean theorem only works for right angled triangle. In fact, we can say the Pythagorean theorem is a special case of cosine rule. The reason why the expression is different is that, for the expression, cos 90 is zero, which thus makes our expression bend towards the Pythagorean expression view.

The explanation regarding the law of cosines is the stronger statement if compared with the Pythagorean theorem is explained below.

The Pythagorean theorem is used when there is the right-angled triangle, while on the other hand, the cosine rule is used for any type of triangle. Here the Pythagorean theorem should be considered for the special case of cosine rule. Due to this the cosine law should be stronger if we compared it with the Pythagorean theorem.

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Answer:

the answer is d

Step-by-step explanation:

Answer:

b = [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

period = [tex]\frac{2\pi }{b}[/tex], that is

b = [tex]\frac{2\pi }{period}[/tex] = [tex]\frac{2\pi }{\frac{3\pi }{4} }[/tex] = 2π × [tex]\frac{4}{3\pi }[/tex] = [tex]\frac{8}{3}[/tex]

Answer:

f(x) = 4cos(8/3)x - 3.

The missing space is 8/3.

Step-by-step explanation:

The general form is  f(x) = Acosfx + B    where A = the amplitude, f = frequency and B is the vertical shift..

Here A is given as  4,  B is - 3 and the frequency f = 2 π / period  =

2π / (3π/4)

= 8/3.

So the answer is f(x) = 4cos(8/3)x - 3.

Answer:

(1,-3)

Step-by-step explanation:

the x-axis for A is positive and the y-axis is negative. point A's X value is 1 because it is 1 point away from the origin and the value of the Y is 3 units away from the origin and it has to be negative.

Answer:

105 miles

Step-by-step explanation:

The question seeks to know the number of miles traveled by Tiera given that she received a certain amount of money in payment.

The total amount of money she received is $147. She receives $7 for every 5 miles traveled. The number of 5 miles traveled is calculated as 147/7 = 21

This means she traveled 5 miles 21 times.

Thus, the total number of miles she had traveled would be 21 * 5 = 105 miles in total

Answer:

The first zero after decimal point and 4 only

Step-by-step explanation:

Despite having 5 decimal points, the rules of significant figures dictate that unless there is a digit other than zero after, the only significant numbers are those that come before zero. For this case, the significant digits are only 0.04 but if it was 0.0400005 then all the other zeros would have also be considered significant.

Answer:

666.667 feet

Step-by-step explanation:

Slope = -1

Intercept = 10

y = -t + 10

y is the acceleration

Integrate y fornv

v = -t²/2 + 10t + c

At t=0, v=0 so c = 0

v = -t²/2 + 10t

Turns when v = 0,

-t²/2 + 10t = 0

t = 0, 20

Integrate v for s

s = -t³/6 + 5t² + c

At t = 0, s = 10

10 = c

s = -t³/6 + 5t² + 10

s at t=30,

-(30³)/6 + 5(30)² + 10

= 10m

(Back to starting point)

At t = 20,

Displacement in

-(20³)/6 + 5(20)² + 10

= 343.333

Total distance = 2(343.333-10)

= 666.6667

The total distance the car travels in this 30 second interval is 1333.34 units

From the graph, we have the following points

(0, 10) and (10, 0).

Start by calculating the slope (m) of the graph

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{0 - 10}{10-0}[/tex]

[tex]m =- \frac{10}{10}[/tex]

[tex]m =- 1[/tex]

The equation is then calculated as:

[tex]y = m(x -x_1) + y_1[/tex]

This gives

[tex]y = -1(x -0) + 10[/tex]

[tex]y = -1x+ 10[/tex]

[tex]y = -x+ 10[/tex]

The above equation represents the acceleration (y) as a function of time (x).

Integrate to get the velocity (v)

[tex]v = -\frac{x\²}{2} + 10x + c[/tex]

From the question, we have:

The velocity (v) of the car is 0, when the time (x) is 0.

So, we have:

[tex]0 = -\frac{0\²}{2} + 10(0) + c[/tex]

This gives

[tex]c = 0[/tex]

So, the equation becomes

[tex]v = -\frac{x\²}{2} + 10x + 0[/tex]

[tex]v = -\frac{x\²}{2} + 10x[/tex]

Set v = 0.

So, we have:

[tex]-\frac{x\²}{2} + 10x = 0[/tex]

Multiply through by -2

[tex]x^2 -20x = 0[/tex]

Factorize

[tex]x(x -20) = 0[/tex]

Split

[tex]x = 0\ or\ x -20 = 0[/tex]

Solve for x

[tex]x = 0[/tex] or [tex]x = 20[/tex]  

Integrate velocity (v) to get the displacement (d)

[tex]v = -\frac{x\²}{2} + 10x[/tex]

[tex]d = -\frac{t\³}{6} + 5t\² + c[/tex]

From the question, we have:

The position (d) of the car is 10, when the time (x) is 0.

So, we have:

[tex]-\frac{(0)\³}{6} + 5(0)\² + c = 10[/tex]

[tex]c = 10[/tex]

So, the equation becomes

[tex]d = -\frac{t\³}{6} + 5t\² + 10[/tex]

The position at 30 seconds is:

[tex]d = -\frac{(30)\³}{6} + 5(30)\² + 10[/tex]

[tex]d = 10[/tex]

The position at 20 seconds is:

[tex]d = -\frac{(20)\³}{6} + 5(20)\² + 10[/tex]

[tex]d = 676.667[/tex]

The total distance is then calculated as:

[tex]Total = 2 \times (d_2 -d_1)[/tex]

This gives

[tex]Total = 2 \times (676.667 -10)[/tex]

[tex]Total = 2 \times 666.667[/tex]

[tex]Total = 1333.34[/tex]

Hence, the total distance is 1333.34 units

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Answer:

3.5x + 15 ≥ 55

Step-by-step explanation:

I think the question below contains the missing information.

Josh has a rewards card for a movie theater. - He receives 15 points for becoming a rewards card holder. - He earns 3.5 points for each visit to the movie theatre. - He needs at least 55 points to earn a free movie ticket. Which inequality can Josh use to determine x, the minimum number of visits he needs to earn his firs free movie ticket?

My answer:

Let x is the number of times he visits = 3.5x

Total points = Points received on becoming a member + Points received on x visits

So,

Total Points = 15 + 3.5x

We know the total points must be at least 55 for a free movie ticket.  This can be expressed as:

3.5x + 15 ≥ 55

Answer:

12cm

Step-by-step explanation:

The scoop of Ice Cream is in the shape of a circular solid which is a Sphere.

For the ice cream to fit into the cone, the volume of the cone must be equal to that of the sphere.

Radius of the Sphere=3cm

Volume of a Sphere = [tex]\frac{4}{3}\pi r^3[/tex]

Volume of a Cone=[tex]\frac{1}{3}\pi r^2h[/tex]

[tex]\frac{1}{3}\pi X 3^2h=\frac{4}{3}\pi X 3^3\\\frac{1}{3}h=\frac{4}{3} X 3\\\frac{1}{3}h=4\\h=4 X 3=12cm[/tex]

The Cone of same radius must be 12cm tall.

Mrs. Caldwell will travel 135 miles at an additional 20 mph to catch up to Mr. Caldwell. Therefore, it will take Mrs. Caldwell 6.75 hours to catch up to Mr. Caldwell.

This is a rate time distance problem in mathematics, typically learned in middle school. To calculate how long it will take Mrs. Caldwell to catch up with Mr. Caldwell, we need to compare the distance traveled by each person in the same time. Because rate equals distance over time (r=d/t), we know that the distance each person traveled is rate x time.

Mr. Caldwell left 3 hours before Mrs. Caldwell, so he traveled at 45 mph for 3 hours, or 135 miles. Once Mrs. Caldwell leaves, she needs to cover these 135 miles at a faster speed to catch up. Her speed is 20 mph greater than Mr. Caldwell’s. We divide the distance that Mr. Caldwell has covered (135 miles) by the difference in their speeds (20 mph) to find it will take Mrs. Caldwell 6.75 hours to catch up to him.

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Answer:

2.8 units

You should get 2√(2) or √(8) which is less than 3 and greater than 2.

Answer: 2.8 units

Step-by-step explanation:

The formula for determining the distance between two points on a straight line is expressed as

Distance = √(x2 - x1)² + (y2 - y1)²

Where

x2 represents final value of x on the horizontal axis

x1 represents initial value of x on the horizontal axis.

y2 represents final value of y on the vertical axis.

y1 represents initial value of y on the vertical axis.

From the given points

x2 = 5

x1 = 3

y2 = 4

y1 = 2

Therefore,

Distance = √(5 - 3)² + (4 - 2)²

Distance = √2² + 2² = √4 + 4 = √8

Distance = 2.8 units

Final answer:

To find the solutions to the system of equations, use the substitution method. The solutions are (1/2, -3/2) and (7, 5).

Explanation:

To find the solutions to the system of equations, we can use the substitution method. First, solve one of the equations for y in terms of x. Let's solve the second equation for y:

y = x - 2

Now substitute this expression for y into the first equation:

x - 2 = 2x^2 - 8x + 5

Now we have a quadratic equation. Rearrange it into standard form:

2x^2 - 9x + 7 = 0

Next, factor the quadratic equation:

(2x - 1)(x - 7) = 0

Set each factor equal to zero and solve for x:

2x - 1 = 0, x - 7 = 0

x = 1/2, x = 7

Now substitute these values of x back into either of the original equations to find the corresponding values of y:

For x = 1/2: y = 1/2 - 2 = -3/2

For x = 7: y = 7 - 2 = 5

So the solutions to the system of equations are (1/2, -3/2) and (7, 5).

Answer:

x = 2

y = 2 +  t

z = -20 -20t

Step-by-step explanation:

First, we are going to find the equation for this parabola. We replace x = 2 in the equation of the paraboloid, thus:

[tex]z = 6-x-x^{2} -5y^{2}[/tex]

if x = 2, then

[tex]z = 6-(2)-2^{2}-5y^{2}[/tex]

[tex]z = -5y^{2}[/tex]

Now, we calculate the tangent line to this parabola at the point (2,2,-20)

The parametrization of the parabola is:

x = 2

y = t  

[tex]z = -5t^{2}[/tex]  since [tex]z = -5y^{2}[/tex]

We calculate the derivative

[tex]\frac{dx}{dt}= 0[/tex]

[tex]\frac{dy}{dt}= 1[/tex]

[tex]\frac{dz}{dt}= -10t[/tex]

we evaluate the derivative in t=2, since at the point (2,2,-20) y = 2 and y = t

Thus:

[tex]\frac{dx}{dt}= 0[/tex]

[tex]\frac{dy}{dt}= 1[/tex]

[tex]\frac{dz}{dt}= -10(2)= -20[/tex]

Then, the director vector for the tangent line is (0,1,-20)

and the parametric equation for this line is:

x = 2

y = 2 +  t

z = -20 -20t

The parametric equation of the tangent line is [tex]L(t)=(2,2+t,-20-20t)[/tex]

The equation of Paraboloid is,

                 [tex]z =6-x-x^{2} -5y^{2}[/tex]

Equation of parabola when [tex]x = 2[/tex] is,

       [tex]z=6-2-2^{2} -5y^{2} \\\\z=-5y^{2}[/tex]

The parametric equation of parabola will be,

     [tex]r(t)=(2,t,-5t^{2} )[/tex]

Now, we have to find Tangent vector to this parabola is,

    [tex]T(t)=\frac{dr(t)}{dt}=(0,1,-10t)[/tex]

We get, the point [tex](2, 2, -20)[/tex] when [tex]t=2[/tex]

The tangent vector will be,

 [tex]T(2)=(0,1,-20)[/tex]

The tangent line to this parabola at the point (2, 2, −20) will be,

     [tex]L(t)=(2,2,-20)+t(0,1,-20)\\\\L(t)=(2,2+t,-20-20t)[/tex]

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Answer:

m+p-n

Step-by-step explanation:

given that Jerry manages a local car dealership. At the beginning of the month, his lot had m vehicles. During the month his salesman sold n vehicles, and he purchased p vehicles more

We are to find the number of vehicles did the dealership have at the end of the month

At the end of the month the dealer would have

no of vehicles at the start of the month- sales of the vehicle in that month+Purchase of vechicles during that month

No of vehicles at the start of the month = m

Purchase during month                           =p

Total vehicles including purchase         = m+p

LESS: Vehicles sold in the month         =   n

No of vehicles at the end                      = m+p-n

Answer:

(96π + 160) cm2

Step-by-step explanation:

Answer:

P =  x³ − 9x² + 36x − 54

Step-by-step explanation:

Complex roots come in conjugate pairs.  So if 3−3i is a zero, then 3+3i is also a zero.

P = (x − 3) (x − (3−3i)) (x − (3+3i))

P = (x − 3) (x − 3 + 3i) (x − 3 − 3i)

P = (x − 3) ((x − 3)² − (3i)²)

P = (x − 3) ((x − 3)² + 9)

P =  (x − 3)³ + 9 (x − 3)

P =  x³ − 9x² + 27x − 27 + 9x − 27

P =  x³ − 9x² + 36x − 54

Answer:

Option C, SAS Postulate

Step-by-step explanation:

I think that it is option C because it does not give you 3 angles or 3 sides, it gives you 2 angles and 1 side.

Answer:  Option C, SAS Postulate

Answer:

5000 + x = 23600  

Step-by-step explanation:

a car that cost = 23600

down payment = 5000

So he needs to pay: 23600 - 5000 = 18600 more to get the car

Let x represent the amount he needs to pay more, an equation for his situation:

5000 + x = 23600  

Answer:

The answer to the question is

The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is  (-∞, 4)

Step-by-step explanation:

To apply look for the interval, we divide the ordinary differential equation by (t-4) to

y'' + [tex]\frac{3t}{t-4}[/tex] y' + [tex]\frac{4}{t-4}[/tex]y = [tex]\frac{2}{t-4}[/tex]

Using theorem 3.2.1 we have p(t) =  [tex]\frac{3t}{t-4}[/tex], q(t) =  [tex]\frac{4}{t-4}[/tex], g(t) = [tex]\frac{2}{t-4}[/tex]

Which are undefined at 4. Therefore the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution, that is where p, q and g are continuous and defined is (-∞, 4) whereby theorem 3.2.1 guarantees unique solution satisfying the initial value problem in this interval.

The existence and uniqueness theorems for ODEs determine that the longest interval where the initial value problem has a unique and twice-differentiable solution is (0, 4), avoiding discontinuities at t=0 and t=4.

The initial value problem provided is a second-order linear ordinary differential equation (ODE) of the form:

t(t-4)y"+3ty'+4y=2, with initial conditions y(3)=0 and y'(3)=-1.

To determine the longest interval in which the solution is guaranteed to be unique and twice-differentiable, we need to consider the existence and uniqueness theorems for ODE's, which are predicated on the functions of the equation being continuous over the interval considered. Here, the coefficients of y" and y' are t(t-4) and 3t respectively. The problematic points occur where the coefficient of y" is zero because it will make the equation not well-defined, which occurs at t=0 and t=4. Therefore, the longest interval around the initial condition t=3 that avoids these points is (0, 4). Within this interval, the coefficients are continuous, and hence, the conditions for the existence and uniqueness of the solution are satisfied.

Answer:

40/13

The decimal form is going to be 3.076

Answer:

A because the linesnever cross.

Step-by-step explanation:

Answer:

There is no solution

Step-by-step explanation:

Answer: the account that earned compound interest has the greater balance at the end of four years.

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the amount invested.

P represents the principal or amount invested.

R represents interest rate

T represents the duration of the investment in years.

From the information given,

P = 1000

R = 4%

T = 4 years

I = (1000 × 4 × 4)/100 = 160

Total amount earned is

1000 + 160 = $1160

The formula for determining compound interest is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 1000

r = 4% = 4/100 = 0.04

n = 1 because it was compounded once in a year.

t = 4 years

Therefore,.

A = 1000(1+0.04/1)^1 × 4

A = 1000(1.04)^4

A = $1170