What are the new vertices of the triangle under the translation (x, y) (x − 1, y − 3)?

Answer:

Ben has mixed up the digit for millions and hundred thousands: he wrote 5 in the place for millions and 6 in the place for hundred thousands, but it should be the other way. I think that he should exchange those two digits in the faulty report.

Answer:

1. C

2. A

3. C

Step-by-step explanation:

1. The equation is most easily solved through the quadratic formula since it’s a term is greater than 1.

2. The equation is most easily factored since it’s a term is 1.

3. The equation is most easily solved by the quadratic formula since it’s a term is greater than 1.

The change in variables s=x+3y, t=y to find the area of the ellipse x²+6xy+10y²≤1 yields; s² +t²≤ 1.

It follows from the equations given that;

Hence, it follows from substitution that;

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By applying a change of variables to the ellipse equation x2+6xy+10y2≤1, this simplifies to the standard ellipse equation from which the area, π*sqrt(10), can be determined using the standard formula for the area of an ellipse.

To find the area of the ellipse defined by the equation x2+6xy+10y2≤1, we can begin by using the provided change of variables, s = x + 3y and t = y. This transformation simplifies the equation of the ellipse to: (s^2) / 10 + (t^2) ≤ 1.

Now the expression looks like the standard equation of an ellipse, where 'a' (the radius on the x-axis) is sqrt(10) and 'b' (the radius on the y-axis) is 1. The area 'A' of an ellipse is given by 'A=πab'. Substituting 'a' and 'b' into the formula gives us 'A = π*sqrt(10)*1 = π*sqrt(10)'

This indicates that the area of the ellipse with the change of variables s=x+3y, t=y for the equation x2+6xy+10y2≤1 is π*sqrt(10).

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Answer:

∠PQR=30°

Step-by-step explanation:

I assuming that the measure of angle PQR is the third internal angle of the triangle

Remember that

The sum of the internal angles of a triangle must be equal to 180 degrees

80°+70°+∠PQR=180°

150°+∠PQR=180°

∠PQR=180°-150°

∠PQR=30°

Answer:

The answer is 30 degrees

Step-by-step explanation:

(80+70) - 180 = 30

because all the angles should add up to 180 degrees so to double check your answer you do 30+70+80=180

Answer:

  6

Step-by-step explanation:

There are 2 service choices and 3 grade choices for each, a total of 2×3 = 6 choices.

Answer:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

y = tan(2x - π)

y = tan (2*(x-π/2))

We can compare it to its parent function

g(x) = tan(x)

The answer is

Option a.

Horizontal shrink by 1/2 and horizontal shift of π/2 to the right

Answer:

a) h(x)

b) q(x)

c) w(x)

Step-by-step explanation:

Finding the answers for this is easy.  Take two values for x that shows a different Y-value for each function on the graph and place them in the equations suggested to see which equation match their Y-value on the graph.

Let's take x = -1 and x = 1.

a) h(x) = | -x + 3 |

| - (-1) + 3| = | 4 | = 4

| - 1 + 3 | = | 2 | = 2

h(x) passes through (-1,4) and (1,2)

b)  q(x) = | x | + 3

|-1| + 3 = 4

| 1 | + 3 = 4

q(x) passes through (-1,4) and (1,4)

c) w(x)  = | x+ 3 |

| -1 + 3 | = | 2 | = 2

| 1 + 3 | = | 4 | = 4

w(x) passes through (-1,2) and (1,4)

For this case we have that by definition, the surface area of a cone is given by:

[tex]SA = \pi * r * S + \pi * r ^ 2[/tex]

Where:

SA: It is the surface area

A: It's the radio

S: It's slant height

Then, replacing the values of the figure in the formula we have:

[tex]SA = \pi * 6 * 15 + \pi * 6 ^ 2\\SA = 90 \pi + 36 \pi\\SA = 126 \pi \ units ^ 2[/tex]

ANswer:

Option A

Answer:

Step-by-step explanation:

1. Equation of a circle:

(x - h)² + (y - k)² = r²

where (h, k) is the center and r is the radius.

If (h, k) is (2, 8) and r = 10:

(x - 2)² + (y - 8)² = 100

2. The vertex and focus have the same x-coordinate, so this is a vertical parabola.  Equation of a vertical parabola is:

y = 1/(4p) (x - h)² + k

where (h, k) is the vertex and p is the distance from the vertex to the focus.

If (h, k) is (2, 2) and p = 5-2 = 3:

y = 1/12 (x - 2)² + 2

3. The directrix is a vertical line, so this is a horizontal parabola.  Equation of a horizontal parabola is:

x = 1/(4p) (y - k)² + h

The distance between the directrix and the vertex is the same as p.

If (h, k) is (5, 2) and p = 5-3 = 2:

x = 1/8 (y - 2)² + 5

Answer:

B

Step-by-step explanation:

The domain is the set of x values for which the function is defined.

The range is the set of y values for which the function is defined.

Attached is the graph of the exponential function.

It is the basic graph of exponential function of y = 5^x which is shifted 6 units above (because of +6 at the end).

Looking at the graph, the domain is the set of all x values.

The range is anything above 6.

Correct answer is B.

Answer: b

Step-by-step explanation:

A P E X

Answer: “A”

Step-by-step explanation: Your Answer Would Be “A”

Answer:

A

Step-by-step explanation:

THAT IS THE BEST ANWSER OPTION

the equation would be y = 30 + x and if your brother will read for 15 minutes then you'll read for 45 minutes i believe.

The equation for the number of minutes you read, y, when your brother reads x number of minutes is y = x + 30. Therefore, if your brother reads for 15 minutes, you will read for 45 minutes.

To write an equation for the number of minutes you read, y, when your brother reads x number of minutes and you decide to read 30 minutes longer than him, you can represent this relationship as y = x + 30. This equation signifies that your reading time (y) is equal to your brother's reading time (x) plus an additional 30 minutes.

If your brother reads for 15 minutes (x=15), you can determine how many minutes you will read by substituting 15 into the equation for x, obtaining y = 15 + 30 = 45 minutes. Therefore, if your brother reads for 15 minutes, you will read for 45 minutes to stay ahead.

Answer:

There's no string in your question so zero. If you find out how long the string is just subtract it from the ribbon

Step-by-step explanation:

the answer is

10 × (4+3) = 70

Answer:

...so cos t = cot t can only happen when cos t is 0 or sin t is 1. (But sin t = 1 only happens when cos t = 0, so cos t = 0 is enough.)  

arccos(0) is pi/2, plus or minus any multiple of pi.

Step-by-step explanation:

cotθ = cosθ  

cosθ/sinθ = cosθ  

sinθ = 1  

θ = π/2

pi also = to 3.14 etc.

Answer:

Step-by-step explanation:

[tex]cot \theta = cos \theta\\ \frac {cos \theta}{sin \theta} = cos \theta[/tex]

An easy solution is if [tex]cos \theta = 0[/tex], or [tex]\theta = \frac \pi 2[/tex], plus or minus any number of half circles.

Answer:

The cost of a candy bar is [tex]\$1.5[/tex]

Step-by-step explanation:

Let

x----> the cost of a soda

y----> the cost of a candy bar

we know that

[tex]3x+4y=10.17[/tex]-----> equation A

[tex]2x+5y=10.28[/tex]-----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point [tex](1.39,1.5)[/tex]

see the attached figure

therefore

The cost of a soda is [tex]\$1.39[/tex]

The cost of a candy bar is [tex]\$1.5[/tex]

8+6+12+10 = 36

6+12+10 = 28

28/36

7/9

Hope this helps ❤️

Answer:  0.80

Step-by-step explanation:

P (2 ≤ x ≤ 4) is: P(X = 2) + P(X = 3) + P(X = 4)

                   =     0.36    +    0.12    +     0.32

                   =             0.48             +     0.32

                   =                            0.80

It can also be calculated as: 1 - P(X = 1)

                                           =  1 -  0.20

                                           =     0.80

Answer:

the answer is he rode 17 miles in the morning and 40 miles in the afternoon

Step-by-step explanation:

so in the afternoon, it says that 6 more than twice as many miles in the afternoon as in the morning. this means that if the morning is x then in the afternoon it will be 2x+6 but it says altogether it is 57 miles so the you have to add x too.

so the equation is 2x+6+x=57

then this should be easy to solve.

2x+6+x=57

3x+6=57

3x=51

x=17

so if the morning is 17 miles then the afternoon will be:

2(17)+6

this equals to 40.

I hope that this is helpful!

Answer:

11/12

Step-by-step explanation:

18/36 + 15/36= 33/36 = 11/12

The  probability that the chosen animal feeds on seeds or insects or both is:

                [tex]\dfrac{3}{4}[/tex]

Let A denote the event that the animal feed on seeds.

B denote the event that the animal feed on insects

and A∩B denote the event that the animal feed on both seed and insects.

and A∪B denote the event that the animal feeds on seeds or insects or both.

Let P denote the probability of an event.

Now, based on the information from the question we have:

[tex]P(A)=\dfrac{18}{36}\\\\P(B)=\dfrac{15}{36}\\\\P(A\bigcap B)=\dfrac{6}{36}[/tex]

Now, we know that:

[tex]P(A\bigcup B)=P(A)+P(B)-P(A\bigcap B)[/tex]

Hence, on putting the values we have:

[tex]P(A\bigcup B)=\dfrac{18}{36}+\dfrac{15}{36}-\dfrac{6}{36}\\\\\\P(A\bigcup B)=\dfrac{18+15-6}{36}\\\\\\P(A\bigcup B)=\dfrac{27}{36}=\dfrac{3}{4}[/tex]

Answer:

Chris is correct. (Choice letter C)

Step-by-step explanation:

We can eliminate choices A and B from the get-go because the problem stated that both hikers are traveling at 1mi/hr. This means that the slope of the equation would equate to 1, so just x.

That leaves us with C and D. The two equations both have a slope of 1, but C has a y-intercept of -2 and D has a y-intercept of 2, which represents the starting location of the second hiker. The first hiker is the one who is ahead by 2 miles, so it can't be D. This leaves us with choice C. Chris is correct.

Answer:

C. Chris said, “The equation y = x – 2 represents the distance traveled by the second hiker.”

Step-by-step explanation:

Answer:

CD = 9.2 cm

Step-by-step explanation:

The arc of any circle is calculated as

arc = circumference × fraction of circle

     = 2πr × [tex]\frac{66.4}{360}[/tex]

     = 2π × 7.9 × [tex]\frac{66.4}{360}[/tex]

     = [tex]\frac{2(7.9)(66.4)\pi }{360}[/tex] ≈ 9.2

arc CD is approximately 9.2 cm

Answer:

C

Step-by-step explanation:

Answer:

option c is the answer

hope it helps

and ur welcm

For this case it is observed that the border of the region is not dotted, then the inequality includes an equal.

Thus, we discard options C and D.

We substitute the point (0,0) and see if it is fulfilled:

[tex]y\geq\frac {3} {2} x-3\\0 \geq\frac {3} {2} (0) -3\\0 \geq0-3\\0 \geq-3[/tex]

It is fulfilled, so the correct option is A.

Answer:

Option A

Answer:

A. [tex]y\geq \frac{3}{2} x-3[/tex]

Step-by-step explanation:

We are given a graph and we are to determine which inequality is described by the graph.

Since the graph has a solid line that means that the inequality includes the points on the line and must contain an equal sign.

So we will substitute the point (0, 0) to find the correct inequality.

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

[tex]0\geq \frac{3}{2} (0)-3[/tex]

[tex]0\geq 3[/tex] - true

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

[tex]0\leq \frac{3}{2} (0)-3[/tex]

[tex]0\leq 3[/tex] - false

Therefore, the correct inequality is [tex]y\geq \frac{3}{2} x-3[/tex].

Answer:

the solution is (40, 21)

Step-by-step explanation:

Let the two numbers be x and y.

Then x + y = the sum = 61, and

         x - y = the difference = 19.

Solve the system of linear equations

x + y = 61

x - y  = 19

Combining these two equations:

x + y = 61

x - y  = 19

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

2x    =  80, so x must be 40.

Substituting 40 for x in the first equation, we get 40 + y = 61.  

Combining the constants, we get y = 21.

Then the solution is (40, 21).

The numbers whose sum is 61 and difference 19 are 40 and 21. This is obtained by using algebraic expression for the given condition.

Given that sum of numbers is 61 and difference is 19.

Let the larger number be x and smaller number be y.

Then we can write that, x+y=61 (sum) and x-y=19 (difference)

By solving the algebraic equations we can find the numbers.

(19+y) + y = 61

19+2y = 61

2y = 61 - 19 = 42

y=42/2=21 ⇒ y=21 is the smaller number

x = 19+y = 19+21 =40 ⇒ x=40 is the larger number

Hence the numbers whose sum is 61 and difference 19 are 40 and 21.

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Answer:

tan(Sin^-1 x/2)=  [tex]\frac{x/2}{\sqrt{1-x^{2}/4 } }[/tex]

Step-by-step explanation:

Let sin^-1 x/2= θ

then sinθ= x/2

on the basis of unit circle, we have a triangle with hypotenuse of length 1,   one side of length x/2 and opposite angle of θ.

          tan(Sin^-1 x/2) = tanθ

           tanθ= sinθ/cosθ

as per trigonometric identities cosθ= √(1-sin^2θ)

           tanθ= sinθ/ √(1-sin^2θ)

substituting the value sinθ=x/2 in the above equation

             tanθ= [tex]\frac{x/2}{\sqrt{1-x^{2}/4 } }[/tex]

now substituting the value sin^-1 x/2= θ in above equation

             tan(sin^-1 x/2) =  [tex]\frac{x/2}{\sqrt{1-x^{2}/4 } }[/tex]

!

Answer:

50%

Step-by-step explanation:

hence angle between vectors is option a ,173 degree

When an equation has both direction as well as magnitude it refers to vector equation.

Formula used [tex]\alpha =cos^{-1} (\frac{u.v}{|u||v|})[/tex]

u.v=1*(-1)+[tex]\sqrt{7} *(-4)[/tex]

|u|=[tex]\sqrt{ 1^{2} +\sqrt{7} ^{2}}[/tex]=[tex]2\sqrt{2}[/tex]

|v|=[tex]\sqrt{ (-1^{2}) +(-4^{2})[/tex]=[tex]\sqrt{17}[/tex]

[tex]\alpha =cos^{-1} (\frac{-1-4\sqrt{7} }{|2\sqrt{2} ||\sqrt{17} |})[/tex]

[tex]\alpha =cos^{-1} (\frac{-1-10.58}{2.82*4.12})[/tex]

[tex]\alpha =cos^{-1} (\frac{-11.58}{11.61})[/tex]

[tex]\alpha =cos^{-1} (-0.99)[/tex]

hence option a 173 degree is correct

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Answer:

Step-by-step explanation:

139 +10 = 149

149 / 8 = 18.625

round  to nearest hundredth = 18

Answer:

4 quarts

Step-by-step explanation: