Andy was playing a memory game with his sister. He turned over a tile to reveal a picture of the sun at the coordinates (5, 4). He looked under a tile that was 3 units to the left and 2 units down but revealed a picture of a tree. His sister knew that the other sun was 1 unit to the left and 1 unit up from the tree. What are the coordinates of the second sun? (JUSTIFY)

Answer:

80

Step-by-step explanation:

If there is any cyclic quadrilateral, which is a quadrilateral inscribed inside a circle, there is one simple property that is

the opposite angles add upto 180.

Thus we can say

96 + c = 180

and

d + 100 = 180

Since we need d, we use 2nd equation:

d + 100 = 180

d = 180 - 100

d = 80

the question is already in slope intercept form.

The y-intercept is 12.

y=mx+b whereas m=slope, and b=y-intercept.

hope this helped!

The function is linear function of a form,

[tex]f(x)=ax+b[/tex]

Which always intersects point,

[tex]P(x, n)[/tex]

Or in this case,

[tex]f(x)=2x+12[/tex]

The point is therefore,

[tex]P(x,y)\Longrightarrow\boxed{P(x, 12)}[/tex]

The y-intercept is 12.

Hope this helps.

r3t40

Answer:

2^ (-1)

1/2

Step-by-step explanation:

Add the exponents which have common bases.

3 + (-4) = -1

2^ (-1)

1 / 2

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For more information, please comment below and I'll respond ASAP!

Answer:

The simplified form of the provided expression is [tex]2^{-1}\ or\ \frac{1}{2}[/tex]

Step-by-step explanation:

Consider the provided expression:

[tex](2^3)(2^{-4})[/tex]

Use the product rule of exponent:

[tex]a^m \cdot a^n=a^{m+n}[/tex]

Now use the above formula to simplify the provided expression.

[tex](2^3)(2^{-4})=2^{3+(-4)}[/tex]

[tex](2^3)(2^{-4})=2^{3-4}[/tex]

[tex](2^3)(2^{-4})=2^{-1}[/tex]

Hence, the simplified form of the provided expression is [tex]2^{-1}\ or\ \frac{1}{2}[/tex]

Answer:

640 miles per hour.

Step-by-step explanation:

I calculated this by 3200/5

Is this appropriate?

Answer:  The required scale factor of the dilation is 4.  

Step-by-step explanation:  Given that the parallelogram FGHJ was dilated and translated to form similar parallelogram F'G'H'J'.

We are to find the scale factor of the dilation.

From the graph, we note that

JH = 2 units   and   J'H' = 8 units.

We know that

[tex]\textup{Scale factor of dilation}=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the correponding side of the original figure}}.[/tex]

Therefore, the scale factor of the given dilation is

[tex]S=\dfrac{J'H'}{JH}\\\\\\\Rightarrow S=\dfrac{8}{2}\\\\\Rightarrow S=4.[/tex]

Thus, the required scale factor of the dilation is 4.  

Answer:

4 on edge

Step-by-step explanation:

Answer: 13

Step-by-step explanation:

2x-27=-1

2x=26

X=13

The expression of the given mathematical phrase Twenty-seven less than twice a number is -1 is 2x - 27 = -1 and that number will be 13.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given,

Twenty-seven less than twice a number is -1

Let's say that number is x.

Twice of x = 2x

27 less will be 2x - 27

It is equal to -1.

2x - 27 = -1

2x = -1 + 27

2x = 26

x = 13

Hence "The expression of the given mathematical phrase Twenty-seven less than twice a number is -1 is 2x - 27 = -1 and that number will be 13".

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Explanation:

Rewrite the left side in terms of sine and cosine, then rearrange.

[tex](1+\tan^2{A})+(1+\dfrac{1}{\tan^2{A}})=\dfrac{1}{\sin^2{A}-\sin^4{A}}\\\\(1+\dfrac{\sin^2{A}}{\cos^2{A}})+(1+\dfrac{\cos^2{A}}{\sin^2{A}})=\\\\\dfrac{\sin^2{A}+\cos^2{A}}{\cos^2{A}}+\dfrac{\sin^2{A}+\cos^2{A}}{\sin^2{A}}=\\\\\dfrac{1}{\cos^2{A}}+\dfrac{1}{\sin^2{A}}=\\\\\dfrac{\sin^2{A}+\cos^2{A}}{(\sin^2{A})(\cos^2{A})}=\\\\\dfrac{1}{(\sin^2{A})(1-\sin^2{A})}=\dfrac{1}{\sin^2{A}-\sin^4{A}} \qquad\text{Q.E.D.}[/tex]

Answer: x^2-6x-8

Step-by-step explanation:

Step 1 : Factor - x^3-11x^2+22x+40: (x-5)(x^2-6x-8)/(x-5)

Step 2 : Divide, which should give you x^2-6x-8

Answer:

27.5 m/s

275 m

Step-by-step explanation:

99 km/hr × (1000 m / km) × (1 hr / 3600 s) = 27.5 m/s

Distance = rate × time

d = 27.5 m/s × 10 s

d = 275 m

Answer:

[tex]\large\boxed{f^{-1}(x)=9x-18}[/tex]

Step-by-step explanation:

[tex]f(x)=\dfrac{1}{9}x+2\to y=\dfrac{1}{9}x+2\\\\\text{exchange x to y and vice versa}\\\\x=\dfrac{1}{9}y+2\\\\\text{solve for y}\\\\\dfrac{1}{9}y+2=x\qquad\text{subtract 2 from both sides}\\\\\dfrac{1}{9}y=x-2\qquad\text{multiply both sides by 9}\\\\9\!\!\!\!\diagup^1\cdot\dfrac{1}{9\!\!\!\!\diagup_1}y=9x-(9)(2)\\\\y=9x-18[/tex]

Answer:

x = - [tex]\frac{1}{2}[/tex], x = 3

Step-by-step explanation:

Given

2x² - 5x - 3 = 0 ← in standard form

Consider the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 3 = - 6 and sum = - 5

The factors are - 6 and + 1

Use these factors to split the x- term

2x² - 6x + x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(x - 3) + 1 (x - 3) = 0 ← factor out (x - 3) from each term

(x - 3)(2x + 1) = 0

Equate each factor to zero and solve for x

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]

x - 3 = 0 ⇒ x = 3

Answer:

Step-by-step explanation:

Area of rectangle = x³-5x²+3x-15

Width of rectangle = x²+3

Length of rectangle= ?

We will apply the formula:

Area= length* width

Hence we know the area and width.

x³-5x²+3x-15/x²+3 = length

By dividing the terms we get (x-5).

Thus the correct option is x-5....

See the attached picture for the solution.

Answer:

Option: C is the correct answer.

                   C. 80

Step-by-step explanation:

PG=9 in. The radius of the circle is 41 inches.

We know that the side CT is given by:

CT=CS+ST

The side CS is calculated by using the Pythagorean Theorem in ΔCSP

i.e.

[tex]CP^2=CS^2+SP^2\\\\i.e.\\\\[/tex]

as CP is the radius of the circle

and SP=PG=9 in.

i.e.

[tex]41^2=9^2+CS^2\\\\i.e.\\\\1681=81+CS^2\\\\i.e.\\\\CS^2=1681-81\\\\i.e.\\\\CS^2=1600\\\\i.e.\\\\CS=40\ units[/tex]

and

similarly in right angled triangle ΔPST

we have:

[tex]TP^2=ST^2+PS^2\\\\i.e.\\\\41^2=9^2+ST^2\\\\i.e.\\\\ST=40\ units[/tex]

Hence,

[tex]CT=CS+ST\\\\i.e.\\\\CT=40+40\\\\i.e.\\\\CT=80\ in.[/tex]

Answer:

12 cans with 3 left over

Step-by-step explanation:

It's pretty simple.

You already know you have 3 left over so all you have to do is 315 divided by 26.

315 ÷ 26 ≈ 12.12 but since you already know you have 3 left over, the answer would be 12.

Answer:

12 cans per carton

Step-by-step explanation:

Subtract the remainder of cans to the total amount.

315 - 3 = 312

Divide by the number of cartons.

312 / 36 = 12 cans per carton

Best of Luck!

Answer:

5.9

Step-by-step explanation:

The mean means arithmetic average (some people just say average here).

The average of 4 numbers is the sum of those 4 numbers divided by the number of numbers which is 4 in this case.

So we have this formula:

[tex]\frac{3.8+4.2+5.3+x}{4}=4.8[/tex]

Multiply both sides by 4:

[tex]3.8+4.2+5.3+x=4(4.8)[/tex]

Simplify:

[tex]13.3+x=19.2[/tex]

Subtract 13.3 on both sides:

[tex]x=19.2-13.3[/tex]

Simplify:

[tex]x=5.9[/tex]

Answer:

-4 is the mimumum of y=-3+cos(x+4)

Step-by-step explanation:

The minimum value of y=cos(x) is -1.

The minimum value of y=cos(x+4) is still -1; the +4 inside the cosine function only affected the horizontal shift.

The minimum value of y=-3+cos(x+4) is -3-1 which is -4.  This brought the graph down 3 units so if the minimum was previously -1 and it got brought down 3 units then it's new minimum is -4.

Answer:

C

Step-by-step explanation:

[tex] \sec( \alpha ) = \frac{1}{ \cos( \alpha ) } \\ \\ \sec( \alpha ) = \frac{1}{ \frac{ad}{hip} } \\ \\ \sec( \alpha ) = \frac{hip}{ad} \\ \\ \sec( \alpha ) = \frac{41}{40} [/tex]

The value of the secθ is 41/40.

Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.

For the given situation,

The diagram shows the right-angled triangle.

The sides of the right-angled triangle are

Hypotenuse side = 41 ft

Opposite side = 9 ft

Adjacent side = 40 ft

The value of secθ is

[tex]sec \theta =\frac{1}{cos \theta}[/tex]

where, [tex]cos \theta =\frac{adjacent}{hypotenuse}[/tex]

⇒ [tex]sec \theta =\frac{hypotenuse}{adjacent}[/tex]

⇒ [tex]sec \theta =\frac{41}{40}[/tex]

Hence we can conclude that the value of the secθ is 41/40.

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The vertices of the triangle are the points where any pair of lines intersect.

We start by setting up the system

[tex]\begin{cases}y=-x+2\\y=2x-1 \end{cases} \iff -x+2=2x-1 \iff 3x=3 \iff x=1[/tex]

Using one of the two equations we can derive the correspondent y value:

[tex]f(x)=-x+2 \implies f(1)=-1+2 = 1[/tex]

So, one vertex is (1, 1)

We choose the other two pairs of lines to find the other vertices:

[tex]\begin{cases}y=-x+2\\y=x-2 \end{cases} \iff -x+2=x-2 \iff x=2 \implies y = 0[/tex]

[tex]\begin{cases}y=x-2\\y=2x-1 \end{cases} \iff x-2=2x-1 \iff x=-1 \implies y=-3[/tex]

So, the three vertices are (1, 1), (2, 0), (-1, -3).

Answer:

(1, 1), (2, 0), and (-1, -3)

Step-by-step explanation:

I got right on the test.

Answer:

The first graph represents how many of each order could be put in a bag hanging from the hook ⇒ 1st

Step-by-step explanation:

* Lets explain how to solve the problem

- The order of jumbo paperclips weighs 2 pounds

- x is the number of orders of paperclips

∴ The weight of the paperclips order is 2 × x = 2x

- The order of packing tape weighs 3 pounds

- y is the number of orders of packing  tape

∴ The weight of the tape order is 3 × y = 3y

- The weight of the total order is 2x + 3y

- The hook can hold no more than 6 pounds

∴ 2x + 3y ≤ 6

- Lets find the graph which represent this inequality

∵ The equation of any line is y = mx + c, where m is the slope of the

  line and c is the y-intercept

- The y-intercept means substitute x in the equation by 0

- The x- intercept means substitute y in the equation by 0

∵ The inequality is 2x - 3y ≤ 6

∵ The equation of the line is 2x + 3y = 6

- Subtract 2x from both sides

∴ 3y = 6 - 2x

- Divide both sides by 3

∴ y = 6/3 - 2/3 x

∴ y = 2 - 2/3 x

- Find the y-intercept

∵ x = 0

∴ y = 2

∴ The line intersect the y-axis at point (0 , 2)

- Find the x-intercept

∵ y = 0

∴ 0 = 2 - 2/3 x

- Add 2/3 x to both sides

∴ 2/3 x = 2

- Multiply both sides by 3

∴ 2 x = 6 ⇒ divide both sides by 2

∴ x = 3

∴ The line intersect the x-axis at point (3 , 0)

- From the figure the first and the second figures have the same

 x-intercept and y-intercept

∵ The inequality is 2x + 3y ≤ 6

- The sign ≤ means the line is sold and the shading is under the line

∴ The first figure is the answer

* The first graph represents how many of each order could be put in a

  bag hanging from the hook

Answer:

Option A.

Step-by-step explanation:

Let x is the number of orders of paperclips and y is the number of orders of packing tape.

An order of jumbo paperclips weighs 2 pounds and an order of packing tape weighs 3 pounds.

Total weight = [tex]2x+3y[/tex]

A hook in an office storage closet can hold no more than 6 pounds. It means total weight must be less than or equal to 6 pounds.

[tex]2x+3y\leq 6[/tex]

The related equation is

[tex]2x+3y=6[/tex]

Substitute x=0 in the above equation.

[tex]2(0)+3y=6[/tex]

[tex]3y=6[/tex]

[tex]y=2[/tex]

The y-intercept is 2.

Substitute y=0 in the above equation.

[tex]2x+3(0)=6[/tex]

[tex]2x=6[/tex]

[tex]x=3[/tex]

The x-intercept is 3.

Check the inequality by (0,0).

[tex]2(0)+3(0)\leq 6[/tex]

[tex]0\leq 6[/tex]

This statement is true, it means (0,0) is included in the shaded region.

The sign of inequity is "≤" it means the related line is a solid line and shaded region lie below the line.

Therefore, the correct option is A.

Answer:

y = 1/3x -8

Step-by-step explanation:

3x+y=−5

First we need to get the equation in slope intercept form to find the slope

Subtract 3x from each side

3x-3x+y=-3x−5

y = -3x-5

The slope is -3

We want a line perpendicular.  Perpendicualr lines have slopes that are the negative reciprocal.  Take the negative reciprocal

m new = - (1/-3) = 1/3

The slope of the new line is 1/3

We have the slope (1/3) and a point (3,-7)

We can use the point slope form for the equation of a line

y-y1 = m(x-x1)

y--7 = 1/3 (x-3)

y+7 = 1/3 (x-3)

or if we want the slope intercept form

Distribute

y+7 = 1/3x -1

Subtract 7 from each side

y+7-7 = 1/3x -1-7

y = 1/3x -8

Answer:

h(x) = 7 * (9/7) ^x

Step-by-step explanation:

h(x) = a b^x

When x=0 h(x) = 7

7 = a * b^0

7 = a *1

7 =a

Rewriting the equation

h(x) = 7 b^x

Let x=1

9 = 7 * b^1

9 = 7 * b

Divide each side by 7

9/7 =7b/7

9/7 =b

h(x) = 7 * (9/7) ^x

Answer:

Incorrectly distributing the 3 and (x-3).

Step-by-step explanation:

A common mistake when solving 3(x-3) <3 would be incorrectly distributing the 3 and (x-3).

Answer:

A) 40

Step-by-step explanation:

The sum of the interior angles of a regular polygon is:

[tex](n - 2) \times 180[/tex]

For a hexagon, we put n=6

[tex](6 - 2) \times 180 = 4 \times 180 = 720[/tex]

Let x be the 6th interior angle, then

[tex]x + 110 + 120 + 90 + 140 + 125 = 720[/tex]

[tex]x + 585 = 720[/tex]

[tex]x = 720 - 585 = 135[/tex]

The largest interior angle is 140°

Therefore the least exterior angle will be:

[tex]180 - 140 = 40[/tex]

The correct choice is A

[tex]\huge{\boxed{\text{3) \bf{9, 40, 41}}}}[/tex]

A Pythagorean triple is a set of three numbers where [tex]a^2 + b^2 = c^2[/tex].

Trying 1:

[tex]1^2+3^2=10^2[/tex]

[tex]1+9=100[/tex]

[tex]10=100[/tex]

Incorrect.

Trying 2:

[tex]4^2+5^2=9^2[/tex]

[tex]16+25=81[/tex]

[tex]41=81[/tex]

Incorrect.

Trying 3:

[tex]9^2+40^2=41^2[/tex]

[tex]81+1600=1681[/tex]

[tex]1681=1681[/tex]

Correct!

Trying 4: (unnecessary, but practice is good)

[tex]16^2+30^2=44^2[/tex]

[tex]256+900=1936[/tex]

[tex]1156=1936[/tex]

Incorrect.

Answer:

$60

The equation is x(5(2))=s or x(10)=s when x = number of weeks

Step-by-step explanation:

For 6 weeks, all you have to do is plug in the 6 where the x is.

6(5(2)) = s

6(10) = s

60 = s

or

6(10) = s

60 = s

Answer: (AoPS)

125

Step-by-step explanation:

A distance of 1 meter is 50 times 2 cm, so the actual distance between the two cities is 50 times 2.5 km, which is 125 km.

To find the actual distance between two cities on a map given a scale, convert the map distance to real-world distance using the scale ratio.

The actual distance between two cities on the map can be calculated as follows:

So, the actual distance between the two cities is 1.25 kilometers.

The domain of the function can be written as [-1,2]-{2}, therefore the function is defined from -1 to 2 except 2.

• Domain is the set of values for which the given function is defined.

• Range is the set of all values which the given function can output.

Since the dark point of the function show that is the beginning of the function therefore the function will be defined from that point to all values of x but will not be defined at the point where there is a blank dot, also, the function is defined till the line is drawn.

Thus, the domain of the function will be,

Domain: [-1,2]-{2}

Hence, the domain of the function can be written as [-1,2]-{2}, therefore the function is defined from -1 to 2 except 2.

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Answer:

D.

Step-by-step explanation:

The y-intercept is where the graph crosses the y-axis.

It crosses the y-axis at (0,5).

The graph is of f(t)=5*2^t where t is the number of years and the value of f(t) is the value of that coin after t years.

So we have (0,5) is on the graph of f which means f(0)=5.

f(0)=5 means at t=0 years the value of the coin is $5.

As per the y-intercept of a function, when the coin was purchased, the value of it was $5.

"The y-intercepts are points where the graph of a function crosses or touches the y-axis of the Cartesian Plane. "

The given function is

[tex]f(t)=5(2^{t})[/tex]

As per the graph of the given function, it starts from the point (0, 5).

Hence, it cuts the y-axis at point (0, 5).

Therefore, at the time of purchasing the coin, the value of the coin was at $5.

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Answer:

W'(-3,3) V'(-4,3) U'(-4,5)

Step-by-step explanation:

The mapping for 90 degrees counterclockwise rotation is;

[tex](x,y)\to (-y,x)[/tex]

The given points have coordinates: W(3,3) V(3,4) U(5,4)

[tex](x,y)\to (-y,x)[/tex]

This implies that:

[tex]W(3,3)\to W'(-3,3)[/tex]

[tex]V(3,4)\to V'(-4,3)[/tex]

[tex]U(5,4)\to U'(-4,5)[/tex]

The required points of the image are:

W'(-3,3) V'(-4,3) U'(-4,5)

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 4x + 9 ← is in slope- intercept form

with slope m = - 4

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex], hence

y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line

To find c substitute (4, 5) into the partial equation

5 = 1 + c ⇒ c = 5 - 1 = 4

y = [tex]\frac{1}{4}[/tex] x + 4 ← equation of perpendicular line → C