Which of the following best describes the locust of points equidistant from a given directrix and focus?
A. Parabola
B. Circle
C. Ellipse
D. Hyperbola

X is left to right. Since the translation is X + 1 , you are adding 1 to the X direction, which moves the shape 1 place to the right.

Y is up and down, the translation is y - 2, which means the shape moves 2 places down.

Looking at one point on the original image, lets use Point C. It is located at X = 2 and Y = 1. Now add 1 to the X and subtract 2 from the y:

The new location for C needs to be X = 2+1 = 3 and Y = 1-2 = -1

The image that has C at (3,-1) is C.

Answer:

Step-by-step explanation:

[tex]g(x)=x^2-4\\\\g(5)-\text{put}\ x=5\ \text{to the equation of the function}\ g(x):\\\\g(5)=5^2-4=25-4=21[/tex]

The value of the function g(x) = x² - 4 at g(5) is 21. Option C is correct.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The expression is solved as:-

g(x) = x² - 4

To calculate the value g(5) put x=5 in the expression.

g(5) = ( 5 )² - 4

g(5) = 25 - 4

g(5) = 21

Therefore, the value of the function g(x) = x² - 4 at g(5) is 21. Option C is correct.

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Answer:

13. A

14. C.

Step-by-step explanation:

A relation is a function if there is only one y assigned to each x.

That is if you have a set of points, there should be no repeated x value.

So looking at {(0,0),(-2,4),(-2,-4),(-3,7)} this is not a function because you have two x's that are the same. A.

The slope-intercept form of a linear equation is y=mx+b where m is the slope and b is the y-intercept.

The y-intercept is where the graph goes through the y-axis at.  It goes through at -1 so b=-1.

The slope is rise/run.  So starting from the y-intercept (0,-1) we need to find another point to count the rise & run to... How about (3,1)? That works.  You can do the counting if you want. You could also use the slope formula.

To use the slope formula, I just like to line the points up vertically and subtract vertically then put 2nd difference over the 1st difference.

(0,-1)

-(3,1)

--------

-3  -2

So the slope is -2/-3 or just 2/3.

So the equation is y=2/3 x-1

C.

Answer:

D) 20 in

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h  where r is the radius and h is the height

Substituting what we know

980 pi = pi (7)^2 h

Divide each side by pi

980 pi /pi= pi 49 h/pi

980 = 49h

Divide each side by 49

980/49 = 49h/49

20 =h

Answer:

h ≈ 20 inches

Step-by-step explanation:

Given volume 980 pi inches cubed and radius 7 inches.

Using the height formula for right cylinder

h = V/π r^2

h = 3078.78/π7^2

h ≈ 20 inches

Answer:

  166 mm²

Step-by-step explanation:

The area is given by ...

  A = (1/2)Pa . . . . . where P is the perimeter and "a" is the apothem

One side of a 6-sided figure is shown as 8 mm, so the perimeter is ...

  P = 6·(8 mm) = 48 mm

Filling in the apothem value, we have ...

  A = (1/2)(48 mm)(4√3 mm) = 96√3 mm² ≈ 166 mm²

The area of the hexagon is about 166 mm².

Final answer:

There are three pairs of parallel faces in a cube, as each face has one parallel counterpart. An icosahedron has no parallel faces. When standing between two parallel mirrors, an infinite series of images is theoretically created, but only a finite number can be seen due to practical limits.

Explanation:

To determine the number of pairs of parallel faces in a geometric shape, we have to consider the characteristics of the shape provided. In the case of a cube, which seems to be the most closely related shape mentioned in the details provided, there are three pairs of parallel faces. Each face of a cube is parallel to one other face that is opposite to it. For instance, the top face of the cube is parallel to the bottom face, one of the side faces is parallel to the face directly opposite to it, and the same applies to the front and back faces.

If the student's question instead pertains to an icosahedron, which is mentioned among the details, an icosahedron does not have any parallel faces as it is made up of equilateral triangles, and each face is inclined to the others.

For the discussion question regarding images formed between two parallel mirrors, an infinite number of images would be formed. This is because the mirrors reflect not only the object but also the images in the other mirror, thus creating a series of reflections that seem to go on indefinitely. However, due to practical limitations such as the quality of the mirror and ambient light, only a finite number of these images can actually be observed.

Answer:

[tex]\%increase = 12\%[/tex]

Step-by-step explanation:

The formula to calculate the percentage of increase is:

[tex]\% = \frac{x_f-x_i}{x_i}*100\%[/tex]

Where

[tex]x_i[/tex] is the initial amount and [tex]x_f[/tex] is the final amount

So:

[tex]\% = \frac{28000-25000}{25000}*100\%[/tex]

[tex]\% = \frac{3000}{25000}*100\%[/tex]

You can write it as:

[tex]\% = \frac{3*1000}{25*1000}*100\%[/tex]

This is:

[tex]\% = \frac{3}{25}*100\%[/tex]

[tex]\%increase = 12\%[/tex]

Answer:

B: 1/5

Step-by-step explanation:

If the lines are perpendicular, they have negative reciprocal slopes

s has a slope of -5

t must have a slope of - (1/ -5)

                                    = 1/5

Answer:

V=90m³

Step-by-step explanation:

If a rectangular prism has a length of 5 meters, a width of 6 meters, and a height of 3 meters, the volume of the prism is 90m³.

Formula: V=whl

V=whl=6·3·5=90m³

Answer:

The coordinates of vertex D are (1,2).

Step-by-step explanation:

Let the coordinates of D are (a,b).

It is given that ABCD is a parallelogram and the vertices of the parallelogram are A(-2,4), B(1,3) and C(4,1).

According to the property of parallelogram, the diagonals of the parallelogram bisect each other.

AC and BD are diagonals of the parallelogram ABCD.

Midpoint formula:

[tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Using midpoint formula, the midpoint of AC is

[tex]Midpoint_{AC}=(\frac{-2+4}{2},\frac{4+1}{2})=(1,\frac{5}{2})[/tex]

Using midpoint formula, the midpoint of BD is

[tex]Midpoint_{BD}=(\frac{1+a}{2},\frac{3+b}{2})[/tex]

Midpoint of both diagonals is the intersection point of the diagonals.

[tex]Midpoint_{AC}=Midpoint_{BD}[/tex]

[tex](1,\frac{5}{2})=(\frac{1+a}{2},\frac{3+b}{2})[/tex]

On comparing both the sides we get

[tex]1=\frac{1+a}{2}[/tex]

[tex]2=1+a[/tex]

[tex]2-1=a[/tex]

[tex]1=a[/tex]

The value of a is 1.

[tex]\frac{5}{2}=\frac{3+b}{2}[/tex]

[tex]5=3+b[/tex]

[tex]5-3=b[/tex]

[tex]2=b[/tex]

The value of b is 2.

Therefore the coordinates of vertex D are (1,2).

The coordinates of point D in the parallelogram formed by points A(-2,4), B(1,3), and C(4,1) are (7,2), calculated based on the property of parallelograms, where opposite sides are congruent.

In order to find the coordinates of point D forming a parallelogram with points A(-2,4), B(1,3), and C(4,1), we can use the property of a parallelogram that opposite sides are equal. This means the vector from A to B is equivalent to the vector from D to C. The vector AB is calculated through subtraction of the coordinates: B minus A (1-(-2), 3-4) = (3, -1).

Applying the same vector (movement) to point C to find point D (since D to C equals B to A), we get D as C plus the vector (4+3, 1-(-1)) = (7,2). So, the coordinates of point D in the parallelogram are (7,2).

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Answer:

D. 2x + y = -4​

Step-by-step explanation:

Standard form for the equation of a line is Ax + By =C where A is a positive integer and B and C are integers

y + 1 = -2x - 3

Add 2x to each side

2x+y + 1 = -2x+2x - 3

2x+y +1 = -3

Subtract 1 from each side

2x+y +1-1 = -3-1

2x+y = -4

Answer:

y=-2x-4

Step-by-step explanation:

There are many  standard form of any equations. One of them is called the

y intercept form. The standard form is

y=mx+c

where m is the slope and c is the y intercept

Let us see our given equation

y+1= -2x - 3

subtracting 1 from both sides we get

y = -2x - 3 - 1

y= -2x - 4

Here if we compare it with the standard equation we get

m = -2 and c = -4

Answer:

This was occur sometimes in year 2002.4

Step-by-step explanation:

* Lets explain how to solve the problem

- The value of China's exports of automobiles and parts

  (in billions of dollars) is approximately f(x) = 1.8208 e^(0.3387 x)

# You must pay attention about the function is already calculated in

  billions dollars so you will not multiply the value of f(x) by 10^9 to

  change it to billions

∵ The value of x = 0 at 1998

- Remember that e^(0) = 1

∴ f(0) = 1.8208 e^(0) = 1.8208 billion dollars

- You need to calculate the year that the export reaches 8 billion

∵ f(x) = 1.8208 e^(0.3387 x)

∵ f(x) = 8 billion

∴ 8 = 1.8208 e^(0.3387 x)

- Divide both sides by 1.8208

∴ 4.393673111 = e^(0.3387 x)

- Insert ㏑ in both sides

∴ ㏑(4.393673111) = ㏑[e^(0.3387 x)]

- Remember ㏑(e^n) = n ㏑(e), ㏑(e) = 1, then ㏑(e^n) = n

∴ ㏑(4.393673111) = 0.3387 x

- Divide both sides by 0.3387

∴ x = ㏑(4.393673111) ÷ 0.3387

∴ x = 4.37 ≅ 4.4

- Lets add the number of years to 1998

∴ The year is 1998 + 4.4 = 2002.4

∴ This was occur sometimes in year 2002.4

The value of China's exports of automobiles and parts reached $8 billion in approximately the year 2001.8. The mathematical calculation is based on the exponential function representing the export values over time with the base year 1998.

The student has asked to determine the year in which China's exports of automobiles and parts reached $8 billion.

To solve for the year when exports reach $8 billion, we use the given exponential function for the value of China's exports of automobiles and parts, which is f(x) = 1.8208e0.3387x, where x = 0 corresponds to the year 1998. We need to solve the equation f(x) = 8 for x.

Firstly, set f(x) = 8:

Next, divide both sides of the equation by 1.8208 to isolate the exponential part:

Then, take the natural logarithm of both sides to solve for x:

Finally, add the result to the base year 1998 to get the approximate year:

Therefore, the exports reached $8 billion in approximately 2001.8, or the year 2001 when considering just the full year.

Answer:

x = 12

x = 4

Step-by-step explanation:

Answer:

X=12

X=4

Step-by-step explanation:

Step-1 : Multiply the coefficient of the first term by the constant 1 • 48 = 48

Step-2 : Find two factors of 48 whose sum equals the coefficient of the middle term, which is -16 .

-48 + -1 = -49

-24 + -2 = -26

-16 + -3 = -19

-12 + -4 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -4

x2 - 12x - 4x - 48

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-12)

Add up the last 2 terms, pulling out common factors :

4 • (x-12)

Step-5 : Add up the four terms of step 4 :

(x-4) • (x-12)

Which is the desired factorization

Answer:

24

Step-by-step explanation:

36= three part in a length

so, one part=36/3=12

smaller triangle's length=2/3=12×2=24

Answer:

24 millimeters

Step-by-step explanation:

We have 2 triangles with proportional sides. The smaller side has a length of 2/3 of the similar triangle:

[tex]L_1=\frac{2L_2}{3}[/tex]

[tex]L_1=\frac{2*36}{3}[/tex]

[tex]L_1=24 mm[/tex]

24 millimeters

Answer:

5/9, 2/7, 3/10 are all rational numbers

Step-by-step explanation:

Remember that all rational numbers are able to be written as a fraction or ratio of two integers.

Answer:

[tex]\frac{2}{7}+\sqrt{121}[/tex]

Step-by-step explanation:

Since, a real number is called rational number if it can be expressed in the form of [tex]\frac{p}{q}[/tex],

Where, p and q are integers,

S.t. q ≠ 0,

If the number is not a rational number then it is irrational,

Now, the sum or difference of two rational numbers is a rational number,

While, the sum or difference of a rational number and an irrational number is an irrational number.

∵ √18, √11 and [tex]\pi[/tex] are irrational numbers,

Also, [tex]\frac{5}{9}[/tex], [tex]\sqrt{16}[/tex] and [tex]\frac{3}{10}[/tex] are rational number,

[tex]\implies \frac{5}{9}+\sqrt{18},\pi+\sqrt{16}, \frac{3}{10}+\sqrt{11}\text{ are irrational numbers}[/tex]

Now,

[tex]\frac{2}{7}\text{ and }\sqrt{121}\text{ are rational numbers}[/tex]

Hence,

[tex]\frac{2}{7}+\sqrt{121}\text{ is rational number}[/tex]

Answer:

39.34 juniors and 30.1 seniors

Answer:

The closest number of juniors and seniors who were inducted is 69.

Step-by-step explanation:

At Lincoln High School, approximately 7% of enrolled juniors and 5% of enrolled seniors were inducted into the National Honor Society last year.

There were 562 juniors and 602 seniors enrolled at Lincoln High School last year.

We will calculate the number of students as:

[tex]0.07(562)+0.05(602)[/tex]

= [tex]39.34+30.1[/tex]

= 69.44

Therefore, the closest number of juniors and seniors who were inducted is 69.

Answer:

Step-by-step explanation:

x + 2 = 5       subtract 2 from both sides

x + 2 - 2 = 5 - 2

x = 3

Check:

3 + 2 = 5     CORRECT :)

Answer:

[tex]\frac{7\sqrt{5} }{8}[/tex]

Step-by-step explanation:

Using the rules of radicals

[tex]\sqrt{\frac{a}{b} }[/tex] = [tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex]

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Given

[tex]\sqrt{\frac{245}{64} }[/tex] = [tex]\frac{\sqrt{245} }{\sqrt{64} }[/tex]

Simplifying the radicals

[tex]\sqrt{245}[/tex]

= [tex]\sqrt{5(7)(7)}[/tex]

= [tex]\sqrt{49(5)}[/tex]

= [tex]\sqrt{49}[/tex] × [tex]\sqrt{5}[/tex] = 7[tex]\sqrt{5}[/tex]

and

[tex]\sqrt{64}[/tex] = 8

The simplified radical is

[tex]\frac{7\sqrt{5} }{8}[/tex]

Answer:

First part:

Set h(t) = 17and solve for t.

-16t²+ 58t + 7= 17

-16t² + 58t - 10 = 0

Solve this quadratic equation for t. You should get 2 positive solutions. The lower value is the time to reach 17 on the way up, and the higher value is the time to reach 17 again, on the way down.

Second part:

Set h(t) = 0 and solve the resulting quadratic equation for t. You should get a negative solution (which you can discard), and a positive solution. The latter is your answer.

The time required to reach 17 feet and the ground by the ball is required.

The time taken to reach 17 feet is 0.181 s.

To reach the ground the time taken is 3.74 s.

The equation is

[tex]h=-16t^2+58t+7[/tex]

[tex]h=17[/tex]

[tex]17=-16t^2+58t+7\\\Rightarrow -16t^2+58t-10=0\\\Rightarrow t=\frac{-58\pm \sqrt{58^2-4\left(-16\right)\left(-10\right)}}{2\left(-16\right)}\\\Rightarrow t=0.181,3.44[/tex]

The time taken reach a height of 17 feet while going up is 0.181 s.

On the ground [tex]h=0[/tex]

[tex]0=-16t^2+58t+7\\\Rightarrow t=\frac{-58\pm \sqrt{58^2-4\left(-16\right)\times 7}}{2\left(-16\right)}\\\Rightarrow t=-0.12,3.74[/tex]

The time taken to reach the ground is 3.74 s.

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Answer:

[tex]3x - y = - 2[/tex]

Step-by-step explanation:

The given line PQ passes through the points P(-5,-13) and Q(5,17) .

Find the slope using the formula:

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

Plug in the points to get:

[tex]m = \frac{17 - - 13}{5 - - 5} [/tex]

[tex]m = \frac{30}{10} [/tex]

[tex]m = 3[/tex]

Use the point-slope formula :

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

Substitute the point (5,17)

[tex]y - 17 = 3(x - 5)[/tex]

Expand:

[tex]y - 17 = 3x - 15[/tex]

The standard form is when the equation is put in the form

[tex]ax + by = c[/tex]

Regroup the terms to get:

[tex]3x - y = - 17 + 15[/tex]

The standard form is

[tex]3x - y = - 2[/tex]

Answer:

70%

Step-by-step explanation:

The probability it rains on at least one of the days is:

P = P(Sat & not Sun) + P(Sun & not Sat) + P(Sat & Sun)

P = (0.40)(1−0.50) + (0.50)(1−0.40) + (0.40)(0.50)

P = 0.20 + 0.30 + 0.20

P = 0.70

Another way to look at it is 1 − the probability that it doesn't rain on either day.

P = 1 − P(not Sat & not Sun)

P = 1 − (1−0.40)(1−0.50)

P = 1 − 0.30

P = 0.70

There is a 70% probability that it will rain on at least one day.

The probability that it will rain on at least one day over the weekend is 70%, based on independent probabilities given for Saturday and Sunday.

The subject of your question is probability, a branch of mathematics that studies randomness and the likelihood of events occurring. To calculate the probability that it will rain over the weekend, i.e., on at least one of the days (Saturday or Sunday), we first need to find the probability that it won't rain on either day.

The probability it doesn't rain on Saturday is 60% (100% - 40%), and the probability it doesn't rain on Sunday is 50% (100% - 50%). Since these events are independent, we multiply these probabilities to find the joint probability. Therefore, the probability it doesn't rain on either day is 30% (0.6 × 0.5 = 0.3).

Now, this is the case which we don’t want (no rain), so the case we want (that it rains at least one day) is the complementary event of this. Thus, we subtract this from the total probability, which is 1, yielding a 70% (1 - 0.3) probability that it will rain on at least one of the days over the weekend.

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Answer:

It will take 143 minutes to take the pictures

Answer:

n=4p

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

35 and 36

Step-by-step explanation:

If the smaller dimension is x, then the larger dimension is x + 1.  Therefore:

2x + 2(x + 1) = 142

2x + 2x + 2 = 142

4x = 140

x = 35

One dimension is 35, and the other dimension is 36.

Answer:

The dimensions of the rectangle are 35 inches by 36 inches.

Step-by-step explanation:

If the length and width are consecutive integers and L=n, then W=n+1 assuming the width is larger.

We are given the perimeter is 142 inches so: 2L+2W=142.

Substituting L=n and W=n+1 we have:   2(n)+2(n+1)=142.

Let's solve it:

2(n)+2(n+1)=142

Distribute:

2n+2n+2=142

Combine like terms:

4n+2=142

Subtract 2 on both sides:

4n=140

Divide both sides by 4:

n=140/4

n=35

Since L=n, then the length is 35 inches.

Since W=n+1, then the width is 36 inches.

The dimensions of the rectangle are 35 inches by 36 inches.

Y = 6

13 + [tex]\frac{6}{y}[/tex] means that we are adding 13 and 1 together because 6 divided by 6 is 1.

13 + 1 = 14

Answer:

After  x/450 minutes

Step-by-step explanation:

The speed uphill is 200 ft/min

The speed down hill is 250 ft/min

Lets take the hiking distance top to down hill is x ft

Remember speed=distance/time

Relative speed =200+250=450ft/min

Time to meet=distance/relative speed

Time to meet=x/450 min

Final answer:

To find out how long it will take until you meet, we need to determine the distances each hiker covers and then divide it by their respective rates.

Explanation:

To find out how long it will take until you meet, we need to determine the distances each hiker covers and then divide it by their respective rates.

The first hiker covers a certain distance while hiking uphill, while the second hiker covers a certain distance while hiking downhill. When they meet, their combined distances will add up to the total distance of the trail.

Let's say it takes x minutes for you to meet. The first hiker covers a distance of 200x feet in x minutes, while the second hiker covers a distance of 250x feet in the same x minutes. When they meet, their combined distances will equal the length of the trail, so we can set up the equation: 200x + 250x = total distance. Solving for x will give us the time it takes for you to meet.

Answer:

A. Louisa made an error when determining the original solution of x = 56.

Step-by-step explanation:

1/4x - 3 = 3/8x + 4

To verify x=56 is a solution, substitute x=56 into the equation

1/4(56) - 3 = 3/8(56) + 4

Multiply

14 -3 = 21 +4

Combine like terms

11 = 25

The steps are correct.

x=56 must not be a solution to the equation

Answer:

option A

Step-by-step explanation:

Given that Louisa states that the solution to the equation 1/4x - 3 = 3/8x + 4 is x = 56.

She did the following steps

Step 1 is right because she substituted x=14 to check whether right side = left side

Step 2: Multiplication is done correctly

Step 3: Is incorrect because 11 can never be equal to 25 in Mathematics.

Hence the mistake she did is not in substitution, multiplication or addition/subtraction. But in determining the original solution

Hence A)  Louisa made an error when determining the original solution of x = 56.

Answer : The length of the rectangle (a) is, 8 cm

Step-by-step explanation :

As we are given that,

Area of rectangle = [tex]24cm^2[/tex]

Length of rectangle = a

Breadth of rectangle = a - 5

As we know that,

Area of rectangle = Length × Breadth

Now put all the given values in this formula, we get the value of 'a'.

[tex]24cm^2=(a)\times (a-5)[/tex]

[tex]24cm^2=a^2-5a[/tex]

[tex]a^2-5a-24=0[/tex]

By the solving the term 'a', we get the value of 'a'.

a = 8

Thus,

Length of rectangle = a = 8 cm

Breadth of rectangle = a - 5 = 8 - 5 = 3 cm

Therefore, the length of the rectangle (a) is, 8 cm

The length a of the rectangle is 8 cm

To solve the above questions, we need to recall some of the formulas as follows:

Area of Square = (Length of Side)²

Perimeter of Square = 4 × (Length of Side)

Area of Rectangle = Length × Width

Perimeter of Rectangle = 2 × ( Length + Width )

Area of Rhombus = ½ × ( Diagonal₁ + Diagonal₂ )

Perimeter of Rhombus = 4 × ( Length of Side )

Area of Kite = ½ × ( Diagonal₁ + Diagonal₂ )

Perimeter of Kite = 2 × ( Length of Side₁ + Length of Side₂ )

Let us now tackle the problem !

Given:

Area of Rectangle = A = 24 cm²

Length of Rectangle = L = a cm

Width of Rectangle = W = (a - 5) cm

Unknown:

Length of Rectangle = a = ?

Solution:

This problem is about Area of Rectangle.

[tex]\text{Area of Rectangle} = \text{Length} \times \text{Width}[/tex]

[tex]A = L \times W[/tex]

[tex]24 = a \times (a - 5)[/tex]

[tex]24 = a^2 - 5a[/tex]

[tex]a^2 - 5a - 24 = 0[/tex]

[tex](a - 8)(a +3) = 0[/tex]

[tex](a - 8) = 0[/tex]

[tex]a = \boxed {8 ~ \text{cm}}[/tex]

Grade: College

Subject: Mathematics

Chapter: Two Dimensional Figures

Keywords: Perimeter, Area , Square , Rectangle , Side , Length , Width

Answer:

The measure of the arc x is 130°

Step-by-step explanation:

we know that

The semi-inscribed angle is half that of the arc it comprises

so

65°=(1/2)[arc x]

solve for x

arc x=(2)(65°)=130°