Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.
x = 5t − 2, y = 2t + 1.

Answer:

g(x) is the reflection of f(x) over the y-axis.

hope it helps

Answer:

step 1:  g(x) = 1.5(0.5)^-x

step 2: g(0) = 1.5

step 3: plot points on graph

step 4: g(1) = 3    g(-1) = .75

step 5: Plot the points

step 6:  y=0

step 7:  The smooth curve includes these points

Step-by-step explanation:

Just took this on edge 2021

Answer:

pretty sure its A n B = {1,5}

Step-by-step explanation:

Step-by-step explanation:

10 is less than 10.01

10.01-10=0.01

10 is 0.01 less than 10.01

So, 10 is less than 10.01.

Hope it helps you!!

Answer:

The horizontal line test is used to determine if a functions inverse will be a function. You will compose the functions (that is, plug x into one function, plug that function into the inverse function, and then simplify) and verify that you end up with just "x". Here's what it looks like: Determine algebraically whether f (x) = 3x – 2 and g(x) = (x + 2)/3 are inverses of each other.

Use the horizontal line test to determine if a function is a one-to-one function.

If ANY horizontal line intersects your original function in ONLY ONE location, your function will be a one-to-one function and its inverse will also be a function.

hope this helps

The horizontal line test is used to determine if a function's inverse will be a function is true. Correct option is 4.

1. This statement is not true. For a pair of functions to be inverses, their compositions (f(g(x)) and g(f(x))) must result in the identity function (1) for all values of x, not just for a specific value.

2. This statement is not true. In an inverse relation, the coordinates of the ordered pairs are swapped (x becomes y and y becomes x), not multiplied by 2.

3. This statement is not true. While many functions have inverses that are also functions, it is not a universal rule. Some functions may not have an inverse that is a function.

4. This statement is true. The horizontal line test is used to determine if a function has an inverse that is also a function. If a horizontal line intersects the graph of the function at more than one point, then the function does not have an inverse that is a function. However, if every horizontal line intersects the graph at most once, then the function does have an inverse that is a function.

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Answer: [tex]\frac{\sqrt{3} }{2}[/tex]

Step-by-step explanation:

To find sin(60), you need to know the unit circle. Sin(60) is the same as sin(π/3). On the unit circle, sin(π/3) is √3/2. We know this because the coordinates are (cos, sin). Sin is the y coordinate.

Answer:

[tex]\huge\boxed{\sin60^o=\dfrac{\sqrt3}{2}}[/tex]

Step-by-step explanation:

Let's take a right triangle with acute angles 30° and 60°.

We know that the ratio of the sides of such a triangle is 2 : 1 : √3

(look at the picture)

We know:

[tex]sine=\dfrac{opposite}{hypotenuse}[/tex]

In this triangle we have:

[tex]opposite=a\sqrt3\\hypotenuse=2a[/tex]

Substitute:

[tex]\sin60^o=\dfrac{a\sqrt3}{2a}[/tex]         cancel a

[tex]\sin60^o=\dfrac{\sqrt3}{2}[/tex]

idk

Step-by-step explanation:

Answer:

[tex]\Huge \boxed{-x+4}[/tex]

Step-by-step explanation:

[tex]-(x+2)+6[/tex]

Distributing the negative sign to the terms in the bracket.

[tex]-x-2+6[/tex]

Combining like terms.

[tex]-x+4[/tex]

Answer:

[See Below]

Step-by-step explanation:

Here are some pictures to help you.

The quadratic formula is shown below.

The beauty of the quadratic formula is that as long as your quadraticis in the form ax² + bx + c = 0, where a, b, and c are integers, you can go straight to the answer by simply plugging your values for a, b, and c into the quadratic formula.

It's a good idea to memorize it.

Believe me it's worth it, you'll be using it all the time.

Answer:

9

Step-by-step explanation:

18÷2=9

So, Ann could have 9 rows of posters with 2 posters in each row.

Answer:

Proved

Step-by-step explanation:

Given

Integers: a, b, c

Required

Show that c is a multiple of a⁶

First, we need to list out the multiples of a³

[tex]a^3 -> a^3, a^6, a^9, a^{12}...[/tex]

Since b is a multiple of a³, then b can be any of the listed multiples

Next, is to list out the multiples of b²

[tex]b^2 -> b^2,b^4,b^6,b^8,b^{10}....[/tex]

Since c is a multiple of b², then c can be any of the listed multiples

To list out the multiples of a⁶, we have to get the common multiples of a³ and b² in terms of a

Substitute a³ for b in

[tex]b^2 -> b^2,b^4,b^6,b^8,b^{10}....[/tex]

[tex](a^3)^2 -> (a^3)^2,(a^3)^4,(a^3)^6,(a^3)^8,(a^3)^{10}....[/tex]

[tex]a^6 -> a^6,a^{12},a^{18},a^{24},a^{30}....[/tex]

Recall that c is a multiple of b²

From the above listed multiples, we have a⁶ listed as one of the multiple; Hence, c is a multiple of a⁶

Yes C should be multiple of [tex]a^6[/tex]

Since it is mentioned that b should be the multiple of [tex]a^3[/tex]

So,

[tex]b = a^3R[/tex] here some integer should be R

And, the c should be multiple of [tex]b^2[/tex]

So,

[tex]C = b^2 r[/tex] for some integer r

Now we have to substitute the value of b from the first equation

i.e.

[tex]C = (a^3R)^2r = a^6 (R^2r)[/tex]

Here [tex]R^2r[/tex] is some integer

so,

[tex]C = a^6R'[/tex]

Therefore, we can say that Yes C should be multiple of [tex]a^6[/tex]

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Answer:

P(E)=1/2

Step-by-step explanation:

Total numbers=6

Numbers greater than or equal to 4= 3(4,5,6)

P(E)= favourable outcomes/total outcomes

P(E)=3/6

     =1/2

Answer:

4/6

Step-by-step explanation:

probability of rolling a num greater than or equal to 4 = 4/6

=2/3

Answer:

Step-by-step explanation:

Were you given answer choices?  If so, please share them when you post your question.

The best way to improve the experimental probability would be to flip the coin more than 20 times; the more this is done, the better the estimate will be.

Answer:

105 units

Step-by-step explanation:

Height of rectangle = 35 units

Since, base of o rectangle is triple the height.

Therefore, base of rectangle = 3*35 = 105 units

Another way:

h = 35 (given)

b = 3h

b = 3*35 (Plug h = 35)

b = 105 units

Answer: (1.5, 1.5)

Step-by-step explanation:

Answer:

A. -4

Step-by-step explanation:

Given the function f(x) = x + 3 for x ≤ -1 and 2x - c for x > -1, for the function to be continuous, the right hand limit of the function must be equal to its left hand limit.

For the left hand limit;

The function at the left hand occurs at x<-1

f-(x) = x+3

f-(-1) = -1+3

f-(-1) = 2

For the right hand limit, the function occurs at x>-1

f+(x) = 2x-c

f+(-1) = 2(-1)-c

f+(-1) = -2-c

For the function f(x) to be continuous on the entire real line at x = -1, then

f-(-1) = f+(-1)

On equating both sides:

2 = -2-c

Add 2 to both sides

2+2 = -2-c+2

4 =-c

Multiply both sides by minus.

-(-c) = -4

c = -4

Hence the value of c so that f(x) is continuous on the entire real line is -4

The value of 'c' is -4 and this can be determined by using the concept of continuous function and arithmetic operations.

Given :

f(x) is continuous on the entire real line when c f(x) = x + 3 for [tex]x \leq -1[/tex], 2x - c for x > -1.

Remember for a continuous function, the left-hand limit is equal to the right-hand limit. So, determine the left-hand and right-hand limit.

The left-hand limit is calculated as:

f(-1) = (-1) + 3

f(-1) = 2    --- (1)

The right-hand limit is calculated as:

f(-1) = 2(-1) - c

f(-1) = -2 - c   --- (2)

Now, equate both the expression (1) and (2).

2 = -2 - c

c = -4

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Answer:

Step-by-step explanation:

-10x < 40

x > -4

Answer:

B. Short-term memory

Step-by-step explanation:

Response variable is a dependent variable. It is dependent on the explanatory variable that is referred to as the independent variable.

In research study, the response variable is what is usually measured by the researcher. In the case given above, short-term memory is the response variable, which is dependent on exercise.

Don't shade the part A and the part between A and B. Shade the B part only.

Number of raisins in the bag is 160 raisins

Given that;

Ratio of peanuts to raisins = 5:4

Bag of the snack mix contains = 200 peanuts

Find:

Number of raisins in the bag

Computation:

Number of raisins in the bag = 4[200/5]

Number of raisins in the bag = 4[40]

Number of raisins in the bag = 160 raisins

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Answer:

531

Start off by subtracting.

Joe = 987 marbles

Donald = 456 marbles.

987 - 456 = 531.

So that is your answer. Hope it helps!

Answer:

agree with previos answer

Step-by-step explanation:

Answer:

k=21

Step-by-step explanation:

Find the slope of MN which is 1/5, (use the slope formula.)

Use the slope formula for AB using k as y_2

Substitute and you get k=21

21-2.25/-2.25-1.5=-5

The lines are perpendicular because the slopes are the negative reciprocal of one another.

For K = 5.3, the line segments are parallel.

We have endpoints of segment MN have coordinates (0, 0), (5, 1) and  endpoints of segment AB have coordinates (1 1/2 , 2 1/4 ) and (−2 1/4 , k).

We have to determine the value of k that makes these segments parallel.

For lines to be parallel - slope of line 1 should be equal to slope of line 2.

m(1) = m(2)

According to question, we have -

Coordinates of M = (0, 0)

Coordinates of N = (5, 1)

Therefore, the slope of line MN = [tex]\frac{1 -0}{5-0}[/tex] = 1/5

Coordinates of A = (11/2, 21/4)

Coordinates of B = (-21/4, k)

Therefore, the slope of line AB =

[tex]$\frac{k -\frac{21}{4} }{\frac{-21}{4} -\frac{11}{2} }[/tex]  =  [tex]$\frac{k - \frac{21}{4} }{\frac{1}{4} }[/tex]  =  [tex]$\frac{\frac{4k - 21}{4} }{\frac{1}{4} }[/tex]  = 4k -21

Now, for the lines to be parallel -

m(MN) = M(AB)

4k - 21 = [tex]\frac{1}{5}[/tex]

5(4k - 21) = 1

20k - 105 = 1

20k = 106

k = 5.3

Hence, for K = 5.3, the line segments are parallel.

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Answer:

$149.96

Step-by-step explanation:

99.99+12.99+36.98=149.96

Total=$149.96

Answer:

B) C=3.14(2r)

Step-by-step explanation:

Circumference of a circle= 2πr

radius=6 feet

Diameter= 2r

=2*6

=12 feet

π= 3.14

C= 2πr

= 2 * 3.14 * r

= 3.14 * 2 * r

C= 3.14 (2r)

Kierran should use the formula C= 3.14 (2r) to find the circumstance of the circle

Option B is the correct answer

C= 3.14 (2r)

= 3.14 * 2 * 6

= 37.68 eet

Answer:

-9

Step-by-step explanation:

Going down= negative

Answer:

u write negative 9

Step-by-step explanation:

( 5n 3 + n 4 - 5 ) - ( -5 - 6n 3 - 4n 4 )

Simplify the expression.

53 n

Answer:

The simplified solution to this expression is 5n⁴ + 11n³

Step-by-step explanation:

(5n³ + n⁴ - 5) - (-5 - 6n³ - 4n⁴)

Distribute the negative sign to (-5 - 6n³ - 4n⁴)

5n³ + n⁴ - 5 + 5 + 6n³ + 4n⁴

Group like terms.

(4n⁴ + n⁴) + (6n³ + 5n³) + (-5 + 5)

Combine like terms.

5n⁴ + 11n³

His score would have to be -5:

-3 + 3 = 0

0 + 1 = 1

1 + 4 = 5

5 + (-5) = 0

So you know that the su of all the scores is 0.

The scores in the table are cecilia -3, janine 3, sami 1 and ted 4 and travis x, where x is the number that we want to know.

if we sum those, we have : 3 - 3 + 4 + 1 + x = 0

and we get 5 + x = 0

then x= -5, so travis's score is -5 points.

Answer:

Perimeter of A'B'C'D' = 9 units

Step-by-step explanation:

Given:

Perimeter of ABCD = 27 units

Scale factor = 1 / 3

Find:

Perimeter of A'B'C'D'

Computation:

Perimeter of A'B'C'D' = 1/3[Perimeter of ABCD]

Perimeter of A'B'C'D' = 1/3[27]

Perimeter of A'B'C'D' = 9 units

Answer:

Step-by-step explanation:

3/8 x 5/5 = 15/40

7/10 x 4/4 = 28/40

15/40, 28/40

The least common denominator of the two pairs of fractions is 15/40 are 28/40. which is the correct answer would be an option (A).

The lowest common denominator is defined as the set of fraction denominators with the lowest common multiple. The lowest positive integer with more than one denominator in the set is LCD.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

We have to determine the least common denominator of the two pairs of fractions.

The fractions are 3/8, and 7/10

⇒ 3/8

Multiply by 5/5 in the fraction,

⇒ 3/8 × 5/5 = 15/40

⇒ 7/10

Multiply by 4/4 in the fraction,

⇒ 7/10 × 4/4 = 28/40

Therefore, the least common denominator of the two pairs of fractions is 15/40 are 28/40

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Answer:

18 paperclips are in the pile!

Step-by-step explanation:

We know that a dozen paperclips are equal to 9.6g, so we are going to divide 9.6 by 12 to figure out how much each paperclip weighs (0.8g). So we then divide 14.4 by 0.8 to figure out how many paperclips are in the pile! Hope this helps!