What is the range of y=-3si (x)-4

Answer:

1. you start with $ 3 and save $1 each month

2. your total savings is 3 times the number of month multiplied by itself

3. you save $3 the first month and then each month the amount triples

Step-by-step explanation:

1.

as y axis represents savings while x axis represents months

the statement "you start with $ 3 and save $1 each month"

is best described by the graph of straight line having slope of 1 and intercept of 3.

2. your total savings is 3 times the number of month multiplied by itself

          = 3(x)(x)

          = 3x^2

3.  as y axis represents savings while x axis represents months

the statement  "you save $3 the first month and then each month the amount triples" is best described by the exponential graph starting to rise from point (1,3) which means $3 save at 1 month.

!

[tex]\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ f(x)=Asin(Bx+C)+D \qquad \qquad f(x)=Acos(Bx+C)+D \\\\ f(x)=Atan(Bx+C)+D \qquad \qquad f(x)=Asec(Bx+C)+D \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks}\\ ~~~~~~\textit{horizontally by amplitude } A\cdot B\\\\ \bullet \textit{ flips it upside-down if }A\textit{ is negative}[/tex]

[tex]\bf ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{C}{B}\\ ~~~~~~if\ \frac{C}{B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{C}{B}\textit{ is positive, to the left}[/tex]

[tex]\bf \bullet \textit{vertical shift by }D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{function period or frequency}\\ ~~~~~~\frac{2\pi }{B}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ ~~~~~~\frac{\pi }{B}\ for\ tan(\theta),\ cot(\theta)[/tex]

with that template in mind, let's see.

[tex]\bf \stackrel{A = 2}{g(x) = 2cos(Bx+C)}\qquad \begin{cases} \stackrel{\textit{period of 30 seconds}}{\cfrac{2\pi }{B}=30}\\\\ \cfrac{2\pi }{30}=B\\\\ \cfrac{\pi }{15}=B \end{cases}\implies g(x)=2cos\left( \frac{\pi }{15}x+C \right)[/tex]

now, since the period is 30, and cos(x) starts off at 1, recall cos(0) = 1, so then le'ts move the starting point over by simply doing a horizontal shift to the right by a quarter of the period, 30/4 = 15/2 units, that way the initial "hump" starts off at 0.

[tex]\bf \stackrel{\textit{horizontal shift of }\frac{15}{2}}{\cfrac{15}{2}=\cfrac{C}{B}}\implies \cfrac{15}{2}=\cfrac{C}{~~\frac{\pi }{15}~~}\implies \cfrac{15}{2}=\cfrac{15C}{\pi }\implies 15\pi =30C \\\\\\ \cfrac{15\pi }{30}=C\implies \cfrac{\pi }{2}=C~\hfill \stackrel{\textit{horizontally to the right}}{-\cfrac{\pi }{2}=C} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill g(x)=2cos\left(\frac{\pi }{15}x-\frac{\pi }{2} \right)~\hfill[/tex]

Check the picture below.

Answer:

The number per hour = 5400 ÷ 8 = 675 action figures

Step-by-step explanation:

* Lets explain how to solve the problem

- A toy manufacturer uses 90 pints of plastic to make 600 action figures

- they use 810 pints of plastic in an 8 hour shift

- To find how many action figures are made per hour we must to find

  how many action figures in an 8 hour shift and then find the number

  of the action figures per hour

∵ The toy manufacture  uses 90 pints of plastic to make 600 action

   figures

∵ They use 810 pints

- Lets find how many action figures are made by this numbers of pints

∴ 90/600 = 810/x ⇒ x is the number of action figures

- Use the cross multiplication to find x

∴ 90 x = 810 × 600

∴ 90 x = 486000 ⇒ divide both sides by 90

∴ x = 5400

∴ They will use 810 pints to make 5400 action figures

∵ They use 810 pints in an 8 hour shift

∴ They make 5400 action figures in 8 hours

- To find the number of the action figures per hour divide the number

  of them in 8 hours by 8

∴ The number per hour = 5400 ÷ 8 = 675 action figures

ANSWER

[tex]211.2 {in}^{2} [/tex]

EXPLANATION

The surface area of a triangular prism is

equal to the area of two triangular faces

plus the area of the three rectangular faces.

The area of the equilateral triangle is calculated using the formula:

[tex] = 2 \times \frac{ \sqrt{3} }{4} {s}^{2} + 3 \times \: bh[/tex]

where s=6 is the length of one side.

and b=6 is the breadth of the rectangle and h=10 is the height of the rectangle.

Surface area

[tex]= 2 \times \frac{ \sqrt{3} }{4} \times {6}^{2} + 3 \times \: 6 \times 10[/tex]

[tex]= 18\sqrt{3} + 180[/tex]

=211.2square inches.

the answer to this question is C

y=2x+6×

Answer:

both option (A) & (B) is description of given distribution.

Step-by-step explanation:

The outlier is a point which lies differently or far away from rest points in datasets or distribution.

Here we can self-time for one apple on the 10th day is outlier present in the distribution. Thus Option (A) is correct.

We divide the heterogeneous group into many homogeneous groups, these homogeneous group is known as Cluster. It can be seen naturally.

Also, here distribution is divided into many clusters and we can see given distribution has many clusters and one of them is from 4 to 6 days. Thus Option (B) is also a correct option here.

here are my analyses of the possible answer choices based on the image you sent:  The distribution clusters around 4-6 days and has a few potential outliers above 8 days.

here are my analyses of the possible answer choices based on the image you sent:

(A) The distribution has an outlier.

There are a few data points that are higher than the rest of the distribution, so in that sense, yes, there are outliers. However, it is important to consider what an outlier is in the context of the data. If the data is normally distributed, then outliers are data points that fall more than two standard deviations away from the mean. In this case, it is difficult to say for sure whether the data is normally distributed, so it is also difficult to say for sure whether there are outliers. However, there are a few data points that are higher than the rest of the distribution.

(B) The distribution has a cluster from 4 to 6 days.

There is a cluster of data points from 4 to 6 days, so yes, this statement is accurate.

In conclusion, the accurate descriptions of the distribution are:

Answer:

Step-by-step explanation:

The slope-intercept form:

y = mx  + b

m - slope

b - y-intercept (0, b)

We have (0, 2) → b = 2 and m = -1/2. Substitute:

y = -1/2x + 2            multiply both sides by 2

2y = -x + 4             add x to both sides

x + 2y = 4

Analyzing the given function F(x), we can predict that it is a quartic function with various possible shapes and intersection points with the x-axis. However, a comparison or correlation to function G(x) cannot be accurately made without additional information about graph G(x).

Given the function F(x)=x^4-3x^2-1 and the unspecified G(x) graph, it's difficult to make an accurate statement without observing the shape, slope, and specific points on the G(x) graph. However, by understanding the given function F(x), we can still provide some insights. The function F(x) here is a quartic function (as the largest exponent is 4). The graph of a quartic function can have various shapes - it may have zero, one or two extreme points, and it may pass through the x-axis at zero, two or four points. It is essential to look at two-dimensional graphing to properly analyze and correlate F(x) and G(x).

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The width of the garden would be found by dividing the area by the length.

Width = 324 / 24 = 13.5 feet.

Now you need to find the total perimeter of the garden:

Perimeter = 2 x length + 2 x width

Perimeter = 2 x 24 + 2 x 13.5

Perimeter = 48 + 27

Perimeter = 75 feet.

He will need 75 feet of fence.

Answer:

75 feet of fence

Step-by-step explanation:

324/24=13.5

13.5+13.5+24+24=75

Answer:

39

Step-by-step explanation:

Answer:

4% of 975 is 39

Step-by-step explanation:

4% of 975 = 0.04 x 975 = 39

Answer

4% of 975 is 39

The answer is 1 and 3/4 because if you divide 21 by 12 you get 1.75 convert the decimal into a fraction and get 1 and 3/4. :)

She will need 1 3/4 cups of milk

Number of batches of pancake to be made = 3 batches

Number of cups of milk needed for each batch = 7/12

Therefore, in order to get the total number of cups of milk needed for the batches will be calculated thus:

= 7/12 × 3

= 21/12

= 1 9/12

= 1 3/4

Therefore, she will need 1 3/4 cups of milk.

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Answer:

-9/2 , 3/2

Step-by-step explanation:

The coordinates of the midpoint of the line segment that has endpoints (-3,4) and (-6,-1) are (-4.5, 1.5).

Suppose we've two endpoints of a line segment as A(p,q), and B(m,n), then let the midpoint be M(x,y) on that line segment. Then, its coordinates are x =(p+m)/2 and y = (q+n)/2.

Given the endpoints of the line segment are A(-3,4) and B(-6,-1), then the coordinates of the midpoint will be,

x = (-3-6)/2 = -9/2 = -4.5

y = (4-1)/2 = 3/2 = 1.5

Hence, the coordinates of the midpoint of the line segment that has endpoints (-3,4) and (-6,-1) are (-4.5, 1.5).

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Answer:

The age of youngest friend = 14 years

Step-by-step explanation:

It is given that, four friends were born on consecutive years the sum of their ages is 62

Let 'x' be the age of youngest friend

age of other friends are (x + 1), (x + 2) and (x + 3)

To find the age of youngest friend

From the given information we can write,

x +  (x + 1) + (x + 2) + (x + 3) = 62

4x + 6 = 62

4x = 62 - 6 = 56

x = 56/4 = 14

Therefore age of youngest friend = 14

ANSWER

Focus:

[tex](- \frac{1}{4} ,0)[/tex]

Directrix:

[tex]x=\frac{1}{4} [/tex]

EXPLANATION

The given parabola has equation:

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

We compare this to the general equation,

[tex] {y}^{2} = - 4px[/tex]

Comparing the coefficient of x, we have:

-4p=-1

[tex]p = \frac{1}{4} [/tex]

The focus is (-p,0)

[tex](- \frac{1}{4} ,0)[/tex]

The equation of the directrix is

x=p

[tex]x = \frac{1}{4} [/tex]

Answer:

A

Step-by-step ex

only if youre lazy like me to read it, its A

Answer:

The correct answer is last option 80 cm

Step-by-step explanation:

From the given figure we can see a parallelogram LMNO

To find the perimeter of parallelogram

Here side length of the parallelogram  is 18 cm and 22 cm

Perimeter = sum of side lengths

= 22 + 22 + 18 + 18 = 80 cm

Therefore the perimeter of parallelogram  LMNO = 80 cm

The correct answer is last option 80 cm

The perimeter of the parallelogram is P = 80 cm

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The sum of angles of a parallelogram is 360°

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as LMNO

Now , the measure of side MN = 18 cm

The measure of side LM = 22 cm

And , the side MN is parallel and congruent to OL

And , the side LM is parallel and congruent to side ON

So , the perimeter of parallelogram = LM + OL + ON + MN

P = 22 + 18 + 22 + 18

P = 80 cm

Hence , the perimeter is 80 cm

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Answer:

275 miles

Step-by-step explanation:

3.5 cm = 175 and 2 more centimeters past that is 100 so 175 +100=275

so your answer is a 275 miles

y2-y1/x2-x1

Y(subscript 2) - Y(subscript 1) / X(subscript 2) - X(subscript 1)

The formula for slope is the difference in y-values divided by the difference in x-values. the slope of a line is its steepness or its rate of change. There are 4 types of slopes positive, negative, zero, and undefined.

[tex]

\sum_{3}^{6}2=\sum_{0}^{3}2=2+2+2=\boxed{6}

[/tex]

Or did you mean:

[tex]

6\times\sum{3i}=6\times\sum{6}=6\times6=\boxed{36}[/tex]

Answer:

{6, 16, 24}

Step-by-step explanation:

The least common multiple is the least number that is common to the multiples of two or more numbers.

The LCM of 2,3,4 is 12

The LCM of 6,16,and 24 is 48

The LCM of 3,8, 12 is 24.

The LCM of 6,8, 12 is 24.

The numbers that have the least common multiple of 48 is {6, 16, 24}

[tex]6=2\times 3[/tex]

[tex]16=2^4[/tex]

[tex]24=2^3\times 3[/tex]

The LCM is the product of the highest powers of the common factors

[tex]2^4\times3=48[/tex]

Answer:

Arcsin(1/5) = 0.20

Arcsin(-0.34) = -0.35

Arcsin(0.6) = 0.64

Step-by-step explanation:

Using a calculator we can find the value of each expression:

Arcsin(1/5) = 0.20135792079, rounding to the nearest hundredth we have that: Arcsin(1/5) = 0.20.

Arcsin(-0.34) = -0.346916897527, rounding to the nearest hundredth we have that: Arcsin(-0.34) = -0.35

Arcsin(0.6) = 0.643501108793, rounding to the nearest hundredth we have that: Arcsin(0.6) = 0.64

We found the arc-sin (or inverse sine) of three different values using a calculator, rounding to the nearest hundredth decimal place: Arcsin(1/5) is approximately 0.20, Arcsin(-0.34) is -0.34, and Arcsin(0.6) is about 0.64.

The student asked to find the arc-sine (inverse sine) of three values and round the answers to the nearest hundredth. You use your calculator to find these values:

Note: Arcsine is a trigonometric function which checks the angle whose sine is a given number.

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Answer:

28x + 8y + 2

Step-by-step explanation:

Combine like-terms within the parentheses, then distribute -2.

Hope this helps! :)

Answer:

B

Step-by-step explanation:

Given

- 2(3x + 12y - 5 - 17x - 16y + 4)

Simplify the parenthesis by collecting like terms

= - 2 (- 14x - 4y - 1) ← distribute the terms in the parenthesis by - 2

= 28x + 8y + 2 → B

Answer:

H(G(x)) = 12x - 52

Step-by-step explanation:

We are given the following two functions:

[tex] H ( x ) = - 6 x + 8 [/tex]

[tex] G ( x ) = 1 0 - 2 x [/tex]

And we are to find the value of H(G(x)).

For that, we will apply the function of H on the function of G.

[tex]H(G(x))=H(10-2x)[/tex]

[tex] H ( G ( x ) ) = - 6 ( 1 0 - 2 x ) + 8 [/tex]

[tex]H(G(x))=-60+12x+8[/tex]

H(G(x)) = 12x - 52

Answer:

B. 6.

Step-by-step explanation:

We have been given graph of a function. We are asked to find the average rate of change of our given function for the interval from [tex]x=-4[/tex] to  [tex]x=-2[/tex].

We will use formula [tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex] to solve our given problem.

[tex]\text{Average rate of change}=\frac{f(-2)-f(-4)}{-2--4}[/tex]

[tex]\text{Average rate of change}=\frac{6--6}{-2+4}[/tex]

[tex]\text{Average rate of change}=\frac{6+6}{2}[/tex]

[tex]\text{Average rate of change}=\frac{12}{2}[/tex]

[tex]\text{Average rate of change}=6[/tex]

Therefore, the average rate of change for our given function on given interval would be 6 and option B is the correct choice.

Answer:

6

Step-by-step explanation:

just took on A P E X

Answer:

10:8

Step-by-step explanation:

Answer:

.6 meters

Step-by-step explanation:

We need to take the total length and divide it by 4, since that is the number of rods we want and they are all the same length

2.4/4 =.6 meters

Each rod will be .6 meters long

Answer:

G=Seven

Step-by-step explanation:

-two=g-nine

two=nine-?

two=nine-seven

-two=seven-nine

Answer:

Ellen invested $60 and Bob invested $140

Step-by-step explanation:

let the two amounts invested by 3x and 7x

(notice 3x : 7x = 3 : 7 )

then 3x + 7x = 200

10x = 200

x = 20

then 3x = 3(20) = 60

and 7x = 7(20) = 140

60+140=200

Ellen invested $60, and Bob invested $140 in their business.

The student's question involves determining how much each business partner invested in their business based on a given ratio and total investment amount. Ellen and Bob invested money at a ratio of 3 to 7 with a total of $200 invested. To solve this, we need to find out what each 'part' of the ratio is worth in dollars.

Let's consider the total number of parts in the ratio, which is 3 (for Ellen) + 7 (for Bob) = 10 parts in total. Since the total amount invested is $200, each part of the ratio is worth $200 divided by 10, which is $20. Therefore:

Hence, Ellen invested $60, and Bob invested $140 in their business.

Answer:

slope = - 6

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 15 = - 6(x + 7) ← is in point- slope form

with slope m = - 6

The slope of the line that is represented by the equation y-15=-6(x+7) is -6.

The given equation is y-15=-6(x+7).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The standard form of the slope intercept form is y=mx+c.

Where, m=slope and c=y-intercept

Here, y-15=-6(x+7) can be written as y-15=-6x-42

⇒ y=-6x-42+15

⇒ y=-6x-27

So, slope of an equation is -6.

Therefore, the slope of the line that is represented by the equation y-15=-6(x+7) is -6.

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Answer: 200+40x=600

Step-by-step explanation:

200+40x=600

600-200=400

40x=400

40/40= 1 or x

400/ 40=10

x=10

Answer:

b

Step-by-step explanation:

becuase 10p which it states in the equation the 10 dollars per person and plus 50 base and 2.5 is not in the equation