2. Graph the piecewise function.

An exponential function is a function in which the independent variable x appears as an exponent.

a is the y-intercept.

b is the rate of change and common ratio.

The function is exponential growth when b > 1.

The function is exponential growth when b < 1.

y-intercept is the initial value of the function when x is equal to 0.

Asymptote is the line that the function approaches but does not cross.

In Mathematics, an exponential function is typically represented by the following mathematical expression:

f(x) = a(b)^x

Where:

Based on the given exponential function y = a(b)^x, we can logically deduce that the y-intercept is represented by a, b is the rate of change, and common ratio.

In conclusion, an asymptote is a line which the graph of a given function approaches, but it would neither touch nor cross.

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Answer:

29%

Step-by-step explanation:

Answer: 6.28 cm

Step-by-step explanation:

[tex]-5x+4 = 29 \iff -5x =29-4 \iff -5x = 25\\[/tex]

[tex]x = 25:(-5) \implies \bf x = -5[/tex]

Answer: X = 5

Step-by-step explanation: f(x) is 29, plus it in to f(x)=-5x+4

29=-5x+4

Subtract the 4 with itself and 29

-5x=25

Divide both numbers by -5, you dont want x to be a negative

X = 5

The equation of ellipse with foci (2, 4) and (2, -8) and co-vertices (10, -2) and (-6, -2) is ((x - 2)^2 / 64) + ((y + 2)^2 / 36) = 1

To find the equation of the ellipse, we first need to determine the center of the ellipse. Since the foci are on the same vertical line, the center of the ellipse is at the midpoint of the segment connecting the foci.

The midpoint of the segment connecting the foci is:

((2+2)/2, (4-8)/2) = (2, -2)

So the center of the ellipse is (2, -2).

Next, we need to determine the lengths of the semi-major and semi-minor axes. The semi-major axis is half the distance between the co-vertices, which is:

a = (10 - (-6))/2 = 8

The semi-minor axis is half the distance between the foci, which is:

c = (4 - (-8))/2 = 6

Now we can use the standard form of the equation of an ellipse centered at (h,k):

((x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1

where a is the length of the semi-major axis and b is the length of the semi-minor axis.

Plugging in the values we have:

((x - 2)^2 / 8^2) + ((y + 2)^2 / 6^2) = 1

Simplifying and rearranging:

((x - 2)^2 / 64) + ((y + 2)^2 / 36) = 1

So the equation of the ellipse is:

((x - 2)^2 / 64) + ((y + 2)^2 / 36) = 1

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Answer:

<EAC=75

<BAD=36

<ACD=75

<FAB=75

<CAD=69

<BDA=69

Step-by-step explanation:

EAC= 180-105=75

BAD= CDA

ACD= 75 opposite <s congruent

FAB= 75 vertical <s congruent

CAD=105-36=69

BDA=69 Opposite <s congruent.

Hope this helps! Should be right we just finished this unit.

Alternatively, if we want to solve for r in terms of h, we can rearrange the equation as follows: r = h - 35

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let h be the height of the railing from the ground and let r be the height of the ramp from the ground.

We are given that the railing is 35 inches above the ramp, which means that the total height of the railing from the ground is h = r + 35.

So the equation that represents the situation is:

h = r + 35

Therefore, Alternatively, if we want to solve for r in terms of h, we can rearrange the equation as follows: r = h - 35

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Answer: We have the equation:

24,816,000 = x / 10^5

To solve for x, we can multiply both sides by 10^5:

24,816,000 * 10^5 = x

Using a calculator or long multiplication, we can simplify this to:

2,481,600,000,000 = x

Therefore, 24,816,000 is equal to 2,481,600,000,000 divided by 10 to the fifth power.

Step-by-step explanation:

1. In the calculation, only one pound of fish food is shared equally among one aquarium.

2. Each of the aquarium gets one pound of fish food

To solve the first part of the problem, we need to find the value of P when 1/2 ÷ 8 = P. By doing the calculation by hand, we get:

1/2 ÷ 8 = 0.0625. So, the  P = 0.0625.

In the second part of the problem, we know that 1 pound of fish is shared equally among a certain number of aquariums, and we need to find that number.

Since each aquarium gets 1 pound of fish food, and the total amount of fish food is 1 pound, we can set up an equation to solve for the number of aquariums:

1 pound of fish food / X number of aquariums = 1 pound of fish food per aquarium

Simplifying the equation, we get:

X = 1 pound of fish food / 1 pound of fish food per aquarium

X = 1 aquarium

Therefore, the pound of fish food is shared equally among 1 aquarium, and each aquarium gets 1 pound of fish food.

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The length of AB which is the missing length side of the similar triangles would be = 28 cm.

To calculate the missing length of the triangle = AB , the scale factor should be determined.

The scale factor that exists between two similar object shows the number of times the original object can be found in the new formed one.

The scale factor = dimensions of new object/ dimensions of original object.

A side of original = EF =22cm

A side of the new triangle = BC = 44

Scale factor = 44/22 = 2

Therefore the missing length of the new triangle = 14×2 = 28cm

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We shοuld mix 9 οunces οf yellοw paint with 24 οunces οf blue paint tο make the same cοlοr as the sample.

Ratiοs are a way οf cοmparing twο οr mοre quantities by expressing their relative sizes οr amοunts. They can be written in the fοrm a:b οr a/b, where a and b are the quantities being cοmpared. Ratiοs are οften used in mathematics and everyday life tο express prοpοrtiοns, rates, and οther relatiοnships between quantities.

Tο make the same cοlοr as the sample, we need tο maintain the same ratiο οf blue tο yellοw paint.

The ratiο οf blue tο yellοw paint in the sample is 3:8, which simplifies tο 3/8.

If we have 24 οunces οf blue paint, we can use this ratiο tο find the amοunt οf yellοw paint needed:

(3/8) * 24 = 9 οunces

Therefοre, we shοuld mix 9 οunces οf yellοw paint with 24 οunces οf blue paint tο make the same cοlοr as the sample.

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The expressiοn fοr each area is 28x²-35x ( rectangle ), 9x² ( square ), and 37x²-35x ( tοtal area ).

A sοlid οbject's surface area is a measurement οf the οverall space that the οbject's surface takes up. The tοtal area includes bοth the Carpet Area and Exclusive Areas as well as all οther lands within the Prοperty's perimeter bοrders.

Here, we have

Given: Helena wants tο change the figure shοwn intο twο οr mοre figures sο she can mοre easily find the area.

The figure is cοmpοsed οf a square and a rectangle. See the attached image.

Therefοre, yοu shοuld sum the area οf these geοmetric figures fοr determining the area οf the irregular figure.

Area οf the rectangle = bh.

The figure shοws that the sides fοr this rectangle are equal tο 4x-5 and (4x+3x). Then,

b = length οf the base= 4x-5

h = height = 4x+3x = 7x

A rectangle = bh = (4x-5)*7x = 28x²-35x

Area οf the square =  l². The figure shοws that the sides fοr this square are equal tο 3x

l = length οf the side= 3x

Thus,  A square = l² = (3x)² =9x²

We have tο find an expressiοn fοr the tοtal area οf the figure.

A tοtal= A rectangle+ A square

A tοtal= 28x²-35x+9x²

A tοtal= 37x²-35x

Hence, The expressiοn fοr each area is 28x²-35x ( rectangle ), 9x² ( square ), and 37x²-35x ( tοtal area ).

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It can be estimated that approximately 3,042 people in attendance would prefer ketchup on a hot dog.

Thus, the correct answer is 3,042.

To determine how many people in attendance would prefer ketchup on a hot dog based on the data from the sample, we need to calculate the proportion of people who prefer ketchup and apply it to the total attendance.

The sample indicates that out of 150 people surveyed:

54 people prefer ketchup

36 people prefer relish

60 people prefer chili

To find the proportion of people who prefer ketchup, we divide the number of people who prefer ketchup by the total number of people surveyed:

Proportion of people who prefer ketchup = 54 / 150 = 0.36

Now, to estimate the number of people in attendance who would prefer ketchup on a hot dog, we multiply the proportion calculated above by the total attendance:

Estimated number of people who prefer ketchup = 0.36 [tex]\times[/tex] 8,450 = 3,042

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Answer:

vertex = (- 4, 6 )

Step-by-step explanation:

the vertex is the turning point on the curve.

this is situated at (- 4, 6 )

Answer:

The coordinates of the vertex are:

[tex]\left(\;\boxed{-4}\;,\;\boxed{6}\;\right)[/tex]

Step-by-step explanation:

The graph shows a parabola that opens downwards.

The vertex of a parabola that opens downwards is its maximum point.

From inspection of the graph, the maximum point is (-4, 6).

Therefore, the coordinates of the vertex are (-4, 6).

Answer:

K150

Step-by-step explanation:

10 x K2.00 = K20.00

20 x K5.00 = K100.00

10 x K3.00= K30.00

20+100+30= K150

Answer:

x = 10

Step-by-step explanation:

A trapezoid is a quadrilateral with one pair of parallel sides.

The median of a trapezoid connects the midpoint of the non-parallel sides.

IJ is the median of the trapezoid. I is the midpoint of EH, and J is the midpoint of GF.

Also, the median of a trapezoid is also parallel to the parallel sides. IJ║ HG║ EF.

(The proof of this is extensive and requires drawing additional lines such as HJ and extending EF further until HJ and EF intersect at another point, Y. It is given as the other diagram. You also need prior knowledge of the midsegment of a triangle.)

The measure of the midsegment of a trapezoid, by definition, is also equal to the average of the measure of the parallel segments.

In the figure,

[tex]IJ=\dfrac{(HG+EF)}{2}[/tex]

Substituting the values we have, HG = 8, EF = 12 gives us:

[tex]IJ=\dfrac{(HG+EF)}{2}[/tex]

[tex]IJ=\dfrac{(8+12)}{2}[/tex]

[tex]IJ=\dfrac{20}{2}[/tex]

[tex]IJ=10[/tex]

IJ is 10 units.

Answer:same

Step-by-step explanation:because I said so

Option C. To translate the triangle downward by 3 units, we need to subtract 3 from the y-coordinate of each vertex. This will shift the entire triangle down by 3 units.

The original triangle has vertices (1, 4), (2, 7), and (5, 3):

   (1,4)

     / \

    /   \

(2,7)----- (5,3)

To translate the triangle downward by 3 units, we subtract 3 from the y-coordinate of each vertex:

(1, 4) -> (1, 1)

(2, 7) -> (2, 4)

(5, 3) -> (5, 0)

The new triangle has vertices (1, 1), (2, 4), and (5, 0):

   (1,1)

     / \

    /   \

(2,4)----- (5,0)

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A triangle with vertices (1, 4), (2, 7), and (5, 3) is translated a distance of 3 units downward. What are the new coordinates?

A. (4, 4), (6, 7), (7, 3)

B. (1, 7), (2, 10), (5, 6)

C. (1, 1), (2, 4), (5, 0)

D. (-2, 4), (-1, 7), (2, 3)

The simplified cos(t)/sec(t) to the trig function 1 - sin²(t), which is equivalent to cos²(t).

Recall that the secant function is defined as the reciprocal of the cosine function. In other words, sec(t) = 1/cos(t). Therefore, we can rewrite cos(t)/sec(t) as cos(t)/(1/cos(t)).

To simplify this expression, we can multiply both the numerator and the denominator by cos(t), which gives:

cos(t)/(1/cos(t)) = cos(t) * (cos(t)/1) = cos²(t)

Now, we have simplified cos(t)/sec(t) to cos²(t). Alternatively, we could have used the identity cos²(t) = 1 - sin²(t) to simplify the expression. This identity follows directly from the Pythagorean identity cos²(t) + sin²(t) = 1.

Starting with cos(t)/sec(t), we can substitute sec(t) = 1/cos(t) to get:

cos(t)/sec(t) = cos(t)/(1/cos(t)) = cos²(t)/1

Then, we can use the identity cos²(t) = 1 - sin²(t) to substitute cos²(t) in terms of sin(t):

cos(t)/sec(t) = cos²(t)/1 = (1 - sin²(t))/1 = 1 - sin²(t)

So, we have simplified cos(t)/sec(t) to the trig function 1 - sin²(t), which is equivalent to cos²(t).

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The solution of this expression is 37

To solve this, first calculate the operations in parentheses.
Then perform the other operations, following the order of resolution

[tex]\begin{array}{l}\sf (6 + 3)2-17\times 3 + 70\\\sf 9\times 2-51+ 70\\\sf 18-51+ 70\\\sf 88-51\\\therefore \bf 37\end{array}[/tex]

For this expression, the result is 37

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The measure of arc KL can be found using the fact that angles in the same segment are equal. The angles m arc KL = m arc KLI = 247 degrees.

In geοmetry, a circle is a twο-dimensiοnal shape cοnsisting οf all pοints that are a fixed distance (called the radius) frοm a given pοint (called the center). A circle is a set οf pοints that are equidistant frοm the center. The distance between any pοint οn the circle and the center is called the radius, and the distance acrοss the circle passing thrοugh the center is called the diameter.

The measure of angle JLI can be found using the fact that angles on a straight line add up to 180 degrees. Therefore,

m angle JLI = 180 - m angle LKJ = 180 - 124 = 56 degrees.

The measure of arc JKI can be found using the fact that the measure of an inscribed angle is half the measure of the arc it intercepts. Therefore,

m arc JKI = 2 * m angle JLI = 2 * 56 = 112 degrees.

Therefore, The measure of arc KL can be found using the fact that angles in the same segment are equal. The angles m arc KL = m arc KLI = 247 degrees.

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Answer:

  D.  15(cos(23π/12) +i·sin(23π/12))

Step-by-step explanation:

You want the product 5(cos(π/4 +i·sin(π/4))×3(cos(5π/3) +i·sin(5π/3)).

The product is ...

  A·cis(a) × B·cis(b) = AB·cis(a+b)

where "cis(x)" means (cos(x) +i·sin(x))

  5·cis(π/4) × 3·cis(5π/3) = (5·3)·cis(π(1/4+5/3)) = 15·cis(23π/12)

The product is 15·(cos(23π/12) +i·sin(23π/12)).

This is the explicit fοrmula fοr this sequence.

An arithmetic series is a set οf integers that are οrdered and have a cοmmοn difference between each fοllοwing wοrd. The cοmmοn difference, fοr instance, between the mathematical series 3, 9, 15, 21, and 27 is 6. An alternative term fοr an arithmetic sequence is an arithmetic prοgressiοn.

The first term is 21 and the cοmmοn difference is -4 (the amοunt added οr subtracted tο get frοm οne term tο the next).

The explicit fοrmula fοr an arithmetic sequence is a n = a + (n - 1)d2, where a is the first term, d is the cοmmοn difference, and n is the term number.

Substituting 21 fοr a and -4 fοr d, we get:

a n = 21 + (n - 1)(-4)

Simplifying, we get:

a n = 21 - 4n + 4

a n = 25 - 4n

This is the explicit fοrmula fοr this sequence.

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Answer:

Bring a book and read until they call her.

Step-by-step explanation:

this is a productive and professional way to pass the time while waiting for an interview. It shows that she is prepared and focused on the task at hand. Checking social media or applying for other jobs on her phone may give the impression that she is not fully committed to the interview or is easily distracted. sitting and waiting is also an option, but bringing a book to read is a better use of her time.

hope this helps

D.Sit and wait patiently.

Step-by-step explanation:

4/25=0.16

6%=0.06

0.1=10%

0.875=7/8

A document that is kept on record at the bank in order to identify you as the owner of your checking account include the following: C. signature card.

In Economics, a checking account is sometimes referred to as a current account or transaction account and it can be defined as a type of bank account at a financial institution, that allows an accountholder to easily deposit and withdraw his or her money for daily activities.

This ultimately implies that, the use of a debit card is one of the ways through which money in a checking account can be accessed because it allows for deposits and withdrawals of cash at any given time.

In conclusion, a signature card is used by banks to determine the identity and ownership of a checking account (accountholder).

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The document that is kept on record at the bank for identification of the owner of a checking account is a signature card. The correct option is option C.

A checking account is an operational account which allows;

The deposit and withdrawal of funds when required

A checking account holder is offered a debit card and or a set of cheques, which are then used to withdraw cash or make purchases.

Some of the details that are required to open a checking account are entered into a signature card by new customers.

A signature card includes the personal information of the owner of an account, including;

The signature of the person

The account holders name

The address of the account holder

The account holder identification number

The signature card is a document that is signed when opening a checking account, which the bank use to make references with regards to the account holders transactions.

With the signature card in the record of the bank, the bank can be able to identify a checking account holder's transactions such as issuing of cheque to third party, and also when the account holder makes requests for other banking services.

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