After the end of an advertising campaign, the daily sales of a product fell rapidly, with daily sales given by S=3800e−0.05x dollars, where x is the number of days from the end of the campaign.a. What were daily sales when the campaign ended?b. How many days passed after the campaign ended before daily sales were below half of what they were at the end of the campaign?

After The End Of An Advertising Campaign, The Daily Sales Of A Product Fell Rapidly, With Daily Sales

Answers

Answer 1

Since the given equation is

[tex]S=3800e^{-0.05x}[/tex]

S is the amount of the daily sales from ending to x days

Since the form of the exponential function is

[tex]y=ae^x[/tex]

Where a is the initial amount (value y at x = 0)

Then 3800 represents the daily sales when x = 0

Since x = 0 at the ending of the campaign, then

a. The daily sales when the campaign ended is $3800

Since the daily sales will be below half $3800 after x days

Then find half 3800, then equate S by it, then find x

[tex]\begin{gathered} S=\frac{1}{2}(3800) \\ S=1900 \end{gathered}[/tex][tex]1900=3800e^{-0.05x}[/tex]

Divide both sides by 3800

[tex]\begin{gathered} \frac{1900}{3800}=\frac{3800}{3800}e^{-0.05x} \\ \frac{1}{2}=e^{-0.05x} \end{gathered}[/tex]

Insert ln for both sides

[tex]\ln (\frac{1}{2})=\ln (e^{-0.05x})[/tex]

Use the rule

[tex]\ln (e^n)=n[/tex][tex]\ln (\frac{1}{2})=-0.05x[/tex]

Divide both sides by -0.05 to find x

[tex]\begin{gathered} \frac{\ln (\frac{1}{2})}{-0.05}=\frac{-0.05x}{-0.05} \\ 13.86294=x \end{gathered}[/tex]

Since we need it below half 3800, then we round the number up to the nearest whole number

Then x = 14 days

b. 14 days will pass after the campaign ended


Related Questions

Convert the unit to the specified equivalent unit round your answer to at least1 decimal place if necessary

Answers

Given:

There are given that the 209 ounces to convert into the decigram.

Explanation:

According to the concept:

To convert the ounces into the decigram, we need to multiply the mass values by 283.

That means,

The value of 1 ounce is 283 decigram

So,

[tex]\begin{gathered} 209ounces=209\times283decigram \\ =59147decigram \end{gathered}[/tex]

Final answer:

Hence, the value of the 209 ounces is 59147 decigrams.

I need help find the answer to number 10 and 11

Answers

10. We need to identify the value of b in the function:

[tex]f(x)=b^x[/tex]

so that it produces the graph given.

Observing the graph, we see that the point (1,2) lies on it. Thus, we have:

[tex]\begin{gathered} 2=b^1 \\ \\ \Rightarrow2=b \end{gathered}[/tex]

Therefore, the value of the base b is: 2

Using the drawing find y: MzBDJ = 7y + 2, mZJDR = 2y + 7 * HRT O 25 O 19 O O TY

Answers

[tex]\begin{gathered} \angle BDR=m\angle BDJ+m\angle JDR \\ \angle BDR=7y+2+2y+7 \\ \angle BDR=9y+9 \\ 90-9=9y \\ 81=9y \\ y=\frac{81}{9} \\ y=9 \end{gathered}[/tex]

What is the domain of the rational function f of x is equal to the quantity x squared plus x minus 6 end quantity over the quantity x cubed minus 3 times x squared minus 16 times x plus 48 end quantity question mark

Answers

To solve this problem, we have to find the zeros of the expression in the denominator, to do it, factor the expression:

[tex]\begin{gathered} x^3-3x^2-26x+48=0 \\ (x-3)(x-4)(x+4)=0 \\ x-3=0 \\ x=3 \\ x-4=0 \\ x=4 \\ x+4=0 \\ x=-4 \end{gathered}[/tex]

The zeros of the function are x=3,4,-4.

Since these values make the expression be zero, they are not included in the domain of the function. This is because the expression in the denominator can not be zero, otherwise, the function would be undefined.

The correct answer is B:

[tex]\mleft\lbrace x\in R\mright|x\ne-4,3,4\}[/tex]

A box can be formed by cutting a square out of each corner of a piece of cardboard and folding the sides up. If the piece of cardboard is 78 cm by 78 cm and each side of the square that is cut out has length x cm, the function that gives the volume of the box is V=6084x−312x2+4x3. Complete parts (a) and (b) below.

Answers

a) Notice that:

1)

[tex]6084x-312x^2+4x^3=4x(1521-78x+x^2)=4x(x-39)^2\text{.}[/tex]

Therefore V(x)=0 at x=0 and it has a double root at x=39.

2)

[tex]\begin{gathered} V(-1)=6084(-1)-312(-1)^2+4(-1)^3, \\ V(-1)=-6084-312-4<0. \end{gathered}[/tex]

Therefore, V(x)<0 when x is in the following interval:

[tex](-\infty,0).[/tex]

3)

[tex]V(1)=6084(1)-312(1)^2+4(1)^3>0.[/tex]

Therefore, V(x)>0 when x is in the following set:

[tex](0,39)\cup(39,\infty).[/tex]

b) Since x is a length, then it must be greater than zero, also 2x must be smaller than 78, therefore the values of x that makes sense in the context are in the interval:

[tex](0,39)\text{.}[/tex]

Answer:

a) Option B) The values of x that makes V>0 are in the set:

[tex](0,39)\cup(39,\infty).[/tex]

b) Option A) The values of x that give squares that can be cut out to construct a box are the interval:

[tex](0,39)\text{.}[/tex]

(0,39).

how do I solve (-2+5i) (4-i) +(2-i)

Answers

Given:

[tex](-2+5i)(4-i)+(2-i)[/tex]

Using the distributive property for the multiplication then combine the like terms

so, the given expression will be:

Note: i² = -1

[tex]\begin{gathered} (-2+5i)(4-i)+(2-i) \\ =-2(4-i)+5i(4-i)+(2-i) \\ =-8+2i+20i-5i^2+2-i \\ =-8+2i+20i+5+2-i \\ =(-8+5+2)+(2i+20i-i) \\ =-1+21i \end{gathered}[/tex]

So, the answer will be:

[tex]-1+21i[/tex]

What is the average rate of change of the equation f(x)^2+3x-5 from x=2 to x=4?Type your numerical answer below. Use the hyphen (-) to represent a negative sign if necessary.

Answers

Given:

The equation is,

[tex]f\mleft(x\mright)=x^2+3x-5,x=2\text{ to x = 4}[/tex]

To find: The average rate of change

Explanation:

The average rate of the change formula is,

[tex]A\left(x\right)=\frac{f\mleft(b\mright)-f\mleft(a\mright)}{b-a}[/tex]

Here, we have

[tex]\begin{gathered} a=2 \\ b=4 \end{gathered}[/tex]

Substituting we get,

[tex]\begin{gathered} A\lparen x)=\frac{f\mleft(4\mright)-f\mleft(2\mright)}{4-2} \\ =\frac{\left\lbrack4^2+3\left(4\right)-5\right?-\left\lbrack2^2+3\left(2\right)-5\right?}{2} \\ =\frac{16+12-5-\left\lbrack4+6-5\right\rbrack}{2} \\ =\frac{23-5}{2} \\ =\frac{18}{2} \\ =9 \end{gathered}[/tex]

Final answer:

The average rate of change of the given equation is 9.

use the formula for computing future value using compound interest to determine the value of an account at the end of 10 years if a principal amount of $10,000 is deposited in an account at an annual rate of 3% and the interest is compounded quarterly. The amount after ten years will be $_______ (round to the nearest cent as needed). A = P ( 1 + r/m) ^ n

Answers

Given:

P=$10000 : m=4 : r=0.03 : n=40

[tex]A=P(1+\frac{r}{m})^n[/tex][tex]A=10000(1+\frac{0.03}{4})^{40}[/tex][tex]A=10000(1.0075)^{40}[/tex][tex]A=10000(1.3483)[/tex][tex]A=\text{ \$13483}[/tex][tex]1\text{ \$= 100 cent}[/tex][tex]A=13483\times100[/tex][tex]A=\text{ 1348300 cent}[/tex]

Therefore,The amount after ten years will be 1348300 cent.

The mean life of a television set is 97 months with the variance of 169. If a sample of 59 televisions is randomly selected what is the probability that the sample mean would be less than 100.9 months? Round your answer to four decimal places if necessary

Answers

Given that the mean life of a television set is 97 months, you can set up that:

[tex]\mu=97[/tex]

You also know that the variance is:

[tex]\sigma^2=169[/tex]

You can find the standard deviation by taking the square root of the variance. Then:

[tex]\sigma=\sqrt{169}=13[/tex]

You need to find:

[tex]P(X<100.9)[/tex]

You need to find the z-score with this formula:

[tex]z=\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

Knowing that:

[tex]\bar{X}=100.9[/tex]

You can substitute values into the formula and evaluate:

[tex]z=\frac{100.9-97}{\frac{13}{\sqrt{59}}}\approx2.30[/tex]

You have to find:

[tex]P(z<2.30)[/tex]

Using the Standard Normal Distribution Table, you get:

[tex]P(z<2.30)\approx0.9893[/tex]

Then:

[tex]P(X<100.9)\approx0.9893[/tex]

Hence, the answer is:

[tex]P(X<100.9)\approx0.9893[/tex]

Question 5 of 10 Which of the segments below is a secant? B D O A. CD O B. AB O C. ÃO D. BC

Answers

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

Diagram

secant = ?

Step 02:

We must analyze the diagra,m to find the solution.

Secant ===> straight line that cuts a curve in two or more parts

Segments:

CD: FALSE

AB: FALSE

AO: FALSE

BC: TRUE

The answer is:

Segment BC is a secant

Joey buys a home for $205,900. His home is predicted to increase in value 4% each year. What is the predicted value of his home in 22 years? Round answer to thenearest whole number

Answers

Since every year the value of the house increase by 4%, the new value will be the previous value plus 4% of the previous value. To find 4% of a quantity, we just have have to multiply it by 4 and then divide by 100(or, written as a decimal, multiply the number by 0.04).

If we call the previous value of the house as P and the new value as N, the new value after one year will be

[tex]N=P+0.04P=(1+0.04)P=1.04P[/tex]

Every year that passes, to get the new value we multiply again by 1.04. The expression for the predicted value after t years is

[tex]N(t)=P_0(1.04)^t[/tex]

Where P0 represents the initial value of the house. Evaluating t = 22 on this expression, we have

[tex]N(22)=205,900(1.04)^{22}=487,966.279171\ldots\approx487,966[/tex]

The predicted value of his home in 22 years is $487,966.

Hay e escalones desde el pedestal hasta la cabeza de la Estatua de la Libertad. La cantidad de escalones que hay en el Monumento a Washington es 27 menos que 6 veces la cantidad de escalones que hay en la Estatua de la Libertad. ¿Qué expresión representa la cantidad de escalones que hay en el Monumento de Washington en función de e? 27 < 6e 6(e-27) 6e-27 They 6e

Answers

Let

e -----> number of steps from the pedestal to the head of the Statue of Liberty

f ----> number of steps on the Washington Monument

we have that

f=6e-27

therefore

teh answer is

6e-27

Do you understand my explanation?escalones que hay en el Monumento a Washington

we have that

f=6e-27

L) Point A bisects CR. CA = 8x + 1 and AR = 6x+13.Find CA.34927

Answers

We will investigate some application of line bisectors.

We have a line segment denoted as ( CR ). A point ( A ) is said to be bisecting the line segment.

Line bisection involves the process of equally dividing the entire line segment in two equal halves! We can also represent this scenario graphically for clearification:

We can also represent line bisection mathematically in terms of two smaller divisions ( CA and AR ) as follows:

[tex]Bi\sec tion\colon\text{ |CA| = |AR| = }\frac{|CR|}{2}[/tex]

Where, the quantities are expressed as magnitudes/lengths of each segment indicated.

We are given expressions for bifurcated line segments |CA| and |AR| in terms of variable ( x) as follows:

[tex]\begin{gathered} |CA|\text{ = 8x + 1} \\ |AR|\text{ = 6x + 13} \end{gathered}[/tex]

Now we will use the expression given for each smaller division of line |CR| and plug it in the general " Bisection " expression developed above:

[tex]\begin{gathered} |CA|\text{ = |AR|} \\ 8x\text{ + 1 = 6x + 13} \end{gathered}[/tex]

We have constructed an equation with a single variable ( x ). We can solve this equation for the variable ( x ) using basic mathematical operations as follows:

[tex]\begin{gathered} 8x\text{ - 6x = 13 - 1} \\ 2x\text{ = 12} \\ x\text{ = 6} \end{gathered}[/tex]

Once we have solved for the variable ( x ). We will again use the defined expression for each smaller segments and determine the magnitudes as follows:

[tex]\begin{gathered} |CA|\text{ = 8}\cdot(6)\text{ + 1 } \\ |CA|\text{ = 49 units} \\ \\ |AR|\text{ = 6}\cdot(6)\text{ + 13 } \\ |AR|\text{ = 49 units} \\ \\ |\text{ CR | = 2}\cdot|CA|\text{ = 2}\cdot49 \\ |\text{ CR | = 98 units} \end{gathered}[/tex]

is 1,000 feet greater than 300 yards

Answers

hello

to solve this question, we have to know the the dimensions or

Roberto bought a new graduated cylinder for his chemistry class. it holds 650 mililiters of liquid. if the cylinder has a radius of 5 cm, then how tall is the cylinder.

Answers

8.27 cm

Explanation

Step 1

the volume of a cylinder is given by:

[tex]\begin{gathered} \text{Volume}=\text{ area of the circle}\cdot\text{ height} \\ \text{Volume}=(\pi\cdot raidus^2)\cdot\text{height} \end{gathered}[/tex]

then

Let

Heigth=unknown=h

volume=650 ml

radius= 5 cm

also

1 mililiter= 1 cubic centimeter

so,replacing

[tex]\begin{gathered} \text{Volume}=(\pi\cdot raidus^2)\cdot\text{height} \\ \text{650 }=(\pi\cdot(5cm)^2)\cdot\text{h} \\ 650=25\pi\cdot h \\ \text{divide both sides by 25 }\pi \\ \frac{650}{25\pi}=\frac{25\pi h}{25\pi} \\ h=\frac{650}{25\pi}=8.27\text{ cm} \end{gathered}[/tex]

so, the cylinder is 8.27 cm tall.

I hope this helps you

if Sarah has 98 baseball cards in her collection for birthday her she's given 78 new cards and she sold 108 cards how many baseball cards does Sarah have left

Answers

68

1) Gathering the data

Sarah has 98 cards

She's given 78 then we can add

98 +78 = 176 cards

2) And right after that Sarah sold 108 cards, so now we can write

176 -108 = 68

3) Finally, Sarah now has 68 baseball cards left.

given triangle CAT is congruent to triangle DOG. Solve for x

Answers

Answer:

The value of x is 2 or -5.5.

Explanation:

Given that triangle CAT is congruent to triangle DOG, then we have that:

[tex]\angle T\cong\angle G[/tex]

Step 1: We determine the value of angle T.

[tex]\begin{gathered} \angle T=180^0-(87^0+75^0) \\ =180^0-162^0 \\ =18^0 \end{gathered}[/tex]

Step 2: Since angle T is congruent to angle G, then:

[tex](x+4)(2x-1)=18[/tex]

Step 3: We solve the equation above for x.

[tex]\begin{gathered} 2x^2-x+8x-4-18=0 \\ 2x^2+7x-22=0 \\ 2x^2-4x+11x-22=0 \\ 2x(x-2)+11(x-2)=0 \\ (2x+11)(x-2)=0 \end{gathered}[/tex]

Therefore:

[tex]\begin{gathered} 2x+11=0\text{ or x-2=0} \\ 2x=-11\text{ or x=2} \\ x=-5.5\text{ or x=2} \end{gathered}[/tex]

The value of x is 2 or -5.5.

I have a pentagon that 8 and 8 and 6 and 6 and 10 whats the perimeter?

Answers

The perimeter of any closed figure is equal to sum of all sides of the figure.

Determine the perimeter of pentagon by addition of measure of sides of pentagon.

[tex]\begin{gathered} P=8+8+6+10+6 \\ =38 \end{gathered}[/tex]

So answer is 38 cm.

At a food drive, afood bank has a goal to collect 24,000 cans.If the food bank collects 100 fewer cansthan its goal, how many cans did it collect?

Answers

Given:

• Expected number of cans to collect = 24,000 cans.

,

• The food bank collects 100 fewer cans.

Let's find the number of cans it collected.

Since the food bank collected 100 fewer cans, to find the number of cans it collected, let's subtract 100 from the expected goal which is 24000 cans.

Hence, we have:

Number of cans collected = expected goal - 100

Number of cans collected = 24000 - 100 = 23900

Therefore, the number of cans the food bank collected was 23,900 cans.

ANSWER:

23900 cans

1 point 3 John ran 3 les in of an hour Marlon ran s 4 miles in of an hour How lar did Marlon run in one hour?

Answers

Answer:

6.2 miles per hour

Explanation:

Marlon ran 8 1/4 miles in 4/3 of an hour.

So, we first need to transform the mixed number 8 1/4 into a fraction using the following equation:

[tex]\begin{gathered} A\frac{b}{c}=\frac{A\cdot c+b}{c} \\ 8\frac{1}{4}=\frac{8\cdot4+1}{4}=\frac{32+1}{4}=\frac{33}{4} \end{gathered}[/tex]

Then, we need to divide 33/4 miles by 4/3 hour as:

[tex]\begin{gathered} \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c} \\ \frac{\frac{33}{4}}{\frac{4}{3}}=\frac{33\cdot3}{4\cdot4}=\frac{99}{16}=6.2\text{ miles per hour} \end{gathered}[/tex]

So, Marlon ran 6.2 miles per hour.

Sowen rolled two number cubes with sides numbered 1 through 6, 20 times. Her sums are recorded in the table below.49899462.1012879111087935What is the experimental probability of rolling a sum of 9?4/20Сь5/20Od4/365/36

Answers

The total number of experiment, N=20.

From the given data, 9 is obtained 5 times.

The number of times of getting 9, n=5.

Hence, the probability of getting a sum of 9 is,

[tex]\begin{gathered} P=\frac{n}{N} \\ P=\frac{5}{20} \end{gathered}[/tex]

Hence, option b is correct.

I need help with number 16 can I please get help?

Answers

We can break apart the figure into 4 separate figures and find the area of each of these individual figures. Then sum to get area of total figure.

We break apart the figure as shown below:

First,

Area of Triangle = 0.5 * base * height

Area of Rectangle = base * height

Now, let's find each of the Areas A through D:

Area of A:

To find the base of this triangle, we have to use pythagorean theorem. By which we can write:

[tex]b^2+4^2=6^2[/tex]

Where b is the base. let's solve for b:

[tex]\begin{gathered} b^2+16=36 \\ b^2=36-16 \\ b^2=20 \\ b=\sqrt[]{20} \\ b=\sqrt[]{4}\sqrt[]{5} \\ b=2\sqrt[]{5} \end{gathered}[/tex]

Area is

[tex]\begin{gathered} 0.5\cdot\text{base}\cdot\text{height} \\ =\frac{1}{2}\cdot2\sqrt[]{5}\cdot4 \\ =4\sqrt[]{5} \end{gathered}[/tex]

Area of B:

This is a rectangle with base = 10 and height 4, so the area is:

Area = 4 * 10 = 40

Area of C:

Area of C is exactly same as area of B, base is 10 and height is 4. So,

Area = 4 * 10 = 40

Area of D:

Like area of A, we have to find the base of the triangle first, using pythagorean theorem. We can write:

[tex]\begin{gathered} b^2+4^2=4.5^2 \\ \end{gathered}[/tex]

Solving for b:

[tex]\begin{gathered} b^2+4^2=4.5^2 \\ b^2+16=20.25 \\ b^2=\frac{17}{4} \\ b=\frac{\sqrt[]{17}}{\sqrt[]{4}} \\ b=\frac{\sqrt[]{17}}{2} \end{gathered}[/tex]

Now, area of triangle is:

[tex]A=\frac{1}{2}(\frac{\sqrt[]{17}}{2})(4)=\sqrt[]{17}[/tex]

Area of whole figure:

[tex]\begin{gathered} 4\sqrt[]{5}+40+40+\sqrt[]{17} \\ =80+4\sqrt[]{5}+\sqrt[]{17} \end{gathered}[/tex]

Since mulch costs $3 per square feet, we have to multiply the area by "3", so we have:

[tex]3\times(80+4\sqrt[]{5}+\sqrt[]{17})\approx279.202[/tex]

It will cost around:

$279.20

How do I solve for x? Would my answer be 27?

Answers

Given:

[tex]\angle ABC=(4x+2)^o,\angle ACB=(2x-9)^o,\angle XAC=(5x+13)^o[/tex]

[tex]We\text{ know that }\angle BAC\text{ and }\angle XAC\text{ are supplementary angles.}[/tex]

The sum of the supplementary angles =180 degrees.

[tex]\angle BAC+\angle XAC=180^o[/tex]

[tex]\text{ Substitute }\angle XAC=(5x+13)^o\text{ in the equation.}[/tex]

[tex]\angle BAC+(5x+13)^o=180^o[/tex]

[tex]\angle BAC=180^o-\mleft(5x+13\mright)^o[/tex]

We know that the sum of all three angles of the triangle is 180 degrees.

[tex]\angle ABC+\angle ACB+\angle BAC=180^o[/tex]

[tex]\text{ Substitute }\angle ABC=(4x+2)^o,\angle ACB=(2x-9)^o,\angle BAC=180^o-(5x+13)^o\text{.}[/tex]

[tex](4x+2)^o+(2x-9)^o+180^o-(5x+13)^o=180^o[/tex]

[tex](4x+2)^o+(2x-9)^o-(5x+13)^o=180^o-+180^o[/tex]

[tex](4x+2)^o+(2x-9)^o-(5x+13)^o=0[/tex]

[tex]4x+2+2x-9-5x-13=0[/tex]

Adding like terms that have the same variable with the same powers.

[tex]4x+2x-5x+2-9-13=0[/tex]

[tex]x-20=0[/tex][tex]x=20[/tex]

Hence the value of x is 20.

Find the absolute change and the percentage change for the given situation.120 is decreased to 18

Answers

The absolute change is defined as:

[tex]V_2-V_1[/tex]

where V1 and V2 are the initial and final values, respectively.

Plugging the values given we have that:

[tex]18-120=-102[/tex]

Therefore the absolute change is -102. (The minues sign indicate a decrease)

The percentage change is given by:

[tex]\frac{V_2-V_1}{\lvert V_1\rvert}\cdot100[/tex]

plugging the values given we have:

[tex]\frac{18-120}{\lvert120\rvert}\cdot100=-\frac{102}{120}\cdot100=-0.85\cdot100=85[/tex]

Therefore the percentage change is -85% (Once again the minus sign indicate a decrease)

simplifying with like terms; a + 2a -7

Answers

In the expression like terms are a and 2a.

Simplify the expression

[tex]a+2a-7=3a-7[/tex]

So answer is 3a - 7.

2. Line ( has a slope of -7 and a y-intercept of 12. What is the equation for line in slope-intercept form? y =12x-7 y=-7x+12 --7x+12y=0which one of those equations are true

Answers

The general form of a straight line graph is: y = mx + c

where m and c are the slope and slope-intercept respectively.

from the question given, the slope (m) = -7

and the intercept (c) = 12

substituting the values into y = mx + c

then y = -7x + 12

A figure is made up of two triangles and a square. The trianglesand the square have the same base length of 9 feet. Thetriangles have a height of 12.3 feet. What is the total area of thefigure?

Answers

[tex]\begin{gathered} \text{Total area= square´s area + triangles´ area} \\ \text{squares area= }(9)\cdot(9) \\ \text{squares area= 81 ft}^2 \\ \text{Triangles area =2}\cdot\text{ (}\frac{(12.3)\cdot(9)}{2}\text{)} \\ \text{Triangles area =}110.7ft^2 \\ \text{Total area=81 ft}^2\text{ + }110.7ft^2 \\ \text{Total area=191.7}ft^2 \\ \text{The total area of the figure is 191.7}ft^2 \end{gathered}[/tex]

A quadratic equation is shown below:x^2 + 18x + 76 = 0Which of the following is the first correct step to write the above equation in the form (x-p)^2 = q, when p and q are integers? A. Add 9 to both sides of the equationB. Add 5 to both sides of the equationC. Subtract 5 from both sides of the equationD. Subtract 9 from both sides of the equation.

Answers

SOLUTION:

[tex]\begin{gathered} x^2\text{ + 18x + 76 = 0} \\ To\text{ make left hand p}\operatorname{erf}ect\text{ square, we add 5 to both sides} \\ x^2\text{ + 18x + 76 + 5 = 0 + 5} \\ x^2\text{ + 18x + 81 = 5} \\ x^2\text{ }+18x+9^2\text{ = 5} \\ (x+9)^2\text{ = 5} \end{gathered}[/tex]

The correct option B, that is, add 5 to both sides of the equation.

For each coefficient choose whether it is positive or negative. Choose the coefficient with the greatest value. Choose the coefficient closest to zero.

Answers

First we need to find if the coefficients are negative or positive. The function:

[tex]\lvert x\rvert[/tex]

Is always positive which means that its graph must be over the x axis. If this function is multiplied by a positive coefficient then the graph remains over the x axis. On the other hand, if it's multiplied by a negative number then the graph is now under the x axis. A and B graph are over the x axis so they are positive whereas C and D graphs are under the x axis and they are negative and that's the answer for a.

Then we must find the coefficient with the greatest value. Since a positive number is greater than any negative number we can discard C and D. Now we have two options, A and B which we know are different numbers since their graph are different. Both are V shaped but graph B is sharper than graph C. This means that B is greater than C. Then, the answer to part b is coefficient B.

In part c we must choose the coefficient that is closest to 0. Using the same argument as before, the sharper the V shaped graph is the greatest absolute value its coefficient has. This means that the least sharp graph is that of the coefficient that is closer to 0. Looking at the four graphs you can see that the least sharp V is that of coefficient A. Then, the answer to part c is coefficient A.

There are 221 6th graders in the HPS district that are going on field trip to the Detroit Institute of Arts when we get back to school. If each bus holds 46 students, how many buses should be hierd to transport us?

Answers

Students = 221

Each bus holds 46 students

Divide the total number of students (221) by the capacity of each bus (46 )

221 /46 = 4.8 = 5 buses

Other Questions
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