The area in square millimeters of a wound has decreased by the same percentage every day since it began to heal. The table shows the wound's area at the end of each day.
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Given the table showing the number of days since wound began to heal and area of wound in square millimeters
To determine the statement that are correct from the option provided
From the table shown it can be seen that as the day increases by 1, the area of wound in square millimeters decreases by a common ratio of
[tex]\frac{20}{25}=\frac{16}{20}=\frac{12.8}{16}=\frac{10.24}{12.8}=0.8[/tex]Suppose that an expression to represent the area of wound is
[tex]ab^c[/tex]The modelled expression from the table is
[tex]\begin{gathered} a=25 \\ b=0.8 \\ c=n-1 \\ \text{Therefore, we have} \\ 25(0.8^{n-1}) \end{gathered}[/tex]Let us use the modelled expression to verify each of the given conditions
The modelled expression can be simplified as shown below:
[tex]\begin{gathered} 25(0.8^{n-1}) \\ \text{Note},\text{ using indices rule} \\ \frac{a^n}{a}=a^{n-1} \\ \text{Therefore:} \\ 0.8^{n-1}=\frac{0.8^n}{0.8} \end{gathered}[/tex]Then, we have the modelled expression becomes
[tex]25(0.8^{n-1})=25\times\frac{0.8^n}{0.8}=\frac{25}{0.8}\times0.8^n=31.25(0.8^n)[/tex]From the two modelled expression we can see that
[tex]\begin{gathered} \text{when:} \\ c=n-1,a=25,b=0.8 \\ c=n,a=31.25,b=0.8 \end{gathered}[/tex]Then we can conclude that the two conditions that are true from the options are
If the value of c = n, the value of a is 31.25, and
If the value of c = n, the value of b is 0.8
Related Questions
there are 5 adult cats, 6 middle aged cats, and ___ kittens, if there are 19 animals in total, how many kittens are there, solve for the blank.
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ANSWER
There are 8 kittens
EXPLANATION
If the sum of the number of adult cats, middle aged cats and kittens is 19:
[tex]\begin{gathered} \text{adult}+\text{middle aged+kittens=19} \\ 5+6+\text{kittens}=19 \\ \text{kittens}=19-5-6 \\ \text{kittens}=8 \end{gathered}[/tex]Which parabola corresponds to the quadratic function y = 2x2 + 4x - 16? D. A. B. C. 10:13 1618 10- 12 =10 10 28 -20
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We can see that the y-intercept would be (0,-16) since this is the result of replacing x=0 in the function.
We can also find the x-intercepts solving the equation 0=2x^2+4x-16. Doing so, we have:
[tex]\begin{gathered} 0=2x^2+4x-16 \\ 0=x^2+2x-8\text{ (Dividing by 2 on both sides of the equation)} \\ 0=(x+4)(x-2)\text{ (Factoring)} \\ \text{ We can see that the solutions of the equation are x=-4 and x=2} \\ \text{Therefore the x-intercepts are (-4,0) and (2,0)} \end{gathered}[/tex]The graph that satisfies the conditions we have found previously is the option A.
John has two apples, he gives Jane 251. How many apples does John have? Please help 2nd grade is so hard.
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graph the function y=sqrt(x+6)+2. which point lies on the graph
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Explanation
We are given the following function:
[tex]y=\sqrt{x+6}+2[/tex]We are required to graph the function.
Using a graphing calculator, we have:
Hence, the answer is (-2, 4).
The last option is correct.
what is 9.77 with 8% tax
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it will be 9.77+0.08(9.77)=10.5516
Suppose you have a piece of ribbon that is 6 feet long, and you cut off one piece that's 3 2/3
inches long and a second piece that's 2 5/6 inches long. How much ribbon is left in inches?
inches of ribbon left
Answers
Answer:
65 1/2 inches of ribbon is left, my exact work is shown on a piece of paper below if you need it.
Step-by-step explanation:
1 foot = 12 inches
6 x 12 = 72 inches
72 - (3 2/3 + 2 5/6) = ?
My explanation:
The rib ion originally started at 6 feet
You first cut 3 2/3 off, so your now left with 7/3 or 2 1/3 (simplified)
Now your left with 2 1/3.
Then you cut a second piece off, 2 5/6 inches….so 2 5/6 minus 2 1/3 = 1/2
So you should have about 1/2 of a ribbon left.
(I tried btw. I’m very sleepy rn.)
Lines AD and BC are parallel. What is the angle measurement of Angle DAE(Point A)?D150°45°BсFYour answer
Answers
Solution
For this case we can find the angle:
m < ECB = 30º
And we can find the angle CEB and we got:
m < CEB = 180 -30 - 45 = 105
And then the angle DAE would be:
m < DAE = 30º
The crew knows the amount of dirt the truck can hold each trip in cubic yards.
Answers
Given:
Measurements of hole are 48ft 39ft and and 9ft
Required:
Volume in cubic yd
total number of trip
total cost of trip
Explanation:
First we need to convert given measurements from ft to yd
[tex]\begin{gathered} 3ft=1yd \\ 48ft=16yd \\ 39ft=13yd \\ 9ft=3yd \end{gathered}[/tex]
A)
[tex]V=lhw=16*13*3=624yd^3[/tex]B)
11 cubic yd in 1 trip
then
624 cubic yd in x trip
[tex]x=\frac{624}{11}=56.7\approx57[/tex]C)
cost for 1 trip is $1175
then
cost for 57 trip is y
[tex]y=57*1175=66975[/tex]Final answer:
Volume in cubic yd is 624
total number of trips is 57
total cost of trip $66975
in slope intercept form what is the line perpendicular to y=2x -5 that passes through the (2, -5) point
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The most appropriate choice for equation of line in slope intercept form will be given by-
[tex]y = -\frac{1}{2}x - 4[/tex] is the required equation of line
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
The given equation of line is y = 2x-5
Slope of this line = 2
Slope of the line perpendicular to this line = [tex]-\frac{1}{2}[/tex]
The line passes through (2 , -5)
Equation of the required line = [tex]y - (-5) = \frac{1}{2}(x - 2)[/tex]
[tex]y +5=-\frac{1}{2}x+1\\y = -\frac{1}{2}x +1 -5\\y = -\frac{1}{2}x -4[/tex]
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Find the missing number so that the equation has infinitely many solutions.
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we have the equation
-2x-9=-2x-?
Remember that
If in a system of two linear equations, we have two identical lines
then
The system has infinite solutions
therefore
the missing number is 9
-2x-9=-2x-9If a,b ,and c represent the set of all values of x that satisly the equation below, what is the value(A+ b+ c) + (abc)?X^3-20x = x^2(A) -1(B) 0(C) 1(D) 9
Answers
First, we need to find the solutions a, b, and c of the equation:
[tex]x^3-20x=x^2[/tex]We can rewrite it as:
[tex]\begin{gathered} x^3-x^{2}-20x=0 \\ \\ x(x^{2}-x-20)=0 \\ \\ x=0\text{ or }x^{2}-x-20=0 \end{gathered}[/tex]Thus, one of the solutions is a = 0.
To find the other solutions, we can use the quadratic formula. We obtain:
[tex]\begin{gathered} x=\frac{-(-1)\pm\sqrt[]{(-1)^{2}-4(1)(-20)}}{2(1)} \\ \\ x=\frac{1\pm\sqrt[]{1+80}}{2} \\ \\ x=\frac{1\pm\sqrt[]{81}}{2} \\ \\ x=\frac{1\pm9}{2} \\ \\ b=\frac{1-9}{2}=-4 \\ \\ c=\frac{1+9}{2}=5 \end{gathered}[/tex]Now, we need to find the value of the expression:
[tex]\mleft(a+b+c\mright)+abc[/tex]Using the previous solutions, we obtain:
[tex]\mleft(0-4+5\mright)+0(-4)(5)=1+0=1[/tex]Therefore, the answer is 1.
Michael studied the feather lengths of some adult fox sparrows.How long is the shortest feather in the data set?
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From the data set given, 3/4 is the length of the shortest feather of fox sparrow.
Given,
The image is attached with this.
The length of fox sparrow feathers studied by Michael.
1 sparrow with 3/4 inches of feather4 sparrows with 2 inches of feather7 sparrows with 2 1/4 inches of feather5 sparrows with 2 1/2 inches of feather3 sparrows with 2 3/4 inches of feather.We have to find the shortest feather in the data set.
Here,
3/4 inches is the shortest feather and only 1 sparrow has the shortest feather.
2 3/4 inches is the longest feather and 3 sparrows have the longest feather.
That is,
From the data set given, 3/4 is the length of the shortest feather of fox sparrow.
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Please help. I don't really understand monomials and negative exponets
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The standard form of the monomial expression is -1x¹⁰
Monomial expression:
A monomial is an algebraic expression with a single term but can have multiple variables and a higher degree too.
Given,
Here we have the expression
(-2x³)².(-1/4 x⁴)
Now, we have to convert the expression into standard form.
To convert the expression into standard monomial form,
First we have to expand the terms, then we get,
=> (-2²x⁶).(-1/4x⁴)
Then we have to divide the variables and constants separately.
=> (4 x -1/4).(x⁶⁺⁴)
=> -1 . x¹⁰
=> -1x¹⁰
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The area of a semicircle is 0.5652 square inches. What is the semicircle's diameter? Use 3.14 for a inches Submit can you explain
Answers
Given :
The area of semicircle is given as 0.5652 sq.inches.
To find:
The diameter of semicircle which is denoted as d.
Explanation:
The area of semicircle is given as
[tex]A=\frac{\pi r^2}{2}[/tex]The relation between radius and diameter is
[tex]d=2r[/tex]Now substitute the given area in the area of semicircle formula.
[tex]0.5652=\frac{3.14\times r^2}{2}[/tex][tex]r=\sqrt[]{\frac{2\times0.5652}{3.14}}=\sqrt[]{0.36}[/tex][tex]r=0.6in[/tex]The semicircle diameter is determined as
[tex]d=2r\Rightarrow2\times0.6=1.2in[/tex]Answer:
Hence the diameter of semicircle is determined as 1.2 in.
A tank in the shape of a hemisphere has a diameter of 10 feet. If the liquid that fills the tank has a density of 74.4 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answers
Step 1
State the volume of a hemisphere.
[tex]v=\frac{2}{3}\pi r^3[/tex]Where;
[tex]\begin{gathered} r=\frac{diameter}{2}=\frac{10}{2}=5ft \\ \end{gathered}[/tex]Step 2
Find the volume of the hemisphere
[tex]v=\frac{2}{3}\times\pi\times5^3=\frac{250\pi}{3}ft^3[/tex]Step 3
Find the total weight of the liquid in the tank
[tex]\begin{gathered} \text{Density}=\frac{mass}{\text{volume}} \\ 74.4=\frac{mass}{\frac{250\pi}{3}} \\ \text{mass}=19477.87445lb \\ \text{mass}\approx19478lb \end{gathered}[/tex]Hence the total weight of the liquid in the tank to the nearest full pound = 19478lb
A triangle has squares on its three sides as shown below. What is the value of x? 4 centimeters 7 centimeters 5 centimeters 3 centimeters
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54 is 120 percent of what number ?
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Answer:
120% of 54 =
120% × 54 =
120/100 × 54 =
(120 ÷ 100) × 54 =
120 × 54 ÷ 100 =
6,480 ÷ 100 =
64.8
Percentage of 120% of 54
120% of 54 = 64.8
and to prove that we got the right answer do what we did above in reverse below
64.8 ÷ 54 =
1.2 =
1.2 × 100/100 =
(1.2 × 100)/100 =
120/100 =
120%
Step-by-step explanation:
Let v be the vector from initial point P1=(−4,−9) to terminal point P2=(6,2). Write v in terms of i and j.
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Step 1;
P1 = ( - 4 , -9 )
P2 = ( 6 , 2 )
Step 2:
[tex]\begin{gathered} \text{Let P}_1=(x_1,y_1)_{} \\ P_2=(x_2,y_2\text{ ) } \end{gathered}[/tex]Step 3:
[tex]\text{v = (x}_2-x_1)i+_{}(y_2-y_1\text{ ) j}[/tex]Step 4:
[tex]\begin{gathered} \text{v = (x}_2-x_1)i+_{}(y_2-y_1\text{ ) j} \\ \text{v = (6}-(-4))i+_{}(2-(-9)\text{) j} \\ v\text{ = (6+4)i + (2 + 9)j} \\ v\text{ = 10i + 11 j} \end{gathered}[/tex]The quadratic equation y= -16t^2 +4t+2 represents a moving objects trajectory where y is the objects height in feet above the ground after t seconds . At what time will the objects hit the ground ?
Answers
Since y is the object's height, it will be on the ground when y = 0. So let's do that:
[tex]0=-16t^2+4t+2[/tex]Here, we can use Bhaskara's Formula to find the roots of the equation:
[tex]\begin{gathered} t=\frac{-4\pm\sqrt[]{4^2-4\cdot(-16)\cdot2}}{2\cdot(-16)} \\ t=\frac{-4\pm\sqrt[]{16+128}}{-32}=\frac{-4\pm\sqrt[]{144}}{-32}=\frac{-4\pm12}{-32} \\ t_1=\frac{-4+12}{-32}=\frac{8}{-32}=-0.25 \\ t_2=\frac{-4-12}{-32}=\frac{-16}{-32}=0.5 \end{gathered}[/tex]Since the time at start is 0, we can't have a negative sign, it would be like saying what happened before the object was in the air. The it will hit the ground at t = 0.5 s.
Find the area of a circle with a Diameter = 12 ft. Use 3.14 for π and round to 2 decimal places.
Answers
Given:
Diameter of circle = 12ft
pi = 3.14
Solution
The area (A) of a circle can be calculated using the formula:
[tex]\begin{gathered} A\text{ = }\pi r^2 \\ \text{where r is the radius of the circle} \end{gathered}[/tex]Recall that the diamter (d) and radius (r) are related by the formula:
[tex]\begin{gathered} \text{radius = }\frac{diameter}{2} \\ r\text{ = }\frac{d}{2} \end{gathered}[/tex]We can now find the radius (r) of the circle to be:
[tex]\begin{gathered} r\text{ = }\frac{12}{2} \\ r\text{ = 6 ft} \end{gathered}[/tex]We can now find the area by the applying the formula given above:
[tex]\begin{gathered} A\text{ = }\pi\times r^2 \\ A\text{ = 3.14 }\times6^2 \\ =113.04ft^2\text{ (2.dp)} \end{gathered}[/tex]Answer: 113.04 square feet
Parallel and Perpendicular LinesDetermine whether the following lines are parallel, perpendicular, orneither. Write the corresponding letter on the line next to the question.A = parallel, B = perpendicular, or C = neither1. y = }x+6 and y =- *x + 4
Answers
One of the criteria for lines being perpendicular is the fact that the slope of the function in a perpendicular line is the inverse of the slope of the first times -1.
And as you can see m (being the slope of the first equation) is the inverse of the second equiation:
[tex]m=\frac{7}{3},m_1=-\frac{1}{m}[/tex][tex]-\frac{1}{m}=-\frac{1}{\frac{7}{3}}=-\frac{3}{7}[/tex]Therefore line 1 is perpendicular to line 2.
I need help with my question
Answers
The opposite of a number is the same as multiplying it by -1. any negative number, it's opposite is that same number positive. And any positive number is that same number negative.
Our number W is 5. Then, the opposite number is - 5.
To draw a point at - 5 from 5, we just need to move the difference between them to the left. The difference between 5 and -5 is given by
[tex]|5-(-5)|=|5+5|=|10|=10[/tex]Then, to draw point V we need to move 10 units to the left of Point W.
The function table below is intended to represent the relationship y=-5x+1. However, one of the entries for y does not correctly fit the relationship with x.
Answers
Answer:
Step-by-step explanation:
none of the answers are correct
What is an equation of the line that passes through the points (-3,-5) and (-5, -3)? Put your answer in fully reduced form.
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Express the general equation of a line passing through two points (x1,y1) and (x2,y2).
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Put (-3,-5) for (x1,y1) and (-5,-3) for (x2,y2) implies,
[tex]\begin{gathered} y+5=\frac{-3+5}{-5+3}(x+3) \\ y+5=\frac{2}{-2}(x+3) \\ y+5=-x-3 \end{gathered}[/tex]Further simplifying gives,
[tex]y=-x-8[/tex]Therefore, the equation of the line is y=-x-8.
A ball is kicked up in the air from the ground. The height of the ball can be modeled as a function of time in seconds. This function is represented on the graph below. Enter the average rate of change for the height of the ball, measured as feet per second, between 0 seconds and 2 seconds._[blank]_ feet per secondEnter your answer as a number, like this: 42
Answers
ANSWER:
2
STEP-BY-STEP EXPLANATION:
The average rate of change is given by the following formula:
[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]Since it is between 0 and 2 seconds, the values of a and b will be these respectively, the evaluated values can be determined by the graph, therefore:
[tex]\begin{gathered} r=\frac{4-0}{2-0}=\frac{4}{2} \\ \\ r=2\text{ feet pe second } \end{gathered}[/tex]The average rate of change is equal to 2 feet per second
Simplify 2(2x-7) show work
Answers
Given:
[tex]2(2x-7)[/tex]Aim:
We need to simplify the given expression.
Explanation:
Use the distributive property.
[tex]a(b+c)=ab+ac.\text{ Here a =2, b=2x and c=-7.}[/tex][tex]2(2x-7)=(2\times2x)+(2\times(-7))[/tex]Multiply 2 and 2x, we get 4x and multiply 2 and (-7), we get (-15).
[tex]=4x+(-14)[/tex][tex]Use\text{ \lparen +\rparen\lparen-\rparen=\lparen-\rparen.}[/tex][tex]=4x-14[/tex]Final answer:
[tex]2(2x-7)=4x-14[/tex]Which of the following is the horizontal asymptote for the graph below?10A x=-7B. X=0ООC. y - 0C D. y = -7
Answers
A horizontal like y = k, where k is not part of the graph, but guides the function for x-values “far” to the right and/or “far” to the left.
The horizontal asymptote can be observed in the figure below:
Answer: y = 0.
a point is chosen at random in the large square. find the probability that the point is in the smaller shaded square. each side of the large square: 16 cmeach side of the shaded square: 6 cm*round to the nearest hundredth
Answers
The Probability of the point being in the smaller shaded square is 0.79.
What is meant by probability?Probability equals possibility. It is a branch of mathematics concerned with the occurrence of a random event. The value ranges from 0 to 1. Probability has been introduced in mathematics to predict how likely events are to occur.Probability = the number of possible outcomes. the total number of possible outcomes For example, the probability of flipping a coin and getting heads is 12, because there is only one way to get a head and the total number of possible outcomes is two (a head or tail).The probability is a measure of the likelihood of an event occurring. It assesses the event's likelihood. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the probability formula.Therefore,
|Ω| = 6² = 36
< br / > |A| = 3.14.3² = 278.26
Then we get,
< br / > P |A| = 28.26/36 ≈ 0.79
∴ the probability that the point is in the smaller shaded square is 0.79
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How do I do this, I’m unsure how to go about it
Answers
Given:
[tex]\sqrt{\frac{6}{x}}\cdot\sqrt{\frac{x^2}{24}}[/tex]Simplify:
[tex]=\sqrt{\frac{6}{x}}\cdot\frac{\sqrt{x^2}}{\sqrt{24}}=\sqrt{\frac{6}{x}}\cdot\frac{x}{2\sqrt{6}}[/tex]Apply the properties of fractions:
[tex]=\frac{\sqrt{\frac{6}{x}}x}{2\sqrt{6}}[/tex]Simplify:
[tex]=\frac{\frac{\sqrt{6}}{\sqrt{x}}x}{2\sqrt{6}}=\frac{\sqrt{6}\sqrt{x}}{2\sqrt{6}}[/tex]Eliminate common terms:
[tex]=\frac{\sqrt{x}}{2}[/tex]Answer:
[tex]\frac{\sqrt{x}}{2}[/tex]Kristy downloads two songs to her MP3 player. The songs are 3 1/10 minutes and 4 2/3 minutes long. About how many minutes of memory will these two songs use altogether?
Answers
We have:
Song 1 = 3 1/10 minutes
Song 2 = 4 2/3 minutes
Minutes of memory of two songs:
[tex]3\frac{1}{10}+4\frac{2}{3}=\frac{31}{10}+\frac{14}{3}=\frac{3\times31+10\times14}{30}=\frac{93+140}{30}=\frac{233}{30}=7\frac{23}{30}[/tex]Answer:
[tex]7\frac{23}{30}\text{ minutes}[/tex]