We need to know how to Convert the fraction into its decimal representation on level seven using step by step instructions. We especially need to know how to solve 1/7 in level seven
Answers
We want to convert our fractions in a way the denominators are potencys of 10. Let's start with the first one.
[tex]\frac{32}{40}[/tex]If we multiply both the numerator and denominator by 25, we're going to have
[tex]\frac{32\times25}{40\times25}=\frac{800}{1000}=0.8[/tex]Now, with the next fraction
[tex]\frac{12}{48}[/tex]Dividing both numerator and denominator by 12, we have
[tex]\frac{12}{48}=\frac{1}{4}[/tex]Again, If we multiply both the numerator and denominator by 25, we're going to have
[tex]\frac{1}{4}=\frac{25}{100}=0.25[/tex]For the next fraction, it is enough to multiply both numerator and denominator by 4
[tex]\frac{3}{25}=\frac{12}{100}=0.12[/tex]For the next one, we can again multiply both the numerator and denominator by 25
[tex]\frac{18}{40}=\frac{450}{1000}=0.45[/tex]Related Questions
Find the probability of drawing a red ace and then a spade when two cards are dranw (without replacement) from a standard deck of cards.a. 1/102b. 31/102c. 1/2d. 31/64
Answers
a. probability of drawing a red ace (first draw)
In a standard deck, there are 52 cards. Out of these 52 cards, two are red aces. Hence, the probability of drawing a red ace is 2/52 or 1/26.
b. probability of drawing a spade (second draw)
On the second draw, 51 cards are left. Assuming that a red ace was taken on the first draw, 13 spades are left on the deck. Hence, the probability of drawing a spade is 13/51.
So, to get the probability of drawing a red ace AND a spade, simply multiply the two probabilities above.
[tex]\frac{1}{26}\times\frac{13}{51}=\frac{13}{1326}[/tex]Then, reduce 13/1326 into its simplest form by dividing both numerator and denominator by 13.
[tex]\frac{13\div13}{1326\div13}=\frac{1}{102}[/tex]Hence, the probability of drawing a red ace AND a spade is 1/102. (Option A)
Factor the common factor1) -36m + 16
Answers
Given:
-36m + 16
To factor out the common factor, let's find the Greatest Common Factor (GCF) of both values.
GCF of -36 and 16 = -4
Factor out -4 out of -36 and 16:
[tex]-4(9m)-4(-4)[/tex]Factor out -4 out of [-4(9m) - 4(-4)] :
[tex]-4(9m\text{ - 4)}[/tex]ANSWER:
[tex]-4(9m-4)[/tex]I need help with question 4-8, can you please help me?Use f(X) as g(X) for question 5 and 6
Answers
Question 4
The x values for which g(x) = 3
From the graph, we have this value to be:
[tex]0\text{ }\leq\text{ x }\leq\text{ 2}[/tex]Question 5
f(x) = 6, What is x?
From the graph, we can determine the value of x corresponding to f(x)= 6:
[tex]x\text{ = }4[/tex]Question 6:
f(x)= 0, What is x?
From the graph, we can determine the value of x corresponding to f(x) = 0
[tex]x\text{ = 7}[/tex]Question 7
The domain of the function:
The domain is the set of allowable inputs.
[tex]\lbrack0,\text{ 12\rbrack}[/tex]Question 8
The range is the set outputs
[tex]\lbrack0,\text{ 6\rbrack}[/tex]Which of the following measurements form a right triangle? Select all that apply.
Answers
We are asked to find which of the measurements form a right triangle.
A right triangle is a triangle that has an angle of 90°, and also we can use the Pythagorean theorem in them.
The Pythagorean theorem tells us that the sum of the two legs of the triangle squared is equal to the hypotenuse squared:
[tex]a^2+b^2=c^2[/tex]Where a and b are the legs of the triangle and c is the Hypotenuse. Also, in the right triangle, the hypotenuse is the longest side of the triangle.
We will use the Pythagorean theorem formula on all of the options using the first two given measures as a and b, and check that we the third measure as the value of c.
Option A. 7in, 24in, and 25 in.
We define:
[tex]\begin{gathered} a=7 \\ b=24 \end{gathered}[/tex]And apply the Pythagorean theorem:
[tex]7^2+24^2=c^2[/tex]And we solve for c. If the result for x is 25, the triangle will be a right triangle, if not, this will not be an answer.
-Solving for c:
[tex]\begin{gathered} 49+576=c^2 \\ 625=c^2 \end{gathered}[/tex]Taking the square root of both sides we find c:
[tex]\begin{gathered} \sqrt[]{625}=c \\ 25=c \end{gathered}[/tex]Since we get the third measure as the value of c option A is a right triangle.
Option B. 18ft, 23ft, and 29 ft.
we do the same as did with option A. First, define a and b:
[tex]\begin{gathered} a=18 \\ b=23 \end{gathered}[/tex]Apply the Pythagorean theorem:
[tex]18^2+23^2=c^2[/tex]And solve for c:
[tex]\begin{gathered} 324+529=c^2 \\ 853=c^2 \\ \sqrt[]{853}=c \\ 29.2=c \end{gathered}[/tex]We get 29.2 instead of just 29, thus option B is NOT a right triangle.
Option C. 10in, 24in, and 26 in.
Define a and b:
[tex]\begin{gathered} a=10 \\ b=24 \end{gathered}[/tex]Apply the Pythagorean theorem:
[tex]10^2+24^2=c^2[/tex]Solve for c:
[tex]\begin{gathered} 100+576=c^2 \\ 676=c^2 \\ \sqrt[]{676}=c \\ 26=c \end{gathered}[/tex]We get 26 which is the third measure given, thus, option C is a right triangle.
Option D. 10yd, 15yd, and 20yd.
Define a and b:
[tex]\begin{gathered} a=10 \\ b=15 \end{gathered}[/tex]Apply the Pythagorean theorem:
[tex]\begin{gathered} 10^2+15^2=c^2 \\ 100+225=c^2 \\ 325=c^2 \\ \sqrt[]{325}=c \\ 18.03=c \end{gathered}[/tex]We don't get 20yd as the value of c, thus, option D is NOT a right triangle.
Option E. 15mm, 18mm, and 24 mm
Define a and b:
[tex]\begin{gathered} a=15 \\ b=18 \end{gathered}[/tex]Apply the Pythagorean theorem
[tex]\begin{gathered} 15^2+18^2=c^2 \\ 225+324=c^2 \\ 549=c^2 \\ \sqrt[]{549}=c \\ 23.43=c \end{gathered}[/tex]We don't get 24 as the value of c, thus, option E is Not a right triangle.
Answer:
Option A and Option C are right triangles.
What is the sequence that has a recursive formula A(n)= A(n-1)+4 where A(1)=3
Answers
1) Considering that, let's find each term:
[tex]\begin{gathered} a_1=3 \\ a_n=a_{n-1}+4 \\ a_2=a_1+4\Rightarrow a_2=3+4=7 \\ a_3=a_2+4\Rightarrow a_3=7+4\text{ =11} \\ a_4=11+4\text{ }\Rightarrow a_4=15 \end{gathered}[/tex]2) So the sequence is
[tex](3,7,11,15,\ldots)[/tex]As each term, from the 2nd one is 4 units more that's why we can make it using a recursive formula
Lena eats an apple every otherday. Suppose today is Monday,October 1. Lena eats an appletoday.When will Lena eat an appleon a Monday again?AnsLe
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Angles A and B are adjacent on a straight line. Angle A has a measure of (2r +20) and angle B has a measure of 130.. What is the measure of r?
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When two angles are adjacent on a straight line, then the sum of the two angles equals 180 (that is sum of angles on a straight line). Therefore;
[tex]\begin{gathered} (2r+20)+130=180 \\ \text{Subtract 130 from both sides and you'll have} \\ 2r+20=50 \\ \text{Subtract 20 from both sides and you'll have} \\ 2r=30 \\ \text{Divide both sides by 2 and you'll have} \\ r=15 \end{gathered}[/tex]The measure of r is 15
I need help with a 8th-grade math assignment:China has a population of approximately 1,382,323,332 people. The United States has a population of about 324,118,787 people.Part AUsing scientific notation, give the approximation for each population. Round the first factor to the nearest tenth.China: United States: Part BAbout how many more people live in China than in the United States? Express your answer using scientific notation. Round the first factor to the nearest hundredth.
Answers
We have the next given information:
China has a population of approximately 1,382,323,332 people.
The United States has a population of about 324,118,787 people.
a) We need to use scientific notation which is given by the next form:
[tex]ax10^n[/tex]Where a is the coefficient rounded to the nearest tenth.
and a is the terms moved to the decimal point.
For China:
1382323332.0, we moved the decimal point nine spaces to the right.
then
1.382323332
Expressed in scientific notation and rounded to the nearest tenth:
[tex]1.4x10^9[/tex]For the United States:
324,118,787 with the decimal point 324,118,787.0
then
324118787.0
Move the decimal point 8 spaces to the right, then:
3.24118787
Expressed in scientific notation and rounded to the nearest tenth:
[tex]3.2x10^8[/tex]
Part b:
To find how many more people live in China than in the United States, we need to subtract between China and the United States:
Then:
1,382,323,332 - 324,118,787 = 1,058,204,545
Now
1,058,204,545 equal to 1058204545.0
We need to move the decimal point 9 spaces:
1.058204545
Expressed as scientific notation and rounded to the nearest hundredth:
[tex]1.06x10^9[/tex]Solve the exponential equation. Express irrational solutions as decimals correct to the nearest thousandth.5x -5.e-2x = 2eSelect the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The solution set is(Round to the nearest thousandth as needed. Use a comma to separate answers as needed.)OB. The solution is the empty set.
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We are asked to solve the exponential equation given below:
e^5x - 5 * e^-2x = 2e
First let's apply the exponent rules:
5x - 5 - 2x = In(2e)
Solving 5x - 5 - 2x = In(2e)
3x - 5 = In(2e)
Add 5 to both sides:
3x = In(2e) + 5
Divide both sides by 3
x = In(2e) + 5
3
x = 2.23104
x = 2.231 (To the nearest thousand)
Therefore, the correct option is A, which is The solution set is 2.231 (Round to the nearest thousand).
Find the output, f, when the input, t, is 7 f = 2t - 3 f = Stuck? Watch a video or use a hint.
Answers
Answer:
f=11
Explanation:
Given the function:
[tex]f=2t-3[/tex]When the input, t=7
The value of the output, f will be gotten by substituting 7 for t.
[tex]\begin{gathered} f=2t-3 \\ =2(7)-3 \\ =14-3 \\ f=11 \end{gathered}[/tex]The output, f is 11.
Simplify this fraction: 30/36
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To simplify this fraction, we will have to find the common factors of both the numerator and denominator, then divide.
Common factors of 30 and 36 are: 2, 3, and 6
Now both numerator and denominator by the highest common factor which is 6:
[tex]\frac{30}{36}\text{ = }\frac{5}{6}[/tex]
After simplifying the fraction, we have:
[tex]\frac{5}{6}[/tex]A middle school football game has four 12-minute quarters. Jason plays 8 minutes in each quarter.Which ratio represents Jason's playing time compared to the total number of minutes of playing time possible?1 to 3 2 to 33 to 24 to 1I’m
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The total minutes in the game is 48. The total playing game for Jason is 32. The ratio is
[tex]\frac{32}{48}[/tex]Simplifying it, we have
[tex]\frac{32}{48}=\frac{16}{24}=\frac{8}{12}=\frac{4}{6}=\frac{2}{3}[/tex]So, the playing ratio is 2 to 3 for Jason.
Sketch the graph of a function that has a local maximum value at x = a where f'(a) is undefined.
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Derivative and Maximum Value of a Function
The critical points of a function are those where the first derivative is zero or does not exist.
Out of those points, we may find local maxima or minima or none of them.
One example of a function with a derivative that does not exist is:
[tex]y=-x^{\frac{2}{3}}[/tex]This function has a local maximum at x=0 where the derivative does not exist.
The graph of this function is shown below:
A 6000-seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue
of $168,000?
The number of tickets for sale at $24 should be ?
Answers
The number of tickets which should be sold to $24 and $40 are 4500 and 1500 respectively.
Given, A 6000-seat theater has tickets for sale at $24 and $40.
How many tickets should be sold at each price for a sellout performance to generate a total revenue of $168,000 = ?
first, assign variables:
X = # of $24 tickets, Y = # or $40 tickets
write equations based on the data presented:
"6000 seat theater..."
X + Y = 6000 ...equation 1
"total revenue of 168,000"
The revenue from each type of ticket is the cost times the number sold, so:
24X + 40Y = 168,000 .....equation 2
from equation 1:
X = 6000 - Y
substitute this into equation 2: (replace X with 6000-Y)
24 (6000 - Y) + 40Y = 168,000
expand:
144,000 -24Y + 40Y = 168,000
rearrange and simplify:
16Y = 168,000 - 144,000
y = 24000/16
Y = 1500
from equation 1:
X = 6000 - 1500
X = 4500
hence the number of tickets for sale at $24 should be 4500.
Learn more about Linear equations here:
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Solve the inequality |3x+3| + 3 > 15Write the answer in interval notation
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Solution:
Given the inequality:
[tex]|3x+3|+3>15[/tex]To solve the inequality,
step 1: Add -3 to both sides of the inequality.
Thus,
[tex]\begin{gathered} |3x+3|+3-3>-3+15 \\ \Rightarrow|3x+3|>12 \end{gathered}[/tex]Step 2: Apply the absolute rule.
According to the absolute rule:
[tex]\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad \mathrm{or}\quad \:u\:>\:a[/tex]Thus, from step 1, we have
[tex]\begin{gathered} 3x+3<-12\text{ or 3x+3>12} \\ \end{gathered}[/tex][tex]\begin{gathered} when \\ 3x+3<-12 \\ add\text{ -3 to both sides of the inequality} \\ 3x-3+3<-3-12 \\ \Rightarrow3x<-15 \\ divide\text{ both sides by the coefficient of x, which is 3} \\ \frac{3x}{3}<-\frac{15}{3} \\ \Rightarrow x<-5 \end{gathered}[/tex][tex]\begin{gathered} when \\ 3x+3>12 \\ add\text{ -3 to both sides of the inequality} \\ 3x+3-3>12-3 \\ \Rightarrow3x>9 \\ divide\text{ both sides by the coefficient of x, which is 3} \\ \frac{3x}{3}>\frac{9}{3} \\ \Rightarrow x>3 \end{gathered}[/tex]This implies that
[tex]x<-5\quad \mathrm{or}\quad \:x>3[/tex]Hence, in interval notation, we have:
[tex]\left(-\infty\:,\:-5\right)\cup\left(3,\:\infty\:\right)[/tex]Examine the graph and write a statement about the data. Use specific information from the graph.
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This bar graph represents the percentage of the public's trust in the Federal Government from year 1960 to 2015. The public trust was highest in year 1960 at 74% and it was at its lowest in 2015 at 18%.
Can 37° 111° and 32° be measurements of a triangle?
Answers
Answer
The angles given can easily be the measurements of one triangle because they sum up to give 180°.
Explanation
The sum of angles in a triangle is known to be 180°
So, for the given angles to be to belong to one triangle, the sum of all the angles must be equal to 180°
So, we check by adding them
37° + 111° + 32° = 180°
Hope this Helps!!!
Hello, I need help with this practice problem. Thank you so much.
Answers
Answer:
5 units
Explanation:
Given the points:
[tex]\begin{gathered} \mleft(x_1,y_1\mright)=K(-2,-1) \\ \mleft(x_2,y_2\mright)=N(2,2) \end{gathered}[/tex]We use the distance formula below:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute the given values:
[tex]\begin{gathered} KN=\sqrt[]{(2-(-2))^2+(2-(-1))^2} \\ =\sqrt[]{(2+2)^2+(2+1)^2} \\ =\sqrt[]{(4)^2+(3)^2} \\ =\sqrt[]{16+9} \\ =\sqrt[]{25} \\ =5\text{ units} \end{gathered}[/tex]The distance between the two points is 5 units.
What is the image point of (-12, —8) after the transformation R270 oD ?
Answers
Answer
(-12, -8) after R270°.D¼ becomes (-2, 3)
Explanation
The first operation represented by R270° indicates a rotation of 270° counterclockwise about the origin.
When a rotation of 270° counterclockwise about the origin is done on some coordinate, A (x, y), it transforms this coordinates into A' (y, -x). That is, we switch y and x, then add negative sign to x.
Then, the second operation, D¼ represents a dilation of the coordinate about the origin by a scale factor of ¼ given.
The coordinates to start with is (-12, -8)
R270° changes A (x, y) into A' (y, -x)
So,
(-12, -8) = (-8, 12)
Then, the second operation dilates the new coordinates obtained after the first operation by ¼
D¼ changes A (x, y) into A' (¼x, ¼y)
So,
(-8, 12) = [¼(-8), ¼(12)] = (-2, 3)
Hope this Helps!!!
1.The histogram (next page) summarizes the data on the body lengths of 143 wild bears. Write a fewsentences describing the distribution of body lengths.403020103035404570 7580 8550 55 60 65length in inchesBe sure to comment on the shape, center, and spread of the distribution.
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The shape of the distribution is bell-shaped. This is because the distribution presents a normal distribution
The distribution is almost symmetrically skewed with no outlier
The center is about 60 inches(about 59 wild bears before the center and about 84 wild bears beyond the center)
The distribution is widely spread: The data range is the highest inches minus the lowest inches
Therefore, the spread of the distribution is 85 inches - 35 inches, which equals 50 inches.
Please tell me if these are correct if theyre not please help and tell me which ones are the right answers
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Answer:
They're correct
Step-by-step explanation:
the volume of a sphere is 2304pi in^3 the radius of the sphere is ___ inches.
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Answer:
The radius = 12 inches.
Explanation:
Given a sphere with radius, r units:
[tex]\text{Volume}=\frac{4}{3}\pi r^3[/tex]If the volume of a sphere is 2304π in³, then:
[tex]\frac{4}{3}\pi r^3=2304\pi[/tex]We solve the equation for r:
[tex]\begin{gathered} \frac{4\pi r^3}{3}=2304\pi \\ 4\pi r^3=2304\pi\times3 \\ r^3=\frac{2304\pi\times3}{4\pi} \\ r^3=1728 \end{gathered}[/tex]Next. take cube roots of both sides.
[tex]\begin{gathered} r=\sqrt[3]{1728} \\ r=12\text{ inches} \end{gathered}[/tex]The radius of the sphere is 12 inches.
the prompt is in the photo
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By using the given box and whisker plot, the number of students that earned a score from 77 and 90 is: N. 13.
What is a box and whisker plot?A box and whisker plot is also referred to as boxplot and it can be defined as a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread.
In Mathematics, the five-number summary of any box and whisker plot include the following:
MinimumFirst quartileMedianThird quartileMaximumWhat is an interquartile range?IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.
Mathematically, interquartile range (IQR) is the difference between first quartile (Q₁) and third quartile (Q₃):
IQR = Q₃ - Q₁
Based on the given box and whisker plot, we can logically deduce the following quartile ranges:
Third quartile, Q₃ = 90
First quartile, Q₁ = 77
Now, we can calculate the interquartile range (IQR) is given by:
Interquartile range, IQR = Q₃ - Q₁
Interquartile range, IQR = 90 - 17
Interquartile range, IQR = 13
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Given circle O with diameter AC, tangent AD, and the measure of arc BC is 74 degrees, find the measures of all other indicated angles.
Answers
We want to find the measure of the angles 1 to 8, given that the diameter is AC and the measure of the Arc BC is 74°.
The angle 5, ∡BOC is central and it is equal to the measure of the arc it intercepts, the arc BC. Thus the angle 5 is 74°.
The angle 4, ∡AOB also is central, and it is equal to the measure of the arc AB. As the line AC is the diameter of the circle O, the arc AC is equal to 180°, and thus, the sum of the angles 4 and 5 will be 180°:
[tex]\begin{gathered} \measuredangle4+\measuredangle5=180^{\circ} \\ \measuredangle4=180^{\circ}-\measuredangle5=180^{\circ}-74^{\circ}=106^{\circ} \end{gathered}[/tex]Thus, the angle 4 is 106°.
The angle 6 is an inscribed angle, and thus it is half of the arc it intersects, the arc AB. This means that the angle 6 is 106°/2=54°.
The angle 2 also is an inscribed angle, half of the arc BC, and thus, the angle 2 is 74°/2=37°.
Now, the triangle BOC has the angles 5, 6 and 7, and the sum of those angles is 180°. This means that:
[tex]\begin{gathered} \measuredangle5+\measuredangle6+\measuredangle7=180^{\circ} \\ 74^{\circ}+54^{\circ}+\measuredangle7=180^{\circ} \\ 128^{\circ}+\measuredangle7=180^{\circ} \\ \measuredangle7=180^{\circ}-128^{\circ}=52^{\circ} \end{gathered}[/tex]Thus, the angle 7 is 52°.
Following a same argument, we can get the angle 8, as being part of the triangle AOB.
[tex]\begin{gathered} \measuredangle2+\measuredangle4+\measuredangle8=180^{\circ} \\ \measuredangle8=180^{\circ}-37^{\circ}-106^{\circ}=37^{\circ} \end{gathered}[/tex]This means that the angle 8 is 37°.
As the line AD is tangent to the circle O, this means that the lines AC and AD are perpendicular, and thus, the angle 1 is 90°.
Lastly, as the angles 1, 2 and 3 are coplanar, their sum is 180°. This is:
[tex]\begin{gathered} \measuredangle1+\measuredangle2+\measuredangle3=180^{\circ} \\ \measuredangle3=180^{\circ}-\measuredangle1-\measuredangle2 \\ \measuredangle3=180^{\circ}-90^{\circ}-37^{\circ}=180^{\circ}-127^{\circ}=53^{\circ} \end{gathered}[/tex]Thus, the angle 3 is 53°.
Please help me with this word problem quickly, work is needed thank you!
Answers
Given:
Sheila can wash her car in 15 minutes. Bob takes time twice as long to wash the same car.
Required:
Find the time they take both together.
Explanation:
Sheila can wash her car in 15 minutes.
Work done by sheila in a minute =
[tex]\frac{1}{15}\text{ }[/tex]Bob takes time twice as long to wash the same car. He washes the car in 30 minutes.
Work done by Bob in a minute
[tex]=\frac{1}{30}[/tex]If they work together let them take time x per minute.
[tex]\frac{1}{15}+\frac{1}{30}=\frac{1}{x}[/tex]Solve by taking L.C. M.
[tex]\begin{gathered} \frac{2+1}{30}=\frac{1}{x} \\ \frac{3}{30}=\frac{1}{x} \\ \frac{1}{10}=\frac{1}{x} \\ x=10\text{ minutes.} \end{gathered}[/tex]If they work together they will take 10 minutes.
Final Answer:
Sheila and Bob wash the car together in 10 minutes.
a plant is already 44 cm tall, and will grow one cm every month. let H be height in cm and M months. write and equation relating H to M . then use equation to find plants height after 32 months
Answers
H = height in cm
M = months
The plant is already 44 cm tall
GRowth every month = 1 cm
Equation:
H (m) = 44 + m
The height after m months, will be equal to the initial height (44) plus the number of months.
For 32 months, replace m by 32 and solve:
H (32) = 44+32
H (32) = 76 cm
After 32 months, the plant will be 76 cm tall
Referring to the figure, find the unknown measure of ABC.
Answers
According to the Inscribed Angle Theorem, the measure of an angle inscribed in a circle equals half the arc that it intercepts.
Then:
[tex]m\angle ABC=\frac{1}{2}m\overset{\frown}{AC}[/tex]Since the measure of the arc AC is equal to 84º, then:
[tex]m\angle ABC=\frac{1}{2}(84º)=42º[/tex]Therefore, the answer is:
The measure of ABC is 42º.
My name is Nika and I need help in math I’m 73 and done with school but still don’t under algebra
Answers
The given equation is
[tex]2x-3=9[/tex]To solve this equation we have to isolate x on one side and put the numbers on the other side
To do that we will add 3 to each side to move 3 from the left side to the right side
[tex]2x-3+3=9+3[/tex]Simplify it
[tex]\begin{gathered} 2x+0=12 \\ 2x=12 \end{gathered}[/tex]Now we need to move 2 from the left side to the right side, then
Divide both sides by 2
[tex]\begin{gathered} \frac{2x}{2}=\frac{12}{2} \\ x=6 \end{gathered}[/tex]Then the solution of the equation is
x = 6
Choose which function is represented by the graph.111032-11-10 9 8 7 6 5 4-3-2-102 3 4 5 6 7 8 9 10 1110O A. 1(x) = (x − 1)(x +2)(x+4)(x+8)B. f(x) - (x-8)(x-4)(x-2)(x+1)C. f(x)=(x-1)(x+2)(x+4)D. f(x)=(x-4)(x-2)(x+1)876544 4 4 & & To-2X
Answers
The factors of a polynomial tell us the points where the graph intersects the x-axis.
From the graph provided in the question, the graph cuts the x-axis at the points:
[tex]x=-4,x=-2,x=1[/tex]Therefore, the factors will be:
[tex]\begin{gathered} x=-4,x+4=0 \\ x=-2,x+2=0 \\ x=1,x-1=0 \\ \therefore \\ factors\Rightarrow(x+4),(x+2),(x-1) \end{gathered}[/tex]Therefore, the polynomial will be:
[tex]f(x)=(x+4)(x+2)(x-1)[/tex]OPTION C is the correct option.
Create an equation that models the table below. Use the variables in the table for your equation. Write your equation with 'S' isolated.
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The table show piszzas (P) on the left column and the slices of Pepperonin (S) on the right column.
To determine the equation models first check the ratio S/P to determine whether they are proportinal or not.
[tex]\begin{gathered} \frac{36}{3}=12 \\ \frac{96}{8}=12 \\ \frac{228}{19}=12 \end{gathered}[/tex]Now as the ratios are constant it mean the variation is linear and the relationship is proportional.
Thus the model equation can be determine as,
[tex]\begin{gathered} \frac{S}{P}=12 \\ S=12P \end{gathered}[/tex]Thus, the above equation gives the required model equation.