I believe the answer to be c but I'm not the best at word problems this is a practice study guide.
Answers
In order to find the interval of values where 95% of the shoe sizes lie, let's find the values of z-score that represents 2.5% to the left and 2.5% to the right of the standard distribution curve:
Looking at the z-table for the probabilities of 0.025 and 0.975, we have z1 = -1.96 and z2 = 1.96.
Now, we can calculate the values that define the interval using the formula below:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ -1.96=\frac{x-8.1}{1.47} \\ x-8.1=-2.88 \\ x=-2.88+8.1 \\ x=5.22 \\ \\ 1.96=\frac{x-8.1}{1.47} \\ x-8.1=2.88 \\ x=2.88+8.1 \\ x=10.98 \end{gathered}[/tex]Therefore the correct option is the second one. (It's the only option with very close values to the ones calculated)
Related Questions
Consider the following statement:
If Paul is older than Bill and Fred is younger than Bill, then Bill's age is between Paul's and Fred's.
Write the Given statement
Answers
Paul is the oldest and Fred is the youngest of the three.
What is mean by younger?Younger is a comparative adjective that generally indicates more youthful.
Similar to old, elder simply indicates older in age. It is a comparative version of old.
Given that x is a natural number, let Bill's age equal x years.
Paul's age is thus calculated as (x + a) Years, where an is any positive integer.
Fred is also younger than Bill.
So, Fred's age is equal to x - k, where k is any positive integer.
As a result, if we arranged Fred, Bill, and Paul's ages, they would be
Bill, Fred, and Paul
x-k < x < x+a
As a result, we can conclude that Paul is the oldest and Fred is the youngest of the three.
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Find the median and mean of the data set below: 3, 8, 44, 50, 12, 44, 14 Median Mean =
Answers
the median is 25, because:
[tex]=\frac{3+8+44+50+12+44+14}{7}=\frac{175}{7}=25[/tex]the mean value is :
[tex]14[/tex]A. The measure of the angle can not be determined B. 70 degreesC. 110 degreesD. 180 degrees
Answers
Okay, here we have this:
Considering the provided graph, we are going to find the measure of the angle "3", so we obtain the following:
Since angle 3 and 4 form a straight angle, that is to say that these two angles are supplementary, then we have:
[tex]\begin{gathered} m\angle3+m\angle4=180 \\ m\angle3+70=180 \\ m\angle3=180-70 \\ m\angle3=110\text{ degre}es \end{gathered}[/tex]Finally we obtain that the correct answer is the option C.
5. Helen, Riley, and Derrick are on a running team. Helen ran 15 1/4 kilometers last week. Riley ran 4 1/12 less kilometers than Helen, and Derrick ran 7 3/8 more kilometers than Riley. If their goal is to run 60 kilometers in total, how much further do they need to run to meet their goal? I
Answers
Given in the scenario:
a.) Helen ran 15 1/4 kilometers last week.
b.) Riley ran 4 1/12 less kilometers than Helen.
c.) Derrick ran 7 3/8 more kilometers than Riley.
d.) Their goal is to run 60 kilometers in total.
To be able to determine how much further do they need to run to get 60 kilometers in total, we must first determine how many kilometers did Riley and Derrick run.
We get,
A.)
[tex]\text{Riley: }4\frac{1}{12}\text{ less kilometers than Helen}[/tex][tex]\text{ = 15 }\frac{1}{4}\text{ - 4 }\frac{1}{12}[/tex]Recall: To be able to subtract mixed numbers, you must first convert them into an improper fraction with a common denominator. The LCM of the two denominators must be their denominator when converted.
The LCM of 4 and 12 is 12. We get,
[tex]\text{ 15 }\frac{1}{4}\text{ = }\frac{1\text{ + (4 x 15)}}{4}\text{ = }\frac{1\text{ + 60}}{4}\text{ = }\frac{61}{4}\text{ = }\frac{(61)(3)}{12}\text{ = }\frac{183}{12}[/tex][tex]4\text{ }\frac{1}{12}\text{ = }\frac{1\text{ + (4 x 12)}}{12}\text{ = }\frac{1\text{ + 48}}{12}\text{ = }\frac{49}{12}[/tex]Let's now proceed with the subtraction,
[tex]15\frac{1}{4}-4\frac{1}{12}=\frac{183}{12}\text{ - }\frac{49}{12}\text{ = }\frac{183\text{ - 49}}{12}\text{ = }\frac{134}{12}\text{ = }\frac{\frac{134}{2}}{\frac{12}{2}}\text{ = }\frac{67}{6}\text{ or 11}\frac{1}{6}[/tex]Conclusion: Riley ran 11 1/6 kilometers.
B.)
[tex]\text{Derrick: }7\frac{3}{8}\text{ more kilometers than Riley}[/tex][tex]\text{ = 11}\frac{1}{6}\text{ + 7}\frac{3}{8}[/tex]Recall: To be able to add mixed numbers, you must first convert them into an improper fraction with a common denominator. The LCM of the two denominators must be their denominator when converted.
The LCM of 6 and 8 is 24. We get,
[tex]11\frac{1}{6}\text{ = }\frac{1\text{ + (11 x 6)}}{6}\text{ = }\frac{1\text{ + 66}}{6}\text{ = }\frac{67}{6}\text{ = }\frac{(67)(4)}{24}\text{ = }\frac{268}{24}[/tex][tex]7\frac{3}{8}\text{ = }\frac{3\text{ + (7 x 8)}}{8}=\frac{3\text{ + 56}}{8}=\frac{59}{8}=\frac{(59)(3)}{24}=\frac{177}{24}[/tex]Let's now proceed with the addition,
[tex]11\frac{1}{6}\text{ + 7}\frac{3}{8}\text{ = }\frac{268}{24}\text{ + }\frac{177}{24}\text{ = }\frac{268\text{ + 177}}{24}\text{ = }\frac{445}{24}\text{ or 18}\frac{13}{24}[/tex]Conclusion: Derrick ran 18 13/24 kilometers.
C.) To be able to determine how much further do they need to run to get 60 kilometers in total, we subtract 60 by the sum of distance the three people ran.
We get,
[tex]\text{ 60 - (15 }\frac{1}{4}\text{ + 11}\frac{1}{6}\text{ + 18}\frac{13}{24})[/tex]The same process that we did, convert all numbers into similar fractions.
The LCM of 4, 6 and 24 is 24. We get,
[tex]15\frac{1}{4}\text{ = }\frac{1\text{ + }(15\text{ x 4)}}{4}\text{ = }\frac{1\text{ + 60}}{4}\text{ = }\frac{61}{4}\text{ = }\frac{(61)(6)}{24}\text{ = }\frac{366}{24}[/tex][tex]11\frac{1}{6}\text{ = }\frac{1\text{ + (11 x 6)}}{6}\text{ = }\frac{1\text{ + 66}}{6}\text{ = }\frac{67}{6}\text{ = }\frac{(67)(4)}{24}\text{ = }\frac{268}{24}[/tex][tex]\text{ 18}\frac{13}{24}=\text{ }\frac{13+(18\text{ x 24)}}{24}\text{ = }\frac{13\text{ + 432}}{24}\text{ = }\frac{445}{24}[/tex][tex]60\text{ = }\frac{60\text{ x 24 }}{24}\text{ = }\frac{1440}{24}[/tex]Let's proceed with the operation,
[tex]\text{ 60 - (15 }\frac{1}{4}\text{ + 11}\frac{1}{6}\text{ + 18}\frac{13}{24})\text{ = }\frac{1440}{24}-(\frac{366}{24}\text{ + }\frac{268}{24}\text{ + }\frac{445}{24})[/tex][tex]\text{ }\frac{1440\text{ - (366 + 268 + 445)}}{24}\text{ = }\frac{1440\text{ - 1079}}{24}[/tex][tex]\text{ = }\frac{361}{24}[/tex]Therefore, they need to run a total of 361/24 kilometers to be able to meet their goal.
Suppose that the edge lengths x, y, z of a closed rectangular box are changing at the following rates: dx/dt= 1m/s, dy/dt= -2 m/s, and dz/dt= 0.5 m/s.
At the instant x= 2m, y= 3m, z= 5m, find the rates of change:
a) volume of the box
b) surface area of the box
c) diagonal of the box
Answers
a) The rate of change of the volume of the box is 8m³/s.
b) The rate of change of the surface area of the box is -19m²/s.
c) The rate of change of the diagonal of the box is 1m/s.
Let the rate of change of the edge length x, y, and z of a closed rectangular box are:
dx/dt= 1m/s
dy/dt= -2 m/s
dz/dt= 0.5 m/s
a) The volume of the box
From the formula of the volume,
V=xyz
Then,
differentiate w.r.t t
[tex]\frac{dV}{dt} = xy\frac{dz}{dt} + yz\frac{dx}{dt} +xz\frac{dy}{dt}[/tex]
[tex]\frac{dV}{dt} = xy(0.5)+ yz(1)+xz(-2)[/tex]
put the value of x, y, z , then we get
[tex]\frac{dV}{dt} = 2.3.(0.5)+ 3.5.(1)+2.5.(-2)[/tex]
[tex]\frac{dV}{dt} = 3+ 15 - 10[/tex]
[tex]\frac{dV}{dt} = 8m^3/s[/tex]
The rate of change of the volume of the box is 8m³/s.
b) surface area of the box
surface area of the rectangular box is
s = 2xy + 2yz + 2zx
differentiate w.r.t t
[tex]\frac{ds}{dt} = 2(y + z)\frac{dx}{dt} + 2(z + x)\frac{dy}{dt} +2(x + y)\frac{dz}{dt}[/tex]
[tex]\frac{ds}{dt} = 2(y + z)(1) + 2(z + x)(-2)+2(x + y)(0.5)[/tex]
[tex]\frac{ds}{dt} = 2(3 + 5)(1) + 2(5 + 2)(-2)+2(2 + 3)(0.5)[/tex]
[tex]\frac{ds}{dt} = 16 -40 + 5[/tex]
[tex]\frac{ds}{dt} = -19m^2/s[/tex]
The rate of change of the surface area of the box is -19m²/s.
c) diagonal of the box
lengths of the boxes for the diagonal is
s = 2x² + y² + z²
differentiate equation w.r.t t
[tex]\frac{ds}{dt} = 4x\frac{dx}{dt} + 2y\frac{dy}{dt} +2z\frac{dz}{dt}[/tex]
[tex]\frac{ds}{dt} = 4.2.1+ 2.3.(-2) +2.5.(0.5)[/tex]
[tex]\frac{ds}{dt} = 8 -12 + 5[/tex]
[tex]\frac{ds}{dt} =1m/s[/tex]
The rate of change of the diagonal of the box is 1m/s.
a) The rate of change of the volume of the box is 8m³/s.
b) The rate of change of the surface area of the box is -19m²/s.
c) The rate of change of the diagonal of the box is 1m/s.
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Please answer last oneTo graph F using a graphing utility…Either A,B,C, or DLet me know which option
Answers
We have to graph the function F(x) defined as:
[tex]F(x)=\frac{x^2-11x-12}{x+6}[/tex]We can graph it as:
To see the complete graph we have to show the horizontal axis from x = -30 to x = 30 and the vertical axis from y = -80 to y = 80.
Answer: Option B
Fanuela walked for 3.9 miles per hour for 0.72 hours. How far did she walk?
Answers
Answer: Fanuela walked 2.808 miles.
Step-by-step explanation:
If 3.9 = 100 and we need to work out what 72 is we can do this/
3.9 ÷ 10 = 0.39 which = 10
0.39 ÷ 10 = 0.039 which = 1
so with these calculations we can solve the problem.
To get the 70 in 72 we can do 0.39 x 7 (10 x 7) which = 2.73.
To get the remaining 2 in 72 we can do 0.039 x 2 (1 x 2) which = 0.078.
2.73 + 0.078 = 2.808.
Fanuela walked 2.808 miles.
Hope this helps! Feel free to ask any questions if you're still unsure.
3.9=d/0.72
d= 3.9 x 0.72
d= 2.808 miles
I need help with this practice I am new to this subject of mathematics (algebra) Can you show me how to solve this STEP-BY-STEP?
Answers
Given:
[tex]4+x+8=24[/tex]Required:
To find the correct one.
Explanation:
The given quation is:
4 + x +8 =24
Subtract 8 on both sides
4 + x +8 - 8 = 24 -8
4 + x = 16
Final Answer:
Thus the first option is the correct answer.
Josephine bought a bag of garri for
N320.00 and sold it for N400.00.
What was her percentage profit
Answers
The most appropriate choice for profit will be given by-
Profit percent after selling a bag of garri is 25%
What is profit?
If the selling price of an article is more than the cost price of the article, then the difference between selling price and the cost price of the article gives the profit
Profit = SP - CP
Here,
Cost price of a bag of Garri = N320
Selling price of a bag of Garri = N400
Profit = N(400 - 320)
= N80
Profit Percent = [tex]\frac{80}{320} \times 100[/tex]
= 25%
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17. 19yd. 28in.- 16yd. 31in.18. 61wk. 4da.- 18wk. 6da.21. 8tbsp. 2tsp. * 15
Answers
We need to solve the next expressions:
17. 19yd. 28in.- 16yd. 31in
We need to solve subtract each expression.
Then:
19yd. 28in.- 16yd. 31in =
19yd - 16yd and 28in-31in
3yd -3in
Then, we have the next equivalent.
1 yard = 36 in
So:
36 in - 3 in = 33 in
Therefore
19yd. 28in.- 16yd. 31in = 2 yard 33
18 61wk. 4da.- 18wk. 6da.
We need to subtract both expression:
Then
61wk - 18wk = 43kw
4da-6da = -2da
Where 1 week = 7 days
Then
7 da - 2da = 5 da
Hence, 43kw -1 wk = 42 wk.
The result is:
42 wk 5 da
21. 8tbsp. 2tsp. * 15
We need to convert 2ts into tbsp and then multiply the result by 15.
If
1 tsp ------- 0.333tbsp
Then
2tp ------ 2(0.333tbsp)= 0.66666 tbsp
Now
(8tbsp + 0.6666 ) * 15 = 130 tbsp
Drag the curve to the correct location on the graph. A small museum opened in 2004 with 80 pieces of art in its collection. In 2005, the number of pieces of art in the collection was 1.2 times the initial number of pieces of art. Then, in 2006, the number of pieces of art in the collection was 1.2 times the size of the previous year's collection. The directors of the museum plan to continue acquiring pieces of art at the same rate. Complete the graph of this relationship. 1207 ces of Art f(x) 3001 240 180 120
Answers
The most appropriate choice for geometric series will be given by
The equation is [tex]y = 80 (1.2)^x[/tex] and it is a geometric function.
What is geometric series ?
The series in which the ratio between consecutive terms of the series are same is called geometric series
For example, 2, 4, 8, 16, ... is a geometric series in which ratio between two consecutive terms is 2.
Number of pieces of art in 2004 = 80
Number of pieces of art in 2005 = [tex]80 \times 1.2[/tex]
Number of pieces of art in 2006 = [tex]80\times (1.2)^2[/tex]
Number of pieces of art after x years from 2004 = [tex]80 \times (1.2)^x[/tex]
The equation is [tex]y = 80 (1.2)^x[/tex]
This is a geometric function
The graph has been attached here.
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Coronado co. sells product p-14 at a price of $52 a unit. the per unit cost data are direct materials $16, direct labour $12, and overhead $12 (75% variable) Coronado has no excess capacity to accept a special order for 38,700 units at a discount of 25% from the regular price. Selling costs associated with this order would be $3 per unit. Indicate the net income/loss
Answers
The net loss from accepting the special order at a discount of 25% from the regular price, without the existence of excess capacity is $38,700.
How is the net loss determined?Since Coronado Co. lacks the excess capacity for special orders, it implies that it will incur fixed costs per unit of the special order in addition to the variable costs.
Therefore, the company will incur a per unit cost of $40 ($16 + $12 + $9 + $3) while generating a revenue of $39 per unit.
This results in a loss of $1 per unit.
Selling price per unit = $52
Unit Costs:
Direct Materials = $16
Direct Labor = $12
Variable Overhead = $9 (75% of $12)
Total variable cost per unit = $37
Fixed Overhead = $3 (25% of $12)
Special order price per unit = $39 ($52 x 1 - 75%)
Contribution margin per unit = $2 ($39 - $37)
Total contribution margin = $77,400 ($2 x 38,700)
Fixed Overhead without excess capacity = $116,100 ($3 x 38,700)
Net loss = $38,700 ($77,400 - $116,100)
Thus, without excess capacity, it is inadvisable for Coronado to accept the special order at a total loss of $38,700.
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Find the length of the third side. If necessary, write in simplest radical form. 9 5 Submit Answer Answer:
Answers
The Pythagorean theorem states:
[tex]c^2=a^2+b^2[/tex]where a and b are the legs and c is the hypotenuse of a right triangle.
Substituting with c = 9 and a = 5, we get:
[tex]\begin{gathered} 9^2=5^2+b^2 \\ 81=25+b^2 \\ 81-25=b^2 \\ 56=b^2 \\ \sqrt[]{56}=b \\ \sqrt[]{4\cdot14}=b \\ \sqrt[]{4}\cdot\sqrt[]{14}=b \\ 2\sqrt[]{14}=b \end{gathered}[/tex]You can use a calculator to approximate the logarithm. Round to four decimal place
Answers
This is a simple question to solve when we use the calculator (as the question allows us to use it).
For this problem when we have :
[tex]\log \pi[/tex]It can be read as "log base 10 of pi", and using a calculator we find:
And that is the final answer.
NOTE: this result means that:
.
Use your knowledge of area and perimeter to complete the following problems. Use 3.14 for  and round to the nearest hundredths place, whenever necessary. Show all work.Part 1:A farmer bought 30 feet of fencing to build a circular pen for his pigs. What is the diameter of the pen he can build with 30 feet of fencing?The farmer also needs to buy a certain type of seed for the grass in the pen. Each bag of seed can cover 50 square feet of land. How many bags of seed will the farmer need to buy?
Answers
Which is an equation of the line with a slope of2323 passing through the point (4,-1).Group of answer choices=14+23 =−4+23 =23−53 =23−113
Answers
Given that the slope of a line is 2/3, that passes through the point (4, -1), i.e
[tex]\begin{gathered} m=\frac{2}{3} \\ (x_1,y_1)\Rightarrow(4,-1) \end{gathered}[/tex]The formula to find the equation of straight line is
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where m is the slope of the line} \end{gathered}[/tex]Substitute the values into the formula of the equation of a straight line
[tex]y-(-1)=\frac{2}{3}(x-4)[/tex]Solve for y i.e make y the subject
[tex]\begin{gathered} y-(-1)=\frac{2}{3}(x-4) \\ y+1=\frac{2}{3}(x-4) \\ \text{Open the bracket} \\ y+1=\frac{2}{3}x-\frac{2}{3}(4) \\ y+1=\frac{2}{3}x-\frac{8}{3} \\ y=\frac{2}{3}x-\frac{8}{3}-1 \\ y=\frac{2}{3}x-(\frac{8}{3}+1) \\ y=\frac{2}{3}x-(\frac{8+3}{3}) \\ y=\frac{2}{3}x-\frac{11}{3} \end{gathered}[/tex]Thus, the answer is
[tex]y=\frac{2}{3}x-\frac{11}{3}[/tex]Thus, the answer is the last option.
A store had 896 swimsuits that were marked to sale at $44.95/swimsuit. Each suit was marked down $16.90. Find the reduced price using the formula M = S - N, where M is the markdown, S is the original selling price, and N is the reduced price. The reduced price is ?
Answers
Given:
The original selling price of 1 swimsuit = $44.95
The selling price of 1 marked down swimsuit = $16.90
Using the provided formula:
[tex]M\text{ = S - N}[/tex]Where,
M is the markdown
S is the original selling price
N is the reduced price
Substituting we have:
[tex]16.90\text{ = 44.95 - N }[/tex]Solving for N:
[tex]\begin{gathered} \text{Collect like terms} \\ -N\text{ = 16.90 - 44.95} \\ -N\text{ = -28.05} \\ \text{Divide both sides by -1} \\ \frac{-N}{-1}=\text{ }\frac{-28.05}{-1} \\ N\text{ = 28.05} \end{gathered}[/tex]Hence, the reduced price is $28.05
Answer:
$28.05
Hi dear how do I get to know you and
Answers
Given the picture, we have:
Enclosed area: A = x*y
Fence Length: F= 2x+y
is 826,456 divisible by 8
Answers
Answer:
Yes, because if you divide the two numbers, you get a whole number which means it is. Also, since the last numbers are 56, 8 can go into 56 so yes.
Step-by-step explanation:
8.
What is the measure of angle x in the figure?
40°
A 69°
B 71°
C 109°
D 111°
Answers
Answer:
C 109
Step-by-step explanation:
First add all the known angles inside the triangle first to get 109°
Then since all angles in a triangle add to 180°
you take away 109 from 180 so
180-109 which equals 71
Then since all angles on a straight line add up to 180°
you take 71 from 180 so
180-71 = 109
so x = 109°
Which equation is equivalent to - 2x + 5 - 3x = 5x + 25?A. -5 = -30B. -6x + 5 = 5x + 25C. - 10x = 20D. 20x - 5 = 25
Answers
In order to determine which is the equivalent equation, simplify the given expression:
-2x + 5 - 3x = 5x + 25 simplify like terms left side
-2x - 3x + 5 = 5x + 25
-5x + 5 = 5x + 25 subtract 5x both sides and subtract 5 both sides
-5x - 5x = 25 - 5 simplify both sides
-10x = 20
Hence,the equivalent expression is -10x = 20
Which statement is true about the relation shown on the graph below?
Answers
We know that a function has a unique value of y for each value in x so the correct statement is:
c. it is not a function because there are multiple y values for a given x value
f(a)=92.39 and the average rate of change of f over the interval from x=a to x=a+266 is 0.16. What is the value of f(a+266)?f(a+266)=
Answers
Average rate is f(a+266)-f(a))/266
so f(a+266) equals (0.16 x 266) + f(a)
f (a+266)= (0.16 x 266) + 92.39
which of the following is an integer ) 58/81) π) -11) 27.4444....
Answers
-11 is an integer number
An equation is incorrectly solved below.Equation: 2x+3=-4step 1: 2x+3-3=-4-3step 2: 2x=-1step 3: 2x/2=-1/2step 4: x=-1/2What is the first step that shows an error in the solution of the Equation? A. Step 1B. Step 2C. Step 3D. Step 4
Answers
To find the step where the error was made, we are going to correctly solve the equation:
[tex]2x+3=-4[/tex]We need to solve for x, first we subtract 3 from each side:
[tex]\begin{gathered} 2x+3-3=-4-3 \\ 2x=-7 \end{gathered}[/tex]We divide by 2 each side:
[tex]\begin{gathered} \frac{2x}{2}=\frac{-7}{2} \\ x=-\frac{7}{2} \end{gathered}[/tex]The first step that shows an error in the solution of the equation is the Step 2, because when we have two negative numbers, we add them, we do not subtract them.
Answer: B. Step 2
Jan is looking at a mapof Roaring River. The map wascreated using the scale 1 inch :25 miles. If the river is 5.5inches long on the map, then itis actuallymiles long.
Answers
The map of Roaring River shows1 inch to be an equivalent of 25 miles. If therefore, the river is shown as 5.5 inches long on the map;
[tex]\begin{gathered} \text{Scale; 1 inch=25 miles} \\ 5.5\text{ inches=25 x 5.5 miles} \\ 5.5\text{ inches=137.5miles} \end{gathered}[/tex]The river is "actually" 137.5 miles long
15. (09.03) Jim picked a card from a standard deck. What is the probability that Ilm picked a heart or an ace? (1 point) OI 52 O 2 52 O 16 52 O 17 52
Answers
The probability of picking a heart or an ace is 17/52
Here, we want to get the probability
The number of cards in a standard deck is 52 cards
Now, we need to know the number of hearts and the number of ace
There are 13 hearts, and 4 aces
The probability of picking a heart is;
[tex]\frac{13}{52}[/tex]The probability of picking an ace is;
[tex]\frac{4}{52}[/tex]The probability of picking an ace or a heart is the sum of both which is;
[tex]\frac{4}{52}+\frac{13}{52}\text{ = }\frac{17}{52}[/tex]1. describe the end behavior. 2. determine whether it represents an odd degree or an even degree function.3. state the number of real zeroes
Answers
1. Quadratic curve
2. Odd degree function
3. TWO REAL ZEROS
Solve the following system of equations using the elimination method. Give the final answer in (x,y) form.
Answers
Anisha used the substitution method to solve the system of equations.
She is missing the value of y.
To find it we plut the value of x in the first equation, then:
[tex]y=4-5=-1[/tex]Therefore the solution is (4,-1)
How to find postulate
Answers
Note that if plane N and plane M intersects each other in two points (say A and B) it follows that they intersects each other in the line that contains A and B. So they cannot intersect exactly in only two points. Postulate number 10