Answer:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30
Factors of 45: 1, 3, 5, 9, 15, and 45
Step-by-step explanation:
Show that Φ(u,v)=(7u+4,u−v,13u+v) parametrizes the plane 2x−y−z=8. Then: (a) Calculate Tu , Tv, and n(u,v). (b) Find the area of S=Φ(D), where D=(u,v):0≤u≤5,0≤v≤6. (c) Express f(x,y,z)=yz in terms of u and v and evaluate ∬sf(x,y,z)ds(a) Tu= , Tv= , n(u,v)=_______________(b) Area(S)=_______(c) ∬sf(x,y,z)ds=___________
Answer:
Step-by-step explanation:
1.Φ(u,v) gives the parametrization with its x, y, and z components. So, x=7u+4, y=u-v, and z=13u+v. We can use this to get the tangent vectors by taking the respective partial derivatives. Tu=<7, 1, 13> by taking the u derivatives of the components and Tv=<0, -1, 1> by taking the v derivatives of the components.
2. Taking the cross product of Tu and Tv will give the normal vector n(u,v), which is <14, -7, -7>
3. To find Area(S), you have to multiply the area of D by the magnitude of the normal vector from the previous step. D is the region defined by 0<=u<=5 and 0<=v<=6, so the area of D is 5*6=30. Multiply this by the magnitude of the normal vector to find that Area(S)=30sqrt(294)
4. To integrate, we first must put the initial function in terms of the parameters we found in the first step. Replace y with u-v and z with 13u+v. Next, multiply this integrand by the magnitude of the normal vector (sqrt294) and apply the given bounds for u (0<=u<=5) and v (0<=v<=6). From here the problem can be integrated like any other double integral, the final answer being 190sqrt(294)
How do I find and interpret the residual?
(Elementary statistics)
Answer:
y value , r i = y i − y i ^
Step-by-step explanation:
Residual = actual y value − predicted y value , r i = y i − y i ^ . Having a negative residual means that the predicted value is too high, similarly if you have a positive residual it means that the predicted value was too low. The aim of a regression line is to minimise the sum of residuals.
help
The graph of g(x) is obtained by reflecting the graph of f(x)=2|x| over the x-axis.
Which equation describes g(x)?
g(x)=−|x+2|
g begin argument x end argument equals negative begin absolute value x plus 2 end absolute value.
g(x)=|x+2|
g begin argument x end argument equals begin absolute value x plus 2end absolute value.
g(x)=−2|x|
g begin argument x end argument equals negative 2 begin absolute value x end absolute value.
g(x)=2|x|
Responses
g(x)=−|x+2|
g begin argument x end argument equals negative begin absolute value x plus 2 end absolute value.
g(x)=|x+2|
g begin argument x end argument equals begin absolute value x plus 2end absolute value.
g(x)=−2|x|
g begin argument x end argument equals negative 2 begin absolute value x end absolute value.
g(x)=2|x|
An equation which describe the function g(x) after reflecting the graph of function f(x)=2|x| over the x-axis is: C. g(x) = −2|x|. g begin argument x end argument equals negative 2 begin absolute value x end absolute value.
What is a reflection?In Geometry, a reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
What is a reflection across the x-axis?In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection across the x-axis is given by this transformation rule: (x, y) → (x, -y).
By applying a reflection across the x-axis to the function, we have;
f(x) = 2|x|
g(x) = -f(x)
g(x) = -(2|x|)
g(x) = -2|x|
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One equation in a linear system is x + y = 1. Is it possible for the system to have a
solution of (0, 0)? (100, -49)? Explain your reasoning.
answer:
no, because 0+0≠1 and 100+-49≠1 so the values are not a part of the system.
step-by-step explanation:
for this question, plug in the x & y values into the equation x+y=1. if the values add up to be 1, then it's possible for the system to have those solutions. hope that helps!
a study of whether or not customers respond to odors took place in a small pizza restaurant in france on two saturday evenings in may. on one of these evenings, a relaxing lavender odor was spread through the restaurant. on the other evening, no scent was used. the restaurant owners computed the mean amount spent on each night and computed a 95% confidence interval for the difference of means (lavender minus no odor) in euros to be (2.40, 4.82). can the researchers conclude there is a difference between the two means
The limits of the confidence interval are positive and don't include 0.
What is the confidence interval?
A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally used.
Yes, there is a significant difference between the 2 means.
Since both the limits of the confidence interval are positive and
doesn't include 0.
Hence, the limits of the confidence interval are positive and don't include 0.
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1.2x + 4.4 - 0.8x - 2.2
Simplify would be 0.4x + 2.2
Brian slept for eight hours on Monday night. How many minutes did he sleep?
Answer:
480
Step-by-step explanation:
8 * 60 = 480
You play a game of dice at the state fair, but suspect the dice may have been rigged. You observe the game owner rolling the dice 78 times and note the following results:
Face "1" "2" "3" "4" "5" "6"
Observed count 8 13 18 14 19 6
(a) Which hypotheses should be used to test if the dice are fair:
Identify H0:
-H0: p1 = p2 = p3 = p4 = p5 = p6 = 1/6, implying the dice are unfair.
-H0: p1 = p2 = p3 = p4 = p5 = p6 = 0, implying the dice are fair.
-H0: p1 = p2 = p3 = p4 = p5 = p6 = 1/6, implying the dice are fair.
-H0: p1 = p2 = p3 = p4 = p5 = p6 = 0, implying the dice are unfair.
Identify Ha:
-Ha: every p ≠ 1/6, implying the dice are unfair.
-Ha: at least one p≠ 1/6, implying the dice are unfair.
-Ha: every p ≠ 1/6, implying the dice are fair.
-Ha: at least one p ≠ 1/6, implying the dice are fair.
(b) What is the expected count for each side of the dice?
(c) Is the cell count condition met?
-No, because some cells have less than 10 observed counts.
-Yes, because the expected cell count is at least 5 for all cells.
-Yes, because the expected cell count is close to the observed cell count for all cells.
-No, because some cells have less than 30 observed counts.
(d) Calculate the contribution to the test statistic for the dice side with number "1": (Use 4 decimals):
(e) The full test statistic is χ2 = 10.462. What is the P-value? (Use 4 decimals.)
(f) What is the appropriate test conclusion, for α = 0.05?
-There is sufficient evidence the dice are unfair.
-There is insufficient evidence the dice are unfair.
-There is insufficient evidence the dice are fair.
-There is sufficient evidence the dice are fair.
(a) H0: p1 = p2 = p3 = p4 = p5 = p6 = 1/6, implying the dice are fair.
(b) The expected count for each side of the dice is 13
(c) Yes, because the expected cell count is at least 5 for all cells.
Hypothesis :
In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.
Complete question:
You play a game of dice at the state fair, but suspect the dice may have been rigged. You observe the game owner rolling the dice 78 times and note the following results:
Face "1" "2" "3" "4" "5" "6"
Observed count 8 13 18 14 19 6
(a) Which hypotheses should be used to test if the dice are fair:
Identify H0:
-H0: p1 = p2 = p3 = p4 = p5 = p6 = 1/6, implying the dice are unfair.
-H0: p1 = p2 = p3 = p4 = p5 = p6 = 0, implying the dice are fair.
-H0: p1 = p2 = p3 = p4 = p5 = p6 = 1/6, implying the dice are fair.
-H0: p1 = p2 = p3 = p4 = p5 = p6 = 0, implying the dice are unfair.
Identify Ha:
-Ha: every p ≠ 1/6, implying the dice are unfair.
-Ha: at least one p≠ 1/6, implying the dice are unfair.
-Ha: every p ≠ 1/6, implying the dice are fair.
-Ha: at least one p ≠ 1/6, implying the dice are fair.
(b) What is the expected count for each side of the dice?
(c) Is the cell count condition met?
-No, because some cells have less than 10 observed counts.
-Yes, because the expected cell count is at least 5 for all cells.
-Yes, because the expected cell count is close to the observed cell count for all cells.
-No, because some cells have less than 30 observed counts.
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what is the minimum number of students required in a school to be sure that at least 17 students will be in the same class, assuming the school only has grade 1 to grade 6 and each grade has only one class?
The minimum number of students required in a school are 102 , it can be calculated by multiplying the 2 quantities.
What is arithmetic?
Arithmetic is an elementary a part of mathematics that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.
Main body:
Total grades = 1 to 6 = 6
minimum students in each grade required = 17
total students required = 6*17
= 102
hence total minimum number of students required in a school are 102.
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a plane has a cruising speed of 200 miles per hour when there is no wind. at this speed, the plane flew 500 miles with the wind in the same amount of time it flew 300 miles against the wind. find the speed of the wind. speedofthewind:miles/hour
The speed of wind is 380 miles per hour.
What is speed?
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is traveling along a path.
Here, we have
The plane has a cruising speed of 200 miles per hour when there is no wind. at this speed, the plane flew 500 miles with the wind in the same amount of time it flew 300 miles against the wind.
We have to find the speed of the wind.
Time = Distance/speed
Time = 500/200 = 2.5hrs
When the plane moves against the wind its effective speed reduces as it has to overcome the opposing force of the wind since it is given that it cover's a distance of 300 miles at the same time we can write
2.5 = 300/ V(plane) - v(wind)
2.5 = 300/500- v(wind)
v(wind) =380mph
Hence, the speed of the wind is 380mph.
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Drag numbers to use a negative factor to factor the expression –5g + 15h – 25. Numbers may be used once, more than once, or not at all.
–1 –2 –3 –4 –5 1 2 3 4 5
(___-5__g –____3_ h +___5__)
The expression -5g + 15h - 25 can be simplified as -5(g + 3h - 5)
ExpressionExpressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
In the question given, the expression is -5g + 15h - 25;
We have to simplify this to by factoring the expression.
-5g + 15h - 25 = -5(g + 3h - 5)
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B
21
31
20
C
G
42
H
16
28
D
write the slope intercept form of the equation of the line through the given points with given slope
The equation of the line passing through the point (-1, -5) with slope = 6 is y = 6x - 1
The coordinates of the point = (-1, -5)
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line
The slope of the line m = 6
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
Substitute the values in the slope intercept form
-5 = 6(-1) + b
-5 = -6 + b
b = -6+5
b = -1
The slope intercept form
y = 6x - 1
Therefore, the equation of the line is y = 6x - 1
I have answered the question in general, as the given question is incomplete
The complete question is:
Write the slope-intercept form of the equation of the line through the given point with the given slope. Through (-1,-5), slope =6
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PLEASE HELP, WILL GIVE BRAINLIEST! THANK YOU!
Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum
of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and
children weigh about 80 pounds. For each session of bounce time, Natalie charges adults
$3 each and children $2 each. Natalie hopes to make at least $20 for each session.
The set of inequalities formed for the bounce house of Natalie are-
200x + 80y ≤ 1200 and 3x + 2y ≥ 20.
Explain the term set of inequalities?A group of two or even more inequalities for one or more variables is referred to as a system of inequalities. When a problem demands a variety of solutions and those solutions must satisfy many constraints, systems with inequalities are used.The data for the people enrolled for the bounce house.
Let 'x' be the number of adults.
Let 'y' be the number of children.
Then,
Weight of adult = 200 pounds.
Weight of children = 80 pounds.
maximum weight = 1200 pounds
Then, equation becomes-
200x + 80y ≤ 1200
For the price.
adults -$3 each and
children - $2 each
Minimum profit at least $20
3x + 2y ≥ 20.
Thus, the set of inequalities are-
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Please help need this done asap
Simplify the expression to a polynomial in standard form: (-2x-1)(-3x^2+6x+8)
The simplified form of the given expression is 6x³-9x²-22x-8
What is simplification?To simplify a mathematical expression is to represent it in the least complicated form possible.
Given an expression, (-2x-1)(-3x²+6x+8)
(-2x-1)(-3x²+6x+8) = 6x³-12x²-16x+3x²-6x-8
= 6x³-9x²-22x-8
Hence, The simplified form of the given expression is 6x³-9x²-22x-8
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Please Help!!!! 50 pts
Answer:
This may not help but, If you have any notes try using notes to solve this.
Or you can maybe ask your teacher to go over it when you both have free time or maybe have your teacher do a practice problem before or after class! That is what I would do but I hope it helps you! Good luck!
Answer:
A.
Step-by-step explanation:
Layla is thinking of a positive single digit even number. Luis guesses it was 7. What is the sample space??
The sample space for the single digit even number = {2, 4, 6, 8}
What is sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space.
Events are the subset of possible experiment results. Depending on the experiment, a sample space could contain a variety of results.
Given that,
Layla thinks about a positive single digit even number.
There are four single digit even numbers 2, 4, 6 and 8.
The sample space for the single digit even number = {2, 4, 6, 8}
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The length of a rectangular pool is seven less than twice its width. If the
perimeter of the pool is 106 feet, find its dimensions.
Answer:
width = 20 ft; length = 33 ft
Step-by-step explanation:
The formula for perimeter of a rectangle is P = 2l + 2w
Given that the length is seven less than twice its width, we have
[tex]l=2w-7[/tex]
We need to have only one variable or we can't solve.
Thus, we have:
[tex]106=2(2w-7)+2w\\106=4w-14+2w\\106=-14+6w\\120=6w\\20=w\\\\l=2w-7\\l=2(20)-7\\l=40-7\\\\l=33[/tex]
Yuma needs a singer. Singer A is offering her services for an initial $50 in addition to $10 per hour. Singer B is offering his services for an initial $95 in addition to $5 per hour. When will the two singers charge the same amount of money?
After 9 hours, Singer A and Singer B will both charge the same amount.
What is meant by an equation?An equation in French is defined as having one or more variables, whereas an equation in English is any well-formed formula consisting of two expressions combined with an equals sign.
Solving a variable equation includes determining which variables' values result in equality. Unknowns are the variables for which the equation must be solved, while equation solutions are the unknown values that satisfy the equality. An equation is a mathematical phrase with two equal sides separated by an equal sign. An equation is 4 + 6 = 10. We can see 4 + 6 on the left side of the equal sign and 10 on the right.
The Singer A's initial fee is $50.
Singer A's hourly rate is $10.
Singer B's initial fee was $95
Singer B's hourly wage is $5.
Assume the duration after which both singers will charge the same amount = x.
Then 50 +10x =95+5x
10x-5x=95-50
5x=45
x=45/5
x=9 hours
So, after 9 hours, Singer A and Singer B will both charge the same amount.
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HELp plssssss
Travis used the linear model y = 0.3x + 2000 to predict her total salary from achieving total sales of x.
What is her base salary?
What percent commission does she earn?
Answer:
i think it's 6,000
Step-by-step explanation:
just multiple 3.0 x 2,000 and you will get 6,000
a 100 ml beaker holds 170 gg of liquid. part a what is the liquid's density in si units? express your answer with the appropriate units.
The SI unit for density is kilogram per cubic meter (kg/m³)/
The density of liquid is 0.17 × 10⁸.
Kilogram Per Cubic Meter:
The SI unit for density is the kilogram per cubic meter (kg/m3). For many situations, however, this as an inconvenient unit, and we often use grams per cubic centimeter (g/cm3) for the densities of solids and liquids, and grams per liter (g/L) for gases.
According to the question:
Firstly, have to change your units to kilograms and cubic meters. Since there are a thousand grams in a kilogram,
170g = 1.70 x 10⁻¹ kg.
Since there are a thousand milliliters in a liter and a thousand liters in a cubic meter
100ml = 1.00 x 10⁸ cubic meters
Therefore, Density= mass/volume
Density = 1.7 x 10⁻¹/ 1.00 x 10⁸ kg/m³
= 0.17 x 10⁸ kg/m³.
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What is the value of this expression when a = 4, b = -5, and c = -7?
a + 2bc
3a
Answer:
Step-by-step explanation:
a = 4, b = -5, and c = -7
for a + 2bc
4 + 2(-5)(-7)
4 + 70
74
for 3a
3(4)
12
I'm not sure if the 2 parts are connected but if you add them, the answer is 86. If you subtract them, the answer is 62. If you multiply them, the answer is 888. If you divide them, the answer is 7/6.
Could you please give me brainliest? Thank you!
Ten individuals have participated in a diet modification program to stimulate weight loss. Their weight bothbefore and after participation in the program is shown below:Before195,213,247,201,187,210,215,246,294,310
After187,195,221,190,175,197,199,221,278,285
Is there evidence to support the claim that this particular diet-modification program is effective in producingmean weight reduction? Computep-value and state your conclusion usingα= 0.05.
(a)p-value<0.0005; rejectH0(b)p-value<0.0005; do not rejectH0(c)0.25< p-value<0.40; rejectH0(d)0.25< p-value<0.40; do not rejectH0(e)None of the preceding
The evidence is not sufficient to support the claim since the p-value is 0.1833 higher than 0.05, so e) none of the preceding.
How to find p-value?α = significance level = 0.05
n = sample size
df = degree of freedom = n - 1 = 10 - 1 = 9
Before we find the p-value, we use t test formula. But, before that we calculate mean and standard deviation for two population with excel.
In excel we get,
[tex]\bar x_1[/tex] = 231.8
[tex]\bar x_2[/tex] = 214.8
[tex]\sigma_1[/tex] = 41.95
[tex]\sigma_2[/tex] = 37.90
Next, we can calculate t test. So,
t = [tex]\frac{\bar x_1 -\bar x_2}{\sqrt{\frac{\sigma^2_1+\sigma^2_2}{n}}}[/tex]
= [tex]\frac{231.8-214.8}{\sqrt{\frac{41.95^2+37.9^2}{10}}}[/tex]
= [tex]\frac{17}{\sqrt\frac{3,196.2125}{10}}[/tex]
= 0.9509
Using t score to p-value calculator for 0.9509, we get p-value = 0.1833.
Thus, the p-value is 0.1833 is higher than significance level 0.05 so there is no sufficient evidence to support the claim.
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geoff is about to open a restaurant. he has found two possible locations for the restaurant; one closer to the central business district (cbd) and one in the suburbs. geoff is concerned that if he chooses the cbd location, he will have to charge higher prices for his food to cover the higher rent. geoff is uncertain of the affect that this will have on his annual revenue. to help with his decision, geoff will carry out a multiple regression analysis to predict the annual revenue earned by restaurants based on their distance from the cbd in miles and the average price in dollars charged for a dish. geoff has collected a sample of 50 restaurants that are randomly spread around the city. the proximity to the cbd (x1i), average price of a dish (x2i) and annual revenues (yi) were recorded for each of these restaurants (i = 1, 2, ..., 50). Geoff believes that a multiple linear regression is appropriate for this data. After carrying out some analysis, geoff has noticed that moving one mile away from the CBD (assuming that the average price of a dish is held constant) will result in a decrease of $60,000 in annual revenues. Geoff has also noticed that increasing the average price of a dish by $1 (assuming that the distance from the CBD is held constant) will result in an increase of $40,000 in annual revenues. The data shows that a restaurant at the center of the CBD that gave away its food for free would have an annual loss of $20,000. Select the multiple linear regression equation that corresponds to Geoff's analysis: o ĝi = -20,000 - 60,000x11 + 40,000x2i o ĝi = 20,000 + 60,000x11 - 40,000x2i O Vi = -20,000 + 40,000x11 - 60,000x2i © y = 20,000 - 40,000x13 + 60,000x2i
The multiple regression linear regression equation is:
i = -20000 + -60000*x1i + 40000*x2i
The multiple regression equation here will be of the form
i = a*x1i + b*x2i + c
Where i is the annual revenue
a is the coefficient of x1i which is distance from CBD
where b is the coefficient of x2i average price of a dish
C is the constant term.
Given that moving one mile away from the CBD x1i , the annual revenues will i will decrease by $60000. So, the coefficient of x1i, a is -60000
Given that increasing the average price of dish x2i by $1 , the annula revenue will i will increase by $40000. So the coefficient of x2i, b is 40000
The data shows that the restaurant at the center of the CBD which means, x1i = 0 and giving away its food for free which means x2i = 0 is resulting in a loss of $20000. so the value of the constant term is c=20000.
so the multiple regression linear regression equation is:
i = -20000 + -60000*x1i + 40000*x2i
hence option A is correct
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Robert swims a lap in the pool. His coach graphs his distance from the starting block.
A. Determine whether each graph is a function. Justify your answer.
B. Construct Arguments - Which graph must be incorrect. Explain
Answer:
Huh???
Step-by-step explanation:
THERE ARE NO GRAPHS!!!
if the null hypothesis is rejected in hypothesis testing, no conclusions can be drawn from the test. the sample size has been too small. the alternative hypothesis is true. the data must have been accumulated incorrectly.
if the null hypothesis is rejected in hypothesis testing the alternative hypothesis is true.
The relationship between important factors of interest and any apparent connection, according to a competing theory, is most certainly not accidental. The opposite of a null hypothesis is an alternative hypothesis. If we are able to rule out the null hypothesis, it signifies that we have enough data to support the alternative hypothesis. In one test, we cannot rule out both possibilities.
If one is disproven, it indicates that there is evidence to support the other. The opposing view is that a study's potential conclusion will materialize. It claims there is no coincidence in the relationship between important components of interest and the observed connection. As a result, the alternative hypothesis is true if the null hypothesis is disproved during hypothesis testing.
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geometry classifying triangles
The classification of the following triangles are below:
Diagram 1: Scalene triangle. option BDiagram 2: Equilateral triangle. option ADiagram 3: Isosceles triangle. option BDiagram 4: Acute triangle. option ADiagram 5: The value of a in the convex polygon is 40°Diagram 6: The value of s from the measure is 27Diagram 7: The value of m < 1 is 56°Diagram 8: The value of m < 1 is 120°The types of triangleThe types of triangle includes:
Scalene: A triangle having each of its three sides of different lengths.Equilateral triangle: A triangle having all three sides equal.Isosceles triangle: A triangle having two sides equal.Obtuse triangle: A triangle in which one of whose angles is obtuse, that is, an angle greater than 90° but less than 180°Acute triangle: A triangle which all of the angles are acute, that is, all interior angles are less than 90°Right angle triangle: A triangle all of the angles of which are acute.5. a = 180° - (56° + 84°)
= 180° - 140°
= 40°
6.
5s + (3s - 9) + 45 = 180
5s + 3s - 9 + 45 = 180
8s - 36 = 180
8s = 180 + 36
8s = 216
s = 216/8
s = 27
7. 180° - 139° = 41°
m < 1 = 180° - (41° + 83°)
= 180 - 124
m < 1 = 56°
180° - (68° + 52°)
= 180 - 120
= 60°
m < 1 = 180° - 60°
= 120°
Therefore, a triangle is a three sides polygon which also have three angles.
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hat are the zeros of the function: (x) = -x(x+ 2) (x - 6) (x + 4)
Answer:
zero of the function =0,-2,6,-4Step-by-step explanation:
f(x)=-x(x+2)(x-6)(x+4)-x=0 x=0(x+2)=0x=-2(x-6)=0x=6(x+4)=0x=-4