Answers
I can determine a function by drawing a vertical line. If this line pass trought the graph only one time, it's a function.
The only function there is the last one. (Right bottom)
Related Questions
A market trader has 100 oranges for sale, 4 of them are unripe, what is the
probability that an orange chosen at random is ripe?
4/100?
90/100?
2/5?
24/25?
Answers
Explanation:
100/100 - 4/100 = 96/100 = 24/25
[tex]\bold{Answer}:\quad \dfrac{24}{25}[/tex]
Step-by-step explanation:
There are 100 oranges. 4 of them are unripe which means 96 are ripe.
[tex]\dfrac{ripe}{total}=\dfrac{96}{100}\quad \div \dfrac{4}{4}=\large\boxed{\dfrac{24}{25}}[/tex]
iv)
6x+3y=6xy
2x + 4y= 5xy
Answers
Answer:
Ok, we have a system of equations:
6*x + 3*y = 6*x*y
2*x + 4*y = 5*x*y
First, we want to isolate one of the variables,
As we have almost the same expression (x*y) in the right side of both equations, we can see the quotient between the two equations:
(6*x + 3*y)/(2*x + 4*y) = 6/5
now we isolate one off the variables:
6*x + 3*y = (6/5)*(2*x + 4*y) = (12/5)*x + (24/5)*y
x*(6 - 12/5) = y*(24/5 - 3)
x = y*(24/5 - 3)/(6 - 12/5) = 0.5*y
Now we can replace it in the first equation:
6*x + 3*y = 6*x*y
6*(0.5*y) + 3*y = 6*(0.5*y)*y
3*y + 3*y = 3*y^2
3*y^2 - 6*y = 0
Now we can find the solutions of that quadratic equation as:
[tex]y = \frac{6 +- \sqrt{(-6)^2 - 4*3*0} }{2*3} = \frac{6 +- 6}{6}[/tex]
So we have two solutions
y = 0
y = 2.
Suppose that we select the solution y = 0
Then, using one of the equations we can find the value of x:
2*x + 4*0 = 5*x*0
2*x = 0
x = 0
(0, 0) is a solution
if we select the other solution, y = 2.
2*x + 4*2 = 5*x*2
2*x + 8 = 10*x
8 = (10 - 2)*x = 8x
x = 1.
(1, 2) is other solution
Solve the quadratic equation 4x2 – x = 8 using the quadratic formula.
Answers
Answer:
[tex]1x=\frac{1\sqrt{129} }{8}[/tex]
Step-by-step explanation:
In between the 1 and the [tex]\sqrt{129}[/tex] goes this symbol: ±
hope this helps!
The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W. Assume the vectors are in the order bold x1 and bold x2
1 7
-4 -7
0 -6
1 1
The orthogonal basis produced using the Gram-Schmidt process for W is:__________. (Use a comma to separate vectors as needed.)
Answers
Answer:
[tex]y_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex] , [tex]y_2 = \left[\begin{array}{ccc}5\\1\\-6\\-1\end{array}\right][/tex]
Step-by-step explanation:
[tex]x_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex] and [tex]x_2 = \left[\begin{array}{ccc}7\\-7\\-6\\1\end{array}\right][/tex]
Using Gram-Schmidt process to produce an orthogonal basis for W
[tex]y_1 = x_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex]
Now we know X₁ , X₂ and Y₁
Lets solve for Y₂
[tex]y_2 = x_2- \frac{x_2*y_1}{y_1*y_1}y_1[/tex]
see attached for the solution of Y₂
What is viscosity?
O A measure of the oil's quality
O An oil's resistance to flow at different temperatures
A reference to synthetic oil; all oils with viscosity are synthetic
O A new motor oil ingredient
< BACK
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>
Answers
Answer:
viscosity is the state of being thick, sticky, and semifluid in consistency, due to internal friction.
"cooling the fluid raises its viscosity"
a quantity expressing the magnitude of internal friction, as measured by the force per unit area resisting a flow in which parallel layers unit distance apart have unit speed relative to one another.
plural noun: viscosities
"silicone oils can be obtained with different viscosities"
Step-by-step explanation:
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. hope this helps you :)
Answer:
O An oil's resistance to flow at different temperatures
Step-by-step explanation:
Internal friction of a moving fluid .
Cincinnati Paint Company sells quality brands of paints through hardware stores throughout the United States. The company maintains a large sales force whose job it is to call on existing customers as well as look for new business. The national sales manager is investigating the relationship between the number of sales calls made and the miles driven by the sales representative. Also, do the sales representatives who drive the most miles and make the most calls necessarily earn the most in sales commissions? To investigate, the vice president of sales selected a sample of 25 sales representatives and determined:
%u2022 The amount earned in commissions last month (Y).
%u2022 The number of miles driven last month (X2)
%u2022 The number of sales calls made last month (X1)
($000) Calls Driven Commissions
($000) Calls Driven
22 139 2,371 38 146 3,290
13 132 2,226 44 144 3,103
33 144 2,731 29 147 2,122
38 142 3,351 38 144 2,791
23 142 2,289 37 149 3,209
47 142 3,449 14 131 2,287
29 138 3,114 34 144 2,848
38 139 3,342 25 132 2,690
41 144 2,842 27 132 2,933
32 134 2,625 25 127 2,671
20 135 2,121 43 154 2,988
13 137 2,219 34 147 2,829
47 146 3,463
Click here for the Excel Data File
Develop a regression equation including an interaction term. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)
Commissions = + Calls + Miles - X1X2
Complete the following table. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)
Predictor Coef SE Coef T P
Constant
Calls
Miles
X1X2
Compute the value of the test statistic corresponding to the interaction term. (Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)
Value of the test statistic
Is there a significant interaction between the number of sales calls and the miles driven?
Answers
Answer:
There is no significant interaction between the number of sales calls and the miles driven.
Step-by-step explanation:
The variables are defined as follows:
Dependent (Y) = amount earned in commissions last month
Independent (X₁) = number of miles driven last month
Independent (X₂) = number of sales calls made last month
In this case we need to test whether there is a significant interaction between the number of sales calls and the miles driven.
The hypothesis can be defined as follows:
H₀: There is no significant interaction.
Hₐ: There is a significant interaction.
Assume that the significance level of the test is, α = 0.05.
Use the Data Analysis tool in Excel to form the regression equation.
For the regression equation, we need to compute the values of (X₁ × X₂).
Steps:
Go to Data - Data Analysis - Regression. A dialog box will open.Select the Y values in the "Input Y range" and values of X₁, X₂ and X₁ × X₂ in the "Input X range".Click OK.The output of the regression analysis is attached below.
The regression equation is:
[tex]Y=-455.07+3.128\cdot X_{1}+0.143\cdot X_{2}-0.001\cdot X_{1}X_{2}[/tex]
Consider the third table in the regression output.
The test statistic corresponding to the interaction term is:
t = -1.85
The p-value for the test of the interaction term is:
p-value = 0.078.
The p-value of the test is more than the significance value.
The null hypothesis will not be rejected.
Thus, concluding that there is no significant interaction between the number of sales calls and the miles driven.
kamau is now 2 years older than Jane if James age is y now what will be the total age in 10 years
Answers
Answer:
(2y + 22) years
Step-by-step explanation:
kamau is now 2 years older than Jane if Janes age is y now what will be the total age in 10 years.
Answer: If Jane is y years old now and Kamau is 2 years older than Jane, therefore the age of Kamau now would be 2 + y years.
In ten years time Jane age would be y + 10 years while the age of Kamau would be y + 2 + 10 = y + 12 years.
To get their total age we just have to add their individual age. Therefore the total age in 10 years = Age of Kamau in ten years + age of Jane in ten years = (y + 12) + (y + 10) = y + 12 + y + 10 = y + y + 12 + 10 = 2y + 22 years
I NEED HELP!
Rectangle ABCD is drawn with diagonal AC, which has a measure of 20cm. Angle BACmeasures 30°. What is the
perimeter and area of the rectangle?
Answers
Answer:
Perimeter = 54.6 cm
Area = 173 cm²
Step-by-step explanation:
sin 30 = x/20
x = 10
cos 30 = y /20
y = 17.3
perimeter = 10 + 17.3 + 10 + 17.3 = 54.6 cm
area = 10 * 17.3 = 173 cm²
Kite LMNO is shown below.
What is the measure of angle M
Answers
Answer:
<M = 78°
Step-by-step explanation:
The sum of angles in a kite is 360°.
One of the properties of a kite is that one pair of opposite angles are equal.
Since it is not <L and <N, it must be <O and <M
Therefore:
<O = <M = x
=> x + x + 130 + 74 = 360
2x + 204 = 360
2x = 360 - 204
2x = 156
x = 156/2 = 78°
This means that <M = 78°
Help someone!! Thank you
Answers
I suppose this is saying that 20%, 25% and 55% are each a whole number of science students. The GCD is 5%, 1/20th, so minimum 20 people total. 55% are studying biology, that's 11.
Answer: C. 11
The measure of minor arc JL is 60°. Circle M is shown. Line segments M J and M L are radii. Tangents J K and L K intersect at point K outside of the circle. Arc J L is 60 degrees. What is the measure of angle JKL? 110° 120° 130° 140°
Answers
Answer:
120
Step-by-step explanation:
Answer: 120
Hope that helped!(:
Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. 41 52 37 44 42 38 41 48 43 39 36 55 42 35 15 52 39 50 29 30
Answers
Answer:
(a) [tex]Q_1=36.5,M=Q_2=41,Q_3=46[/tex]
(b) [tex]IQR=9.5[/tex]
(c) 15
Step-by-step explanation:
The given data set is
41, 52, 37, 44, 42, 38, 41, 48, 43, 39, 36, 55, 42, 35, 15, 52, 39, 50, 29, 30
Arrange the data in ascending order.
15, 29, 30, 35, 36, 37, 38, 39, 39, 41, 41, 42, 42, 43, 44, 48, 50, 52, 52, 55
Divide the data in four equal parts.
(15, 29, 30, 35, 36), (37, 38, 39, 39, 41), (41, 42, 42, 43, 44), (48, 50, 52, 52, 55)
Now,
[tex]Q_1=\dfrac{36+37}{2}=36.5[/tex]
[tex]M=Q_2=\dfrac{41+41}{2}=41[/tex]
[tex]Q_3=\dfrac{44+48}{2}=46[/tex]
[tex]IQR=Q_3-Q_1=46-36.5=9.5[/tex]
Range for outlier is
[tex][Q_1-1.5IQR,Q_3+1.5IQR]=[36.5-1.5(9.5),46+1.5(9.5)][/tex]
[tex]=[22.25,60.25][/tex]
Since, 15 lies outside the interval [22.25,60.25], therefore 15 is an outlier.
Can someone teach me on how to do these type of problems
Answers
A. 22√2
B. 11 √6/2
C. 11√6/4
D. 11 √2/4
Answers
Answer:
11[tex]\sqrt{x6/4[/tex]
Given:
The triangle on the left ( triangle 1) has a 60º, a 90º, and a side that equals 11.
So we know the triangle on the right (triangle 2) has a 45º and a 90º angle.
Triangle 2
Since triangle angles always have a sum of 180º, we can solve for the third angle of triangle 2. 180 - (45 + 90) = 45. So the third angle of triangle 2 is 45º.
This is a special type of right triangle called a 45-45-90. An image of the leg/hypotenuse is uploaded below. Meaning, if we solve for the leg that joins the two triangles, we can solve for the hypotenuse.
Triangle 1
To solve for the middle leg, we work with the information we have. So first, find the third angle. 190 - (60 + 90) = 30. This brings us to a second type of special right triangle. An image of the leg/hypotenuse is uploaded below.
Given that we have a side angle of 11, we know that is 2x due to orientation. So 2x=11 simplifies to x=5.5. We then plug that back in to find the leg that we want: 5.5[tex]\sqrt{3}[/tex] .
Triangle 2
Now that we have a side length for the second triangle we can solve. x for this triangle is 5.5[tex]\sqrt{3}[/tex] so to find the hypotenuse we plug into x[tex]\sqrt{2}[/tex]. This turns into (5.5[tex]\sqrt{3}[/tex][tex]\sqrt{2}[/tex]) which simplifies into 5.5[tex]\sqrt{6}[/tex] = 13.47
Answers
The answers are not in the correct form. By going through and finding the decimal form of each, you find out that 11[tex]\sqrt{6/4}[/tex] is equivalent to 13.47, therefore your answer.
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
Answers
The complete question is;
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
(a) less than 10 minutes
(b) longer than 5 minutes
(c) between 8 and 15 minutes
Answer:
A) P (x < 10) = 0.6700
B) P (x > 5 ) = 0.9406
C) P (8.0000 < x < 15.0000) = 0.6332
Step-by-step explanation:
A) we are given;
Mean;μ = 8.9 minutes
Standard deviation;σ = 2.5 minutes
Normal random variable;x = 10
So to find;P(x < 10) we will use the Z-score formula;
z = (x - μ)/σ
z = (10 - 8.9)/2.5 = 0.44
From z-distribution table and Z-score calculator as attached, we have;
P (x < 10) = P (z < 0.44) = 0.6700
B) similarly;
z = (x - μ)/σ =
z = (5 - 8.9)/2.5
z = -1.56
From z-distribution table and Z-score calculator as attached, we have;
P (x > 5 ) = P (z > -1.56) = 0.9406
C)between 8 and 15 minutes
For 8 minutes;
z = (8 - 8.9)/2.5 = -0.36
For 15 minutes;
z = (15 - 8.9)/2.5 = 2.44
From z-distribution table and Z-score calculator as attached, we have;
P (8.0000 < x < 15.0000) = P (-0.36 < z < 2.44) = 0.6332
can I get a step by step explanation Thnx
Answers
Answer:
( 2A - kn) /k = m
Step-by-step explanation:
A = k/2(m+n)
Multiply each side by 2/k
2/k *A =2/k * k/2(m+n)
2A /k = m+n
Subtract n from each side
2A /k - n = m+n -n
2A /k - n = m
Getting a common denominator
2A/k - kn/k = m
( 2A - kn) /k = m
Answer:
Step-by-step explanation:
[tex]A=\frac{k(m+n)}{2}\\2A=k(m+n)\\\frac{2A}{k} =m+n\\\frac{2A}{k}-n=m\\2A-kn=km\\\frac{(2A-kn)}{k}=m[/tex]
Write the following numbers in decreasing order: −4; 1 2 3 ; 0.5; −1 3 4 ; 0.03; −1; 1; 0; −10; 54
Answers
Answer:
123 ; 54 ; 1 ; 0.5 ; 0.03 ; 0 ; -1 ; -4 ; -10 ; -134
Step-by-step explanation:
123 ; 54 ; 1 ; 0.5 ; 0.03 ; 0 ; -1 ; -4 ; -10 ; -134
Which graphs represent functions?
Answers
what percentage of 40 is 8?
(A) 5%
(B) 20%
(C) 32%
(D) 150%
Answers
Answer:
20%
Step-by-step explanation:
When you divide 40 by 8, you get 0.2. To convert a decimal into a percent, you multiply by 100 to get 20.
Hence,
8 is 20% of 40.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
Answer:
The answer is option B.
Step-by-step explanation:
Let the percentage be x
We have
[tex] \frac{x}{100} \times 40 = 8 \\ \\ \frac{4}{10} x = 8 \\ \\ 4x = 80 \\ \\ x = \frac{80}{4} \\ \\ x = 20[/tex]
Hope this helps you
The oxygen consumption (in milliliter per pound per minute) for a person walking at x mph is approximated by the function f(x)=\frac{5}{3} x^{2}+\frac{5}{3} x+10 \quad(0 \leq x \leq 9)whereas the oxygen consumption for a runner at x mph is approximated by the function g(x)=11 x+10 \quad(4 \leq x \leq 9) b. At what speed is the oxygen consumption the same for a walker as it is for a runner? What is the level of oxygen consumption at that speed?
Answers
Answer: Speed = 5.6 mph
Oxygen consumption = 71.6 mL/lb/min
Step-by-step explanation: For the oxygen consumption to be the same, functions must be equal:
f(x) = g(x)
[tex]\frac{5}{3}.x^{2} + \frac{5}{3}.x+10=11x+10[/tex]
Resolving:
[tex]\frac{5}{3}.x^{2} + \frac{5}{3}.x - 11x =0[/tex]
[tex]\frac{5}{3}x^{2} + \frac{5}{3}x - \frac{33x}{3}=0[/tex]
[tex]\frac{5}{3}x^{2} - \frac{28x}{3}=0[/tex]
[tex]\frac{x}{3}(5x - 28)=0[/tex]
[tex]\frac{x}{3} = 0[/tex]
x=0
5x - 28 = 0
[tex]x = \frac{28}{5}[/tex]
x = 5.6
The speed when the oxygen consuption is the same is 5.6 mph.
For the level of oxygen consumption:
f(5.6) = g(5.6)
g(5.6) = 11*5.6 + 10
g(5.6) = 71.6
The level of oxygen consumption is 71.6 mL/lb/min
At speed of 5.6 mph the oxygen consumption is same for a walker as it is for a runner.
The level of oxygen consumption is 71.6 milliliter per pound per minute
The oxygen consumption for a person walking at x mph is given by,
[tex]f(x)=\frac{5}{3} x^{2} +\frac{5}{3}x+10[/tex]
The oxygen consumption for a runner at x mph is approximated given by the function,
[tex]g(x)=11x+10[/tex]
To be oxygen consumption same for both walker and runner, both function must be equal.
[tex]f(x)=g(x)\\\\\frac{5}{3} x^{2} +\frac{5}{3}x+10=11x+10\\\\\frac{5}{3} x^{2} +\frac{5}{3}x-11x=0\\\\x(\frac{5}{3} x-\frac{28}{3} )=0\\\\x=0,x=28/5=5.6mph[/tex]
At speed of 5.6 mph the oxygen consumption is same for a walker as it is for a runner.
The level of oxygen consumption at that speed is,
[tex]g(5.6)=11(5.6)+10=71.6[/tex]
Learn more:
https://brainly.com/question/6237128
If f(x) = 2x2 + 2 and g(x) = x2 – 1, find (f – 9)(X).
Answers
Answer:
x^2 +3
Step-by-step explanation:
f(x) = 2x^2 + 2
g(x) = x2 – 1,
find (f – g)(X).
f(x) - g(x) = 2x^2 + 2 -( x^2 – 1)
Distribute the minus sign
= 2x^2 +2 -x^2 +1
= x^2 +3
Which equations are equivalent to Three-fourths + m = negative StartFraction 7 over 4 EndFraction? Select three options. m = StartFraction 10 over 4 EndFraction m = negative StartFraction 10 over 4 EndFraction m = negative five-halves StartFraction 11 over 4 EndFraction + m = negative one-fourth Negative five-fourths + m = negative StartFraction 15 over 4 EndFraction
Answers
Answer:
1) m = negative StartFraction 10 over 4 EndFraction
2) m = negative five-halves
3) m = [tex]-\frac{7}{4} - \frac{3}{4}[/tex]
Step-by-step explanation:
The given equation is:
=> [tex]\frac{3}{4} +m = -\frac{7}{4}[/tex]
Subtracting 3/4 to both sides
=> m = [tex]-\frac{7}{4} - \frac{3}{4}[/tex]
=> m = [tex]\frac{-10}{4}[/tex]
=> m = [tex]-\frac{5}{2}[/tex]
Answer:
-5/2 ye
cause ya do the math
Step-by-step explanation:
Probability can never be equal to 154Probability can never be equal to 154
Answers
Answer: True
Step-by-step explanation:
The probability of an event occurring lies between zero and one. A probability of 0 means that the event has no chance of happening for example, rolling a die once and getting a number greater than 6 while a probability of 1 means the event will definitely happen for example, getting a number less than 7 when you roll a die once.
Every other probability falls in-between this range so probability can never be 154.
Imagine a man in the Chicago suburbs went outside to shovel his driveway after the Feb 10, 2018 snowstorm and had a heart attack while shoveling. When the police discovered the body later that day at 4PM, his body temperature had dropped from 98.6°F to 42°F. The environmental air temperature was 10°F. What time did he die from the heart attack?
Answers
Answer:
I did my best with the information! The Man died at around 11:20 am.
Step-by-step explanation:
So due to the algus mortis process, after death, a body can stay at its regulated temperature for up to 2 to 3 hours postmortem. But after that, the body soon drops at about 1 degrees celsius each hour. 1 degrees celsius is about -33 . So he was found at 42 degrees fahrenheit, which means he died somewhere around 11 o-clock. We do not know how long the postmortem process had his temperature delayed, so it would be roughly I say around 11: 20 am.
A loudspeaker converts electrical energy into the kinetic energy of the speaker. This kinetic energy is transferred to air, and the motion of the air is the sound that people hear. An illustration of speaker with a wide arrow away from it labeled electrical energy 100 J and it splits into 3 arrows labeled sound energy 80 J, thermal energy ? J, and friction 5 J. How much thermal energy is put out by the speaker? 5 J 15 J 80 J 100 J
Answers
Answer:
15 J
Step-by-step explanation:
There is a total of 100 J of energy being used which is then converted into sound energy, thermal energy, and friction. This means the total amount must equal 100 J.
1. Set up the equation
80 + x + 5 = 100
2. Simplify
x + 85 = 100
3. Solve for x by subtracting 85 from both sides
x = 15
Answer:
The correct answer is 15J which is B.
A 6 foot person casts a 26 foot shadow. What is the angle of elevation of the sun? (nearest whole degree)
Answers
Answer:
13°
Step-by-step explanation:
The trigonometric ratio formula can be used in calculating the angle of elevation (x°) of the sun, as the person makes a right angle with the ground.
The height of the person would be the opposite length = 6 ft, the shadow of the person would be the adjacent length = 26 ft
Therefore, according to the trigonometric ratio formula, we would calculate angle of elevation (x°) as follows:
[tex] tan x = \frac{opposite}{adjacent} [/tex]
[tex] tan x = \frac{6}{26} [/tex]
[tex] tan x = 0.2308 [/tex]
x = tan-¹(0.2308)
x = 12.996
x ≈ 13° (to the nearest whole degree)
The angle of elevation of the sun = 13°
Write an equation of the line that passes through the point (–1, 4) with slope 2. A. y+1=−2(x−4) B. y+1=2(x−4) C. y−4=2(x+1) D. y−4=−2(x+1) CHOSE ONE!
Answers
Answer:
[tex]y-4=2\,(x+1)[/tex]
which agrees with answer C in your list of possible answers.
Step-by-step explanation:
We can use the general point-slope form of a line of slope m and going through the point [tex](x_0, y_0)[/tex]:
[tex]y-y_0=m(x-x_0)[/tex]
which in our case, given the info on the slope (2) and the point (-1, 4) becomes:
[tex]y-y_0=m\,(x-x_0)\\y-4=2\,(x-(-1))\\y-4=2\,(x+1)[/tex]
Hermina cut a 10'' by 15'' piece of cardboard down the diagonal. A rectangle is 10 inches wide and 15 inches long. A diagonal cut is shown with a line labeled c. The cut divides the rectangle in half and creates two right triangles. The hypotenuse of each right triangle is the line labeled c. What is the length c of the cut, in inches?
Answers
Answer:
18.03 inches
Step-by-step explanation:
The cardboard is cut as shown below.
The line c cuts the rectangle into 2 right angled triangles.
To find the diagonal (hypotenuse), we have to apply Pythagoras Rule:
[tex]hyp^2 = opp^2 + adj^2\\\\=> c^2 = 10^2 + 15^2\\\\c^2 = 100 + 225 = 325\\\\[/tex]
=> c = 18.03" = 18.03 inches
The length of c, the diagonal, is 18.03 inches.
Proving the sum of the Interior Angle Measures of a Triangle is 180
Answers
Answer:
theres the screenshot of it
The solution to prove the sum of the interior angles of a triangle is 180° is
∠1 + ∠2 + ∠3 = 180° ( angles in a straight line )
∠2 + ∠5 + ∠6 = 180° ( interior angles of a triangle )
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be represented as ABC
Now , the angles inside the triangle are ∠2 , ∠5 and ∠6
Now , the lines l₁ and l₂ are two parallel lines
From the figure ,
The measure of ∠1 = The measure of ∠5 ( alternate interior angles )
The measure of ∠3 = The measure of ∠6 ( alternate interior angles )
Now , for a straight line , the measure of angle = 180°
So , ∠1 + ∠2 + ∠3 = 180° ( angles in a straight line ) ( angle addition )
And , the sum interior angles of a triangle is 180°
So , ∠2 + ∠5 + ∠6 = 180° ( interior angles of a triangle ) ( substitution )
Hence , the sum of the angles inside a triangle is 180°
To learn more about triangles click :
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Answers
Answer:
[tex]\boxed{\sf A. \ 0.34}[/tex]
Step-by-step explanation:
The first triangle is a right triangle and it has one acute angle of 70 degrees.
We can approximate [tex]\sf \frac{WY}{WX}[/tex] from right triangle 1.
The side adjacent to 70 degrees is WY. The side or hypotenuse is WX.
The side adjacent to 70 degrees in right triangle 1 is 3.4. The side or hypotenuse is 10.
[tex]\sf \frac{3.4}{10} =0.34[/tex]
How many real roots and how many complex roots exist for the polynomial
F(x) - X4+ x2 - 5x2 + x -- 6?
O A. 2 real roots and 2 complex roots
B. O real roots and 4 complex roots
O c. 3 real roots and 1 complex root
D. 4 real roots and 0 complex roots
Answers
Answer:
D. 4 real roots and 0 complex roots
Step-by-step explanation:
If I assume that the function you are saying is
[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]
There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.
[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]
There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.