Answers
For the given triangle, the greatest angle is ∠D while the smallest one is ∠C
∠D > ∠B > ∠C
In a triangle,
The shortest side is always opposite the smallest interior angle.
The longest side is always opposite the largest interior angle.
In simple word,
for smaller side of a triangle will have smaller angle, and for longest side it will have larger angle.
In case of triangle ΔBCD
BD = 8m
CD = 9m
BC = 13m
as BC = 13m is largest side, so opposite angle ∠D will be largest one.
again BD = 8m is smallest side, so opposite angle ∠C will be smallest one.
BC > CD > BD
so,
∠D > ∠B > ∠C
The greatest angle is ∠D while the smallest one is ∠C
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Related Questions
Rusell runs 9/10 mile in 5 minutes. at this rate, how many miles can he run in one minute?
Answers
Answer:
in one minute, Rusell can run 9/50 mile.
[tex]\frac{9}{50}mile[/tex]Explanation:
Given that;
Rusell runs 9/10 mile in 5 minutes.
[tex]\begin{gathered} \frac{9}{10}\text{mile }\rightarrow\text{ 5 minutes} \\ \text{dividing both sides by 5;} \\ \frac{9}{10\times5}\text{mile }\rightarrow\text{ }\frac{5}{5}\text{ minutes} \\ \frac{9}{50}\text{mile }\rightarrow\text{ 1 minutes} \end{gathered}[/tex]Therefore, in one minute, Rusell can run 9/50 mile.
[tex]\frac{9}{50}mile[/tex]Let f(x) = x2 - 9a and g(a) = 3 - x?.(f+g)(7) =- (f - 9)(7) =.· (f9)(7) =• (4) (7) -
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Given the functions:
[tex]f(x)=x^2-9x[/tex][tex]g(x)=3-x^2[/tex]1) (f+g)(x) You have to calculate the sum between f(x) and g(x) for x=7
First, calculate the sum between both functions:
[tex]\begin{gathered} (f+g)=(x^2-9x)+(3-x^2) \\ (f+g)=x^2-9x+3-x^2 \end{gathered}[/tex]Order the like terms together and simplify:
[tex]\begin{gathered} (f+g)=x^2-x^2-9x+3 \\ (f+g)=-9x+3 \end{gathered}[/tex]Substitute the expression with x=7 and solve:
[tex]\begin{gathered} (f+g)(7)=-9x+3 \\ (f+g)(7)=-9\cdot7+3 \\ (f+g)(7)=-60 \end{gathered}[/tex]The result is (f+g)(7)= -60
2) (f-g)(7) You have to calculate the difference between f(x) and g(x) for x=7
First, calculate the difference between both functions:
[tex](f-g)=(x^2-9x)-(3-x^2)[/tex]First, erase the parentheses, the minus sign before (3-x²) indicates that you have to change the sign of both terms inside the parentheses, as if they were multiplied by -1, then:
[tex](f-g)=x^2-9x-3+x^2[/tex]Order the like terms and simplify:
[tex]\begin{gathered} (f-g)=x^2+x^2-9x-3 \\ (f-g)=2x^2-9x-3 \end{gathered}[/tex]Substitute the expression with x=7 and solve:
[tex]\begin{gathered} (f-g)(7)=2x^2-9x+3 \\ (f-g)(7)=2(7)^2-9\cdot7+3 \\ (f-g)(7)=2\cdot49-63-3 \\ (f-g)(7)=98-66 \\ (f-g)(7)=32 \end{gathered}[/tex]The result is (f-g)(7)= 32
3) (fg)(7) In this item you have to calculate the product of f(x) and g(x) for x=7
First, determine the product between both functions:
[tex](fg)=(x^2-9x)(3-x^2)[/tex]Multiply each term of the first parentheses with each term of the second parentheses:
[tex]\begin{gathered} (fg)=x^2\cdot3+x^2\cdot(-x^2)-9x\cdot3-9x\cdot(-x^2) \\ (fg)=3x^2-x^4-27x+9x^3 \\ (fg)=-x^4+9x^3+3x^2-27x \end{gathered}[/tex]Substitute with x=7 and solve:
[tex]\begin{gathered} (fg)(7)=-(7^4)+9\cdot(7^3)+3\cdot(7^2)-27\cdot7 \\ (fg)(7)=-2401+9\cdot343+3\cdot49-189 \\ (fg)(7)=-2401+3087+147-189 \\ (fg)(7)=644 \end{gathered}[/tex]The result is (fg)(7)=644
4) (f/g)(7) First, divide both functions:
[tex](\frac{f}{g})=\frac{x^2-9}{3-x^2}[/tex][tex]\begin{gathered} (\frac{f}{g})=\frac{(x-9)x}{3-x^2} \\ (\frac{f}{g})=\frac{(-1)(x-9)x}{(-1)(3-x^2)} \\ (\frac{f}{g})=\frac{(-x+9)x}{(-3+x^2)} \\ (\frac{f}{g})=\frac{(9-x)x}{(x^2-3)} \\ (\frac{f}{g})=\frac{9x-x^2}{x^2-3} \end{gathered}[/tex]Substitute with x=7 and solve:
[tex]\begin{gathered} (\frac{f}{g})(7)=\frac{9\cdot7-7^2}{7^2-3} \\ (\frac{f}{g})(7)=\frac{63-49}{49-3} \\ (\frac{f}{g})(7)=\frac{14}{46} \\ (\frac{f}{g})(7)=\frac{7}{23} \end{gathered}[/tex]The result is (f/g)(7)= 7/23
The GMAT scores of all examinees who took that test this year produced a distribution that is approximately normal with a mean of 430 and a standard deviation of 34.The probability that the score of a randomly selected examinee is between 400 and 480, rounded to three decimal places, is:
Answers
SOLUTION:
Case: Probability from a normal distribution
Given: Mean = 430, Standard deviation: 34
Required: To find the probability that the score of a randomly selected examinee is between 400 and 480
Method:
Steps
Step 1: Get the z-score with the lesser value:
[tex]undefined[/tex]Final answer:
triangle A B C is translated 6 units to the left and 1 unit up to create A'B'C'.
Answers
The correct answer is 6.1 square units.
The translation of triangle ABC to triangle A'B'C' will not change the dimensions of the original triangle.
Hence, the area of triangle ABC will not be affected by the translation.
[tex]\begin{gathered} \text{Area of }\Delta ABC=\frac{1}{2}bh \\ \text{where b=2, h=6.1} \\ \text{Area of}\Delta ABC=\frac{1}{2}\times2\times6.1 \\ \text{ = 6.1 square units} \end{gathered}[/tex]Hence, the correct answer is 6.1 square units
I would like to know the break down to solve for this problem.
Answers
Train A travels at a speed of 25 miles per hour south and train B travels at a speed of 20 mph east.
We can find the distance for each one of the trains by using the following formula:
[tex]X=Vt[/tex]Where X is distance, V is velocity and t is time
Let's find the dinstance that A and B will travel in 6 hours
[tex]\begin{gathered} Xa=Va\cdot t \\ Xa=25\cdot6=150 \end{gathered}[/tex]Train A travels 150 miles in 6 hours
[tex]\begin{gathered} Xb=Vb\cdot t \\ Xb=20\cdot6=120 \end{gathered}[/tex]Train B travels 120 miles in 6 hours
Now, in order to determine how far they are from each other, we need to take into account their direction. From the picture we can see that their route describes a right triangle, so the distance between them is the hypotenuse of this right triangle I will draw...
if D is the distance that separates the two trains, D is given by the following formula
[tex]D=\sqrt[]{150^2+120^2}[/tex]Solving the equation we obtain...
[tex]\begin{gathered} =\sqrt[]{22500+14400^{}} \\ =\sqrt{36900} \\ \end{gathered}[/tex]Solving this square root by using prime factorization and laws of exponents:
[tex]\begin{gathered} =\sqrt{2^2\cdot\:3^2\cdot\:5^2\cdot\:41} \\ =\sqrt{41}\sqrt{2^2}\sqrt{3^2}\sqrt{5^2} \\ =2\cdot\: 3\cdot\: 5\sqrt{41} \\ =30\sqrt{41} \end{gathered}[/tex]which is approximately the same as 192.09372...
if M angle ABD equals 7X - 31 n m a angles c d b equals 4x + 5 find M angle ABD
Answers
The quadrilateral is a rectangle, all of its corner angles are rigth angles.
5)
m∠DAC=2x+4
m∠BAC=3x+1
Both angles are complementary, which means that they add up to 90º
You can symbolize this as:
[tex]m\angle DAC+m\angle BAC=90º[/tex]Replace the expression with the given measures for both angles:
[tex](2x+4)+(3x+1)=90[/tex]Now you have established a one unknown equation.
Solve for x:
[tex]\begin{gathered} 2x+4+3x+1=90 \\ 2x+3x+4+1=90 \\ 5x+5=90 \\ 5x=90-5 \\ 5x=85 \\ \frac{5x}{5}=\frac{85}{5} \\ x=17 \end{gathered}[/tex]Next is to calculate the measure of m∠BAC, replace the given expression with x=17
m∠BAC=3x+1= 3*17+1=52º
6)
m∠BDC=7x+1
m∠ADB=9x-7
Angle m∠BDC is a corner angle of the rectangle, as mentioned before, all corner angles of a rectangle measure 90º, so there is no need to make any calculations.
Note: the diagonals of the rectangle bisect each corner angle, this means that it cuts the angle in half, so m∠BDC=2*(m∠ADB)
It turns out that as ice cream consumption increases, drowning deaths increase. In other words, there is a positive association between ice cream consumption and drowning deaths. However, ice cream consumption does not cause drowning deaths. So why is there a positive association? Explain.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
ice cream consumption ====> increases
drowning deaths ====> increase
Step 02:
We must analyze the question to find the solution.
positive association:
There is an association because both values increase, that is, a positive association suggests that when one variable increases, the value of the other variable also increases.
That is the solution.
How do you know if a sequence is a geometric sequence. A It has a common difference. B It has a common ratio.
Answers
A geometric sequence in which each next term is found by multiplying the previous term by a constant; therefore, every adjacent pair on entires in a geometric sequence have a common ratio. Hence, if any two consecutive entries in a sequence have a common ratio, it is a geometric series; therefore, choice B is the correct one to choose.
Find the area of the shaded region. Use 3.14 to represent pi. Hint: You need to find height of triangle.A: 329.04B: 164.52C: 221.04D: 272.52
Answers
The area of the shaded region is 164.52 inches squared
Here, we wan to calculate the area of the shape given
From what we have, there is a triangle and a semi-circle
So the area of the shape is the sum of the areas of the triangle and the semi-circle
Mathematically, we can have this as;
[tex]\begin{gathered} \text{Area of triangle = }\frac{1}{2}\text{ }\times\text{ b }\times\text{ h} \\ \\ \text{Area of semicircle = }\frac{\pi\text{ }\times r^2}{2} \end{gathered}[/tex]where b represents the base of the triangle which is the diameter of the semicircle
The radius of the semicircle is 6 inches and the diameter is 2 times of this which equals 2 * 6 = 12 inches
The height of the triangle is 18 inches
The radius of the semicircle is 6 inches as above
Thus, we have the area of the shape as follows;
[tex]\begin{gathered} (\frac{1}{2}\times\text{ 18 }\times\text{ 12) + (}\frac{3.14\text{ }\times6^2}{2}) \\ \\ =\text{ 108 + 56.52} \\ \\ =\text{ 164.52 inches squared} \end{gathered}[/tex]numbers. у xt Y y page ted. 8 7+ 6- 5 above in every Good; Fair; 3 2+ 1+ + x -9-8-7-6-5-4-3-2 1 2 3 4 5 6 7 8 9 -2 -3 -5 -6 -77 -87 -9-
Answers
step 1
Find the slope
we need two points
we take
(-6,0) and (0,4)
m=(4-0)/(0+6)
m=4/6
m=2/3
step 2
Find the equation in slope intercept form
y=mx+b
we have
m=2/3
b=4
substitute
y=(2/3)x+43) = A store sells rope by the meter. The equation p = 0.8L represents the price p (in dollars) of a piece of nylon rope that is L meters long. a. How much does the nylon rope cost per meter? b. How long is a piece of nylon rope that costs $1.00?
Answers
(a) Since the equation is:
[tex]p=0.8L[/tex]And "L" is in meters, the cos per meter will be simply the slope of the line. Alternatively, we can just input L = 1 and check the corresponding cost:
[tex]\begin{gathered} p=0.8\cdot1 \\ p=0.8 \end{gathered}[/tex]So, the cost is $0.80 per meter.
(b) Now, we have to the the contrary, we input 1 input "p" and calculate "L":
[tex]\begin{gathered} p=0.8L \\ 1=0.8L \\ L=\frac{1}{0.8} \\ L=1.25 \end{gathered}[/tex]So, it will be 1.25 meters long.
how can you use number patterns to find the greatest common factor of 120 and 360
Answers
Greatest common factor (GCF)
• 120
Finding the factors:
[tex]\begin{gathered} \frac{120}{2}=60\text{ (2 is a factor)} \\ \frac{60}{2}=30\text{ (again 2 is a factor)} \\ \frac{30}{2}=15\text{ (again 2 is a factor)} \\ 15\text{ is not divisible over 2, we search for 3:} \\ \frac{15}{3}=5\text{ (3 is another factor as 15 is divisible over 3)} \\ 5\text{ is not divisible over 2, 3, or 4, we search for 5:} \\ \frac{5}{5}=1\text{ (5 is another factor, and the last one)} \end{gathered}[/tex]Placing the factors as a multiplication:
[tex]120=2\cdot2\cdot2\cdot3\cdot5[/tex]• 360
[tex]360=2\cdot2\cdot2\cdot3\cdot3\cdot5[/tex]The factors that repeat in each integer are: 2, 2, 2, 3, 5
Therefore, the GFC is:
[tex]\text{GFC}=2\cdot2\cdot2\cdot3\cdot5=120[/tex]Answer: 120
D1 ptsQuestion 3The bill of a white pelican can hold about 550 cubic inches of water,Nigel, the pelican from Finding Nemo, scoops up 160 cubic inches ofwater. Write an inequality that represents how much more waterNigel cal add to his bill.
Answers
let the additional water that is needed to add in the bill is x
[tex]\begin{gathered} 160+x\leq550 \\ x\leq550-160 \\ x\leq390 \end{gathered}[/tex]so, Nigel can add 390 cubic inches of water to the bill of a white pelican.
I just need help with part b can you help me please
Answers
b) Recall that to evaluate a function at a given value, we substitute the variable by the given value.
Evaluating P(t) at t=2007-1992=15 we get:
[tex]P(15)=29000(1.06)^{15}.[/tex]Simplifying the above result we get:
[tex]P(15)\approx69500.[/tex]Answer: $69,500.
i need help with this questionsfind the slope to the following graphs?
Answers
Answer:
b
Step-by-step explanation:
What is the probability that the person has no high school diploma and earns more than $30,000?
Answers
Hi, can you help me answer this question, please, thank you!
Answers
Answer
Standard deviation = 1.2083
Step-by-step explanation
[tex]\begin{gathered} \text{Mean = }\sum ^{}_{}xi\cdot\text{ p(xi)} \\ \text{Mean = }0\cdot\text{ 0.2 + 1 }\cdot\text{ }0.05\text{ + 2}\cdot\text{ }0.1\text{ + 3 }\cdot\text{ 0.65} \\ \text{Mean = 0 + 0.05 + 0.2 + 1.95} \\ \text{Mean = 2.2} \\ \text{Standard deviation = }\sqrt[]{\sum^{}_{}}(\text{ x - }\mu)^2\cdot\text{ p(xi)} \\ \text{let }\mu\text{ = 2.2} \\ \text{Standard deviation = }\sqrt[]{(0-2.2)^2\cdot0.2+(1-2.2)^2\cdot0.05+(2-2.2)^2\cdot0.1+(3-2.2)^2\cdot\text{ 0.65}} \\ \text{standard deviation = }\sqrt[]{0.968\text{ + 0.072 + 0.004 + 0.416}} \\ \text{Standard deviation = }\sqrt[]{1.46} \\ \text{Standard deviation = }1.2083 \\ \text{Hence, standard deviation is 1.2083} \end{gathered}[/tex]Can you please tell me
Answers
The area of kite when both diagonals are given is
[tex]A=\frac{d_{}\times D}{2}[/tex]where d=17 m and D=21 m. By substituting the given values, we get
[tex]\begin{gathered} A=\frac{17\times21}{2} \\ A=178.5 \end{gathered}[/tex]then, the answer is 178.5 square meters
2) The shape of a playground is a parallelogram. The city is going to treat the asphalt with sealant this spring with cans that will cover 4 square yards each. The figure below is a drawing of the playground, For how many cans of sealant does the city need to budget for the treatment, if the playground has a perimeter of 34 yards and the height is 1.4 yards less than the diagonal side of the parallelogram? 10.6 yd 6.4 yd a. Write the equation in words. b. Find the unknown height. c. Calculate the area of playground. d. Choose a variable for the unknown quantity and write the equation with the substituted values. e. Solve the equation. Include appropriate units in your answer. f. How many cans of sealant are needed?
Answers
In this situation, you have a parallelogram with lateral sides of L length and top and bottom sides of length D. The letter h represents the height of the parallelogram.
L=6.4 yd and D=10.6 yd. The perimeter is the sum of all 4 edges, so perimeter=2*L+2*D
a) If one can cover 4 square yards and you need to find how many cans you will need for the whole playground area, then you need to find the total area which is calculated by its height times its base (D), so it would be h*D=area. This area divided by 4 square yards will give you the number of cans you need.
b) If the height is 1.4 yards less than the diagonal side, then
[tex]h=L-1.4=6.4-1.4=5\text{ yards}[/tex]c)Then the area is given by:
[tex]h\cdot D=5\cdot10.6=53\text{ square yards}[/tex]d)The number of cans can be represented by a variable called n (n as in number), so:
[tex]n=\frac{area}{4}=\frac{53}{4}[/tex]e) Then, by calculating:
[tex]\frac{53}{4}=13.25\text{ cans}[/tex]f) You will need 14 cans of sealant, you will only use some of it from the last can
Find Q. round your final answer to the nearest tenth
Answers
To find Q, we use the SSS (side-side-side) theorem.
The law of cosine formula:
a^2 = b^2 + c^2 - 2bcCosA
using the letters in the diagram and since we looking for Q, it becomes:
q^2 = p^2 + r^2 -2prCosQ
Making Cos Q, the subject of formula:
q² - p² - r² = -2prCosQ
(q² - p² - r²)/-2pr = -2prCosQ/-2pr
(q² - p² - r²)/-2pr = CosQ
Cos Q = -(q² - p² - r²)/2pr
q =
Amber rolls a 6-sided die. On her first roll, she gets a "6". She rolls again.(a) What is the probability that the second roll is also a "6".P(6 | 6) =(b) What is the probability that the second roll is a "4".P(46) =
Answers
Answer
Explanation
Given the word problem, we can deduce the following information:
1. Amber rolls a 6-sided die.
2. Amber gets a "6" on her first roll.
a)
To determine the probability that the second roll is also a "6", we note first that a 6-sided die has these values: 1,2,3,4,5,6
As we can see, there's only one 6 value on a 6-sided die while the total .So, the probability would be:
P(6 | 6) =1/6
b)
To determine that the second roll is a "4", we use the same reasoning above. Therefore, the probability is:
P(4 | 6) =1/6
Find the lateral surface area and volume please round up to nearest integer
Answers
For this problem we will use the following formula for the surface area of a truncated cone:
[tex]\begin{gathered} SA=\pi(r_1+r_2)\sqrt[]{(r_1-r_2)^2+h^2}+\pi(r^2_1+r^2_2), \\ \text{Where r}_1\text{ is the lower radius, r}_2\text{ is the upper radius, and h is the height.} \end{gathered}[/tex]Substituting:
[tex]\begin{gathered} r_1=\frac{11in}{2}=5.5in, \\ r_2=\frac{14in}{2}=7in, \\ h=21in, \end{gathered}[/tex]we get:
[tex]\begin{gathered} SA=\pi(7in+5.5in)\sqrt[]{(7in-5.5in)^2+(21in)^2}+\pi((5.5in)^2+(7in)^2) \\ =\pi(12.5in)\sqrt[]{2.25in^2+441in^2}+\pi(30.25in^2+49in^2) \\ =\pi(12.5in)(21.05in)+\pi\cdot79.25in^2 \\ =\pi(263.125+79.25)in^2 \\ =\pi(342.375)in^2 \\ \approx1076in^2. \end{gathered}[/tex]Now, to compute the volume we will use the following formula:
[tex]V=\frac{1}{3}\pi(r^2_1+r_1r_2+r^2_2)h\text{.}[/tex]Substituting the given values we get:
[tex]\begin{gathered} V=\frac{1}{3}\pi((5.5in)^2+(5.5in)(7in)+(7in)^2)21in \\ =\frac{1}{3}\pi(30.25in^2+38.5in^2+49in^2)21in \\ =\frac{1}{3}\pi(117.75in^2)21in \\ =824.25\pi in^3 \\ =2589in^3\text{.} \end{gathered}[/tex]Answer: The total surface area is
[tex]1076in^2\text{.}[/tex]The volume is
[tex]2589in^3\text{.}[/tex]A local newspaper delivers 364 papers split evenly among n delivery people. Q is the number of papers delivered by each delivery person. Write a formula for Q as a function of n, including finding the value of any unknown constants. Q =
Answers
The formula for Q is:
[tex]Q(n)=\frac{364}{n}[/tex]where n = the number of delivery people.
We just have to divide the 364 papers to the number of delivery people to determine how many papers each person delivered.
Divide 22 stars to represent the ratio 4:7.
Answers
Answer
Dividing 22 stars into the ratio 4:7 will give
8 stars : 14 stars
Explanation
We need to divide 22 stars into the ratio 4:7
Divide the ratio through by 11 (the sum of the two numbers in the ratio)
4:7 = (4/11) : (7/11)
Multiplying through by 22
(4/11) : (7/11)
= (4 × 22/11) : (7 × 22/11)
= 8 : 14
Hope this Helps!!!
The ratio of the cat's weight to the rabbit's weight is 7 to 4. Together, they weigh 22 pounds. How much does the rabbit weigh?
Answers
cat's weight: rabbit's weight
7:4
[tex]undefined[/tex]You can only use cross multiplication in solving rational equation if and only if you have one fraction equal to one fraction, that is, if the fractions are _______
Answers
Answer:
Proportional
Explanation:
answer step by step pleaseSteve determines that sides DK and BC are congruent. He also measures angle K and angle C and determines that they are congruent. He concludes that the triangles are congruent by SAS theorem. Is Steve correct?
Answers
Data Input
DK and BC are congruent.
Angle K and angle C are congruent.
Procedure.
To determine if the triangles are congruent median SAS, we need to know the size of one of the remaining sides
For them, we will measure the ED and AB sides using the Euclidean distance
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]For ED
E = (-6, 4)
D = (0, 8)
[tex]\begin{gathered} ED=\sqrt[]{(-6-0)^2+(8-4)^2} \\ ED=\sqrt[]{6^2+4^2} \\ \\ ED=\sqrt[]{(36+16)} \\ ED=\sqrt[]{52} \end{gathered}[/tex]For AB
A = (3, 6)
B = (9, 10)
[tex]\begin{gathered} AB=\sqrt[]{(9-3)^2+(10-6)^2} \\ AB=\sqrt[]{6^2+4^2} \\ AB=\sqrt[]{36+16} \\ AB=\sqrt[]{52} \end{gathered}[/tex]Now, AB is equaled to ED
Side-Angle-Side is a rule used to prove whether a given set of triangles are congruent. The SAS rule states that: If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.
Please find arc JK and angle 1. Ignore the entered answers.
Answers
The Solution:
Given the figure below:
Solving for arc JK:
By angle subtends at the center of a circle is twice that subtends on the circumference, we have that:
[tex]2\times118=236^o[/tex]Subtracting 236 from 360, we get
[tex]arcJK=360-236=124^o\text{ (angle at a point)}[/tex]So, the correct answer for question 7 is [option 4]
To answer Question 8:
[tex]\begin{gathered} \angle JKM=\frac{70}{2}=35^o\text{ } \\ \\ \text{ Reason: Angle subtends at the center is twice that subtends} \\ \text{ at the circumference of the circle.} \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} \angle KJL=\frac{60}{2}=30^o \\ \\ \text{Reason: Angle subtends at the center is twice that subtends} \\ \text{ at the circumference of the circle.} \end{gathered}[/tex][tex]\text{ To get }\angle1[/tex][tex]\begin{gathered} \angle1=180-(\angle JLM+\angle KML) \\ \text{ Reason: sum of angles in a triangle.} \end{gathered}[/tex][tex]\begin{gathered} \angle JLM=\angle JKM=35^o \\ \text{ Reason: angles on the same segments.} \\ \text{ Similarly,} \\ \angle KML=\angle KJL=30^o \\ \text{ Reason: angles on the same segments.} \end{gathered}[/tex][tex]\begin{gathered} \angle1=180-(35+30) \\ \text{ Sum of angles in a triangle.} \\ \angle1=180-65=115^o \end{gathered}[/tex]Therefore, the correct answer to Question 8 is 115 degrees.
Find the angle between the vectors u = i – 9j and v = 8i + 5j.
Answers
Answer:
[tex]\theta\text{ = 115.67}\degree[/tex]Explanation:
Here, we want to find the angle between the two vectors
Mathematically, we have that as:
[tex]cos\text{ }\theta\text{ = }\frac{a.b}{|a||b|}[/tex]The denominator represents the magnitude of each of the given vectors as a product while the numerator represents the dot product of the two vectors
We have the calculation as follows:
[tex]\begin{gathered} cos\text{ }\theta\text{ = }\frac{(1\times8)+(-9\times5)}{\sqrt{1^2+(-9)\placeholder{⬚}^2}\text{ }\times\sqrt{8^2+5^2}} \\ \\ cos\text{ }\theta\text{ = }\frac{8-45}{\sqrt{82}\text{ }\times\sqrt{89}} \\ \\ \end{gathered}[/tex][tex]\begin{gathered} cos\text{ }\theta\text{ = }\frac{-37}{\sqrt{82}\text{ }\times\sqrt{89}} \\ cos\text{ }\theta\text{ = -0.4331} \\ \theta\text{ = }\cos^{-1}(-0.4331) \\ \theta\text{ = 115.67}\degree \end{gathered}[/tex]I need help with graphing
Answers
to grpah a line, we need two points and join it
so, we give values for x and find the solution to find one point
[tex]y=-4+\frac{6}{5}x[/tex]x=0
[tex]\begin{gathered} y=-4+\frac{6}{5}(0) \\ \\ y=-4 \end{gathered}[/tex]First point (0,-4)
x=5
[tex]\begin{gathered} y=-4+\frac{6}{5}(5) \\ \\ y=-4+6 \\ y=2 \end{gathered}[/tex]second point (5,2)
now place on the graph and join
this is the line