In ∆OPQ, q =1.7cm, o=3.8 cm and < P=96°. Find < Q, to the nearest 10th of a degree.
Answers
To solve the exercise you can use the law of cosine, which applies to any triangle:
[tex]b^2=a^2+c^2-2ac\cdot\cos (B)[/tex]Where
So, in this case, you have
[tex]\begin{gathered} p^2=o^2+q^2-2oq\cdot\cos (P) \\ p^2=(3.8cm)^2+(1.7cm)^2-2(3.8cm)(1.7cm)\cdot\cos (96\text{\degree)} \\ p^2=14.44cm^2+2.89cm^2-12.92cm^2\cdot\cos (96\text{\degree)} \\ p^2=17.33\operatorname{cm}^2-(-1.35cm^2) \\ p^2=17.33\operatorname{cm}+1.35cm^2 \\ p^2=18.68\operatorname{cm}^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{p^2}=\sqrt[]{18.68\operatorname{cm}^2} \\ p=4.32\operatorname{cm} \end{gathered}[/tex]Now, you can use the law of sine, which applies to any triangle:
[tex]\frac{a}{\sin (A)}=\frac{b}{\sin (B)}=\frac{c}{\sin (C)}[/tex]In this case, you have
[tex]\begin{gathered} \frac{q}{\sin(Q)}=\frac{p}{\sin(P)} \\ \frac{1.7\operatorname{cm}}{\sin(Q)}=\frac{4.32\operatorname{cm}}{\sin(96\text{\degree})} \\ \text{ Apply cross product} \\ 1.7\operatorname{cm}\cdot\sin (96\text{\degree})=\sin (Q)\cdot4.32\operatorname{cm} \\ \text{ Divide by 4.32 cm from both sides of the equation} \\ \frac{1.7\operatorname{cm}\cdot\sin(96\text{\degree})}{4.32\operatorname{cm}}=\frac{\sin(Q)\cdot4.32\operatorname{cm}}{4.32\operatorname{cm}} \\ \frac{1.7\operatorname{cm}\cdot\sin(96\text{\degree})}{4.32\operatorname{cm}}=\sin (Q) \\ 0.39=\sin (Q) \\ \text{ Apply the inverse function }\sin ^{-1}(\theta)\text{ both sides of the equation} \\ \sin ^{-1}(0.39)=\sin ^{-1}(\sin (Q)) \\ 23.0\text{\degree}=Q \end{gathered}[/tex]Therefore, the measure of angle Q is 23 degrees.
Related Questions
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
12y-2x = 108
Answers
Answer: y= x/6+9
Step-by-step explanation:
Which of the following is a simplified version of 11 + 4(x + 3) = 10? A 4x + 4 = 10 B В 4x + 23 = 10 15x + 3 = 10 15x + 45 = 10
Answers
11 + 4(x + 3) = 10
Apply distributive property:
11+ 4(x)+4(3) = 10
11+ 4x+12 = 10
Combine like terms:
4x+11+12 = 10
4x +23 = 10
Write down the expansion of (2x+y)^4
Answers
Use the following formula:
[tex](a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4[/tex]Let:
[tex]\begin{gathered} a=2x \\ b=y \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} (2x+y)^4=(2x)^4+4(2x)^3y+6(2x)^2y^2+4(2x)y^3+y^4 \\ (2x+y)^4=16x^4+32x^3y+24x^2y^2+8xy^3+y^4 \end{gathered}[/tex]kiran ran 1/5 the length of the road which is 9 miles how many miles did he run?
Answers
Answer:0.02
Step-by-step explanation:
hXL for School: Practice & Problem Solving 5.2.PS-19 Question Help Equivalent ratios can be found by extending pairs of rows or columns in a multiplication table. Write 3 3 ratios equivalent to using the multiplication table. 5 Click the icon to view the multiplication table. 3 Find three ratios that are equivalent to 5 12 6 4 IA. B. OC. 20 10 6 15 15 9 OD OE. F. 9 30 15 Click to select your answer(s) and then click Check Answer. All parts showing Clear All Check Answer Review progress Question 7 of 12 Back Next >
Answers
To find equivalent ratios to 3/5, we just have to multiply each part by 4, 2, and 3.
[tex]\begin{gathered} \frac{3\cdot4}{5\cdot4}=\frac{12}{20} \\ \frac{3\cdot2}{5\cdot2}=\frac{6}{10} \\ \frac{3\cdot3}{5\cdot3}=\frac{9}{15} \end{gathered}[/tex]Hence, the right answers are A, B, and F.1) The expression 5p represents the total price of buying 5 movie tickets. • What do the parts of the expression 5p represent? ) The variable p represents the ticket price The number 5 represents the number of tickets Today there is a discount of $10 off a purchase of 5 or more movie tickets. Which expression can you use to find the total price of 5 movie tickets after the discount? 10p + 5 5p - 10 10p - 5 5p + 10
Answers
Solution
The expression 5p represents the total price of buying 5 movie tickets. • What do the parts of the expression 5p represent?
The variable p represents the ticket price The number 5 represents the number of tickets
For this case the correct answer would be:
5p -10
The coefficient 5 represents the price of 1 ticket
for the next part the answer would be:
7 +3x
And the last part
2/3 y -6
Every rational number is also an integer.TrueorFalse
Answers
Every rational number is also an integer.
we have that
The rational numbers include all the integers
so
the answer is trueIf there are three black, four white, two blue, and four gray socks in a drawer, what would be the probability of picking a blue sock? Round your answer to the nearest tenth.15.4%25%22%15.38%
Answers
The formula for determining probability is expressed as
Probability = number of favorable outcomes/number of total outcomes
number of favorable outcomes = number of blue socks = 2
number of total outcomes = number of all socks = 3 + 4 + 2 + 4 = 13
Thus, the probability of picking a blue sock is
2/13 = 0.1538
Converting to percentage, we would multiply by 100. We have
0.1538 x 100
= 15.38%
Solve: x^3= -65 This is for homework
Answers
Step 1
Solve the equation by graphing
You can rewrite the equation as
[tex]x^3+65=0[/tex]step 2
Using a graphin calculator as Desmos
x=-4.021
The solution is x=-4.021
-
7 m The side lengths of the base of a triangular prism are 7 meters, 5 meters, and 8 meters. The height of the prism is 12.5 meters. 12.5 m 6 m What is the lateral surface area of the prism in square meters? 5 m
Answers
Given a triangular prism with side lengths of the base as a, b, and c, and height h, then the lateral surface area, A is given by
[tex]A=(a+b+c)h[/tex]In our case,
[tex]a=5m,b=6m,c=7m,\text{ and }h=12.5m[/tex]Hence,
[tex]A=(5+6+7)12.5=18\times12.5=225m^2[/tex]Therefore, the lateral surface area in square meters is 225
How to find the inverse of the matrix Question number 19
Answers
Okay, here we have this:
We need to find the inverse of the matrix, let's do it:
[tex]\begin{bmatrix}{2} & {4} & {1} \\ {-1} & {1} & {-1} \\ {1} & {4} & {0}\end{bmatrix}[/tex]For that we are going to make the augmented form with the identity matrix and convert the original matrix into the identity:
[tex]\begin{gathered} \begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ -1 & 1 & -1 & | & 0 & 1 & 0 \\ 1 & 4 & 0 & | & 0 & 0 & 1\end{pmatrix} \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 1 & 4 & 0 & | & 0 & 0 & 1\end{pmatrix}\text{ }R_2\leftarrow R_2+\frac{1}{2}R_1 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 0 & 2 & -\frac{1}{2} & | & -\frac{1}{2} & 0 & 1\end{pmatrix}\text{ }R_3\leftarrow R_3-\frac{1}{2}R_1 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 0 & 0 & -\frac{1}{6} & | & -\frac{5}{6} & -\frac{2}{3} & 1\end{pmatrix}R_3\leftarrow R_3-2/3R_2 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_3\leftarrow-6R_3 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & 0 & | & 3 & 3 & -3 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_2\leftarrow R_2+\frac{1}{2}R_3 \\ =\begin{pmatrix}2 & 4 & 0 & | & -4 & -4 & 6 \\ 0 & 3 & 0 & | & 3 & 3 & -3 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_1\leftarrow R_1-R_3 \\ =\begin{pmatrix}2 & 4 & 0 & | & -4 & -4 & 6 \\ 0 & 1 & 0 & | & 1 & 1 & -1 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_2\leftarrow\frac{1}{3}R_2 \\ =\begin{pmatrix}2 & 0 & 0 & | & -8 & -8 & 10 \\ 0 & 1 & 0 & | & 1 & 1 & -1 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_1\leftarrow R_1-4R_2 \\ =\begin{pmatrix}1 & 0 & 0 & | & -4 & -4 & 5 \\ 0 & 1 & 0 & | & 1 & 1 & -1 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_1\leftarrow\frac{1}{2}R_1 \end{gathered}[/tex]Finally the inverse is on the right side of the augmented matrix:
[tex]=\begin{pmatrix}-4 & -4 & 5 \\ 1 & 1 & -1 \\ 5 & 4 & -6\end{pmatrix}[/tex]Which quadrant includes every points with a negative x-coordinate and a negative y-coordinateA) Quadrant IVB) Quadrant IC) Quadrant IID) Quadrant III
Answers
Hello!
Let's analyze the points from each quadrant:
Quadrant I:
x > 0 and y > 0
Quadrant II:
x < 0 and y > 0
Quadrant III:
x < 0 and y < 0
Quadrant IV:
x > 0 and y < 0
So, the answer is:
Alternative D) Quadrant III.
ProbabilityHello need help Thank you. A phone number in Cameroon consists of 9 digits. From the theoretical capacity of the Cameroonian telephone network, say whether the 4 current operators (CAMTEL MTN, NEXTTEL and ORANGE) can meet a demand for 150 million subscriptions. 1) How many different ways can you arrange four people in four numbered chairs? 2)How many ways can you distribute 10 balloons to 3 children, 4 for the first and 3 for each of the other two?
Answers
Answer:
1) 24
2)66
Explanation:
1) How many different ways can you arrange four people in four numbered chairs?
Answer: we have 4 people ands 4 chairs, so we use the factorial of 4 to find the number of ways that we can arrenge the people:
[tex]4!\text{ = 4}\cdot3\cdot2\cdot1=24[/tex]we can arrange 4 people in 4 chairs in 24 different ways
2)How many ways can you distribute 10 balloons to 3 children?
To distribute "n" objects to "r" people (in this case n=10, and r = 3) we use the following combinarions formula:
[tex]C(n+r-1,r-1)[/tex]substituting our values we get:
[tex]C(10+3-1,3-1)[/tex][tex]C(12,2)[/tex]and since C(a,b) is defined as:
[tex]C(a,b)=\frac{a!}{b!(a-b)!}[/tex]For C(12,2) we get the following:
[tex]C(12,2)=\frac{12!}{2!(12-2)!}[/tex]which simplifies to:
[tex]C(12,2)=\frac{12!}{2!(10)!}=66[/tex]We can distribute 10 balloons to 3 people in 66 ways
How do I simplify -88/4
Answers
What is the answer
(3t/t^5)^-5
Answers
The resultant answer of the given expression (3t/t⁵)⁻⁵ is t²⁰/243.
What exactly are expressions?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.To evaluate an algebraic expression, you must substitute a number for each variable and perform the arithmetic operations.The previous example's variable x is equivalent to 6 because 6 plus 6 = 12.If we know the values of our variables, we can replace the original variables with those values before evaluating the expression.So, solve the expression as follows: (3t/t^5)^-5
Apply exponent rule:
(3t/t^5)^-51/((3t/t^5)^5)Simplify as shown:
(3t/t^5)^5: 243/t²⁰1/243/t²⁰Apply function rule:
t²⁰/243Therefore, the resultant answer of the given expression (3t/t⁵)⁻⁵ is t²⁰/243.
Know more about expressions here:
brainly.com/question/28934492
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Suppose a spherical snowball is melting and the volume is decreasing at a constant rate, changing from 12 in^3/min to 10in^3/min in 30min. How fast is the radius changing when the volume is 8in^3/min? (Answer in terms of pi)
Answers
The radius changing when the volume is 8in^3/min by: -512π /30 in³ /min.
How to find the radius?First step is to find the radius changing over time at a constant rate
dr/dt = 10-12 /30
= -2/30 in/min
Now let find the how fast is the radius changing using this formula
dV/dt = 4πr²(dr/dt)
Where,
r =8
Hence,
dV/dt = 4π (8in)² × -2/30 in/min
dV/dt = 4π (64in) × -2/30 in/min
dV/dt = -512π /30 in³ /min
Therefore the change in radius is -512π /30 in³ /min.
Learn more about radius here:https://brainly.com/question/24375372
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It is equally probable that the pointer on the spinner Shown will land on any one of the eight regions number one through eight if the pointer lands on the borderline spin again. find the probability that the pointer will stop on an even number or number greater than three
Answers
SOLUTION
The even numbers here are 2, 4, 6 and 8. That is 4 numbers.
The numbers greater than 3 are 4, 5, 6, 7, and 8, that is 5 numbers.
And we have a total of 8 numbers.
Let P(A) be the probability of the pointer landing on an even number
Let P(B) be the probability of the pointer landing on a number greater than 3
Let P(A or B) be the probability that the pointer stops on an even number or number greater than three
From the probability formula,
[tex]P(\text{A or B) = P(A) + P(B) - P(A}\cap B)[/tex][tex]\text{ P(A}\cap B)\text{ means probability of A and B}[/tex]Hence
[tex]\begin{gathered} P(A)=\frac{4}{8} \\ P(B)=\frac{5}{8} \end{gathered}[/tex][tex]\begin{gathered} \text{ For P(A}\cap B)\text{ we can s}ee\text{ that betwe}en\text{ } \\ \text{the even numbers 2, 4, 6, 8 and } \\ n\text{umbers greater than 3, which are 4, 5, 6, 7, 8} \\ \text{what is common is 4, }6,\text{ 8} \\ So,\text{ } \\ \text{P(A}\cap B)=\frac{3}{8} \end{gathered}[/tex]Therefore, P(A or B) becomes
[tex]\begin{gathered} \frac{4}{8}+\frac{5}{8}-\frac{3}{8} \\ \frac{4+5-3}{8} \\ \frac{6}{8} \\ =\frac{3}{4} \end{gathered}[/tex]Based on sample data, newborn males have weights with a mean of 3242.4 g and a standard deviation of 844.4 g. Newborn females have weights with a mean of 3095.9 g and a standard deviation of 508.6 g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1700 g or a female who weighs 1700 g?
Answers
The formula for calculating z score is expressed as
z = (x - μ)/s
where
x is the sample mean
μ is the mean
s is the sample standard deviation
Considering the newborn males,
x = 1700
μ = 3242.4
s = 844.4
Thus,
z = (1700 - 3242.4)/844.4
z = - 1.83
Considering the newborn females,
x = 1700
μ = 3095.9
s = 508.6
Thus,
z = (1700 - 3095.9)/508.6
z = - 2.74
The most extreme value is the z score that is furthest from zero. It is z = - 2.74. Thus, the female who weighs 1700 g is more extreme relatively
Since the z score for the male is z = - 1.83 and the z score for the female is z = - 2.74, the female has the weight that is more extreme.
Determine the smallest integer value of x in the solution of the following inequality.3x + 4> -18
Answers
We have the following inequality:
3x + 4 > -18
Subtracting 4 from both sides we got:
3x > -22
Dividing both sides by 3 we got:
x > -22/3
Since -22/3 is between -7 and -8 and x must be equal or greater than -22/3, the smallest integer value in the solution of the inequality is -7 (note that -8 isn't part of the solution)
In the image below ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯∥⎯⎯⎯⎯⎯⎯⎯⎯⎯LM¯∥OP¯. Given the lines are parallel, ∠≅∠∠LMN≅∠PON because and that ∠≅∠∠LNM≅∠ONP by the , you can conclude the triangles are similar by the AA Similarity Theorem. If NP = 20, MN = x+ 6, NO = 15, and LN = 2x - 3 then x = .
Answers
Given:
Required:
We need to answer the questions
Explanation:
Angle LMN and angle PON are the congruent because both are alternate angles
Now angle LNM and angle ONP are also congruent because those two triamgles are similar and both are internal angles
Now to find the value of x
[tex]\begin{gathered} \frac{NP}{MN}=\frac{NO}{LN} \\ \\ \frac{20}{x+6}=\frac{15}{2x-3} \\ \\ 40x-60=15x+90 \\ 25x=150 \\ x=6 \end{gathered}[/tex]Final answer:
x=6
How do you figure out what the order pairs are in this equation? 2x-2=y
Answers
Equations express relationships between variables and constants. The solutions to two-variable equations consist of two values, known as ordered pairs, and written as (a, b) where "a" and "b" are real-number constants. An equation can have an infinite number of ordered pairs that make the original equation true.
Here, the given equation is,
[tex]2x-2=y[/tex]Rewriting this equation in terms of x, we have,
[tex]\begin{gathered} 2x-2=y \\ 2x=y+2 \\ x=\frac{y+2}{2} \end{gathered}[/tex]So, now creating a table, with the values, we get the ordered pair. For example, let us take x as 1, then ,
[tex]\begin{gathered} 1=\frac{y+2}{2} \\ 2=y+2 \\ y=0 \end{gathered}[/tex]So, (1,0) is an ordered pair in this equation.
If x =0,
[tex]y=0-2=-2[/tex]So the pair is, (0,-2).
Find the reference angle for a rotation of 129º.
Answers
In order to find a reference angle, we need to find the smallest possible angle formed between the x-axis and the terminal line of the given angle, going either clockwise or counterclockwise.
Since the given angle is 129°, and 90<129<180, it will look something like this:
As we can see, the reference angle will be
[tex]180-129=51[/tex]so it will be 51°.
between 1993 and 1996 there where 6545 injured horses find the ratio of injuries per year
Answers
First, we have to know the total number of years between 1993 and 1996. If we subtract, we find the there are 3 years in between.
Now, we divide the total number of injured horses by the total numbers of years.
[tex]r=\frac{6545}{3}=2,181.7[/tex]However, we can't round to 2,182 because horses are not incomplete.
Therefore, the total number of injured horses per year is 2,181.What is the yintercept of O A. (0,0) O B. (0,1) O C. (1,0) OD (9)
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
y-intercept = ?
f(x) = (1/2) ^ x
Step 02:
y-intercept :
x = 0
[tex]\begin{gathered} y\text{ = (}\frac{1}{2})^0=1 \\ \end{gathered}[/tex]The answer is:
y-intercept
(0 , 1)
z divided by 13=28 i need the answers this is hard for me
Answers
Answer:
364
Step-by-step explanation:
z/13 = 28
z = 13 x 28
z = 364
The graph shows a relationship between two quantities.ДУ200018001600140012001000800600400200ХOd-8 -6 4-2 0 2 4Which equation best represents the relationship between the variables?
Answers
First let't find the slope
Pick any two point and locate its coordinate
(0, 1500) and (2, 1800)
x₁ = 0 y₁=1500 x₂=2 y₂=1800
substitute the values into the formula below to find the slope
[tex]\text{slope(m)}=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]=\frac{1800-1500}{2-0}[/tex][tex]=\frac{300}{2}=150[/tex]The y-intercept(b) of the graph is b=1500
Substitute the values of the slope and intercept into y=mx +b
This gives the equation of the graph.
That is:
[tex]y=150x\text{ + 1500}[/tex]find the volume of a right rectangular prism with the following measurements by multiplying The edge lengths. length 3/4 width 1/2 heigth 2/3
Answers
Explanation
The volume of a rectangular prism is given by:
[tex]\text{Volume}=\text{ length}\cdot width\cdot height[/tex]then,Let
length= 3/4
width=1/2
heigth=2/3
Now, replace,
[tex]\begin{gathered} \text{Volume}=\text{ length}\cdot width\cdot height \\ \text{Volume}=(\frac{3}{4}\cdot\frac{1}{2}\cdot\frac{2}{3}) \\ \text{Volume}=\frac{3\cdot1\cdot2}{4\cdot2\cdot3}=\frac{1}{4} \\ \text{Volume}=\frac{1}{4}\text{cubic units} \end{gathered}[/tex]I hope this helps you
Graph the linear function g(x) = -4+7xGraph the linear function G (x equals negative 4 + 7x
Answers
Given a function,
[tex]g(x)=-4+7x[/tex]At x = 0,
[tex]g(0)\text{ = -4}[/tex]At g(x) = 0,
[tex]\begin{gathered} -4+7x=0 \\ x=\frac{4}{7} \end{gathered}[/tex]At x= 1,
[tex]g(1)\text{ = 3}[/tex]Therefore, the required graph is,
How many possible triangles can be created if measure of angle B equals pi over 6 comma a = 20, and b = 10?
Answers
First, we have to find the height using the following equation:
[tex]h\text{ = }b\sin (B)[/tex][tex]h\text{ = 10}\times\sin (\frac{\pi}{6})=5[/tex]We have found the height. If h < b < a, we can have only one triangle. That is the case. So the answer will be 1 triangle.
what does 1,580÷25=I know the answer, I need to show how I got it.