Answers
Using the law of sines, we would have that:
[tex]\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]Solving for C,
[tex]\begin{gathered} \frac{b}{\sin B}=\frac{c}{\sin C}\rightarrow\frac{\sin C\cdot b}{\sin B}=c\rightarrow\sin C\cdot b=c\cdot\sin B \\ \\ \rightarrow\sin C=\frac{c\cdot\sin B}{b}_{}\rightarrow C=\sin ^{-1}(\frac{c\cdot\sin B}{b}_{}) \end{gathered}[/tex]Plugging in the data given,
[tex]\begin{gathered} C=\sin ^{-1}(\frac{(10.3)\cdot\sin (58.8)}{(10.5)}_{}) \\ \\ \Rightarrow C=57 \end{gathered}[/tex]Therefore, we can conclude that:
Related Questions
Solve using substitution. y = 7x + 3 y = 6x + 4(_ , _)
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We have the following:
[tex]\begin{gathered} y=7x+3 \\ y=6x+4 \end{gathered}[/tex]solving using substitution:
[tex]\begin{gathered} 7x+3=6x+4 \\ 7x-6x=4-3 \\ x=1 \end{gathered}[/tex]for y:
[tex]y=7\cdot1+3=7+3=10[/tex]The answer is (1, 10)
Which of the following transformations are used when transforming the graph of the parent function f(x) = log7x to the graph of g(x) = -log7(3x)+4? Select all that apply.
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In this problem, we have the transformations
option B (shift the graph of f(x) 4 units up
option C reflect the graph of f(x) over the y-axis
-7>-10 true or false
Answers
To answer this question we need to see it on an axis.
-7> -10 , it is true. -7 it's more near to 0.
In the following table of values, what would be the value of “b” in ax2 + bx + c?
–2
–9
–1
–1
0
9
1
21
2
35
1
9
11
22
Answers
The value of b is 11.
From the question, we have
ax² + bx + c
using (0, 9)
substituting the value we get
9 = a(0)² + b(0) + c
c = 9
Therefore,
-1 = a(-1)² + b(-1) + c
-1 = a - b + 9
-1 - 9 = a - b
a - b = - 10
using (-2, -9)
-9 = a(-2)² + b(-2) + 9
-9 - 9 = 4a - 2b
-18 = 4a - 2b
2a - b = -9
combine the equation
a - b = - 10
2a - b = -9
solving the equations we get
a = 1
Then,
1 - b = -10
b = 1 + 10
b = 11
Hence, the value of b is 11.
Subtraction:
The process of removing items from a collection is represented by subtraction. Subtraction is represented by the minus sign. If, for instance, there are nine oranges stacked together (as shown in the above figure), and four of those oranges are then moved to a basket, the stack will contain nine minus four oranges, or five oranges. As a result, 9 minus 4 equals 5, or the difference between 9 and 4. Incorporating subtraction into other types of numbers is possible in addition to using it with natural numbers.
The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference. As the first integer to be subtracted from in a subtraction phrase, a minuend is the first number in the subtraction process.
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I need help with my math
Answers
Given data:
The given points are (-2,-1) and (3, -1).
The slope of the line passing through the given points is,
[tex]\begin{gathered} m=\frac{-1-(-1)}{3-(-2)} \\ =\frac{0}{5} \\ =0 \end{gathered}[/tex]Thus, the slope of the line passing through the given points is 0.
*Will mark brainiest* Rectangle ABCD is rotated 90° clockwise about the origin to produce Rectangle A'B'CD' What is the length, in units of line segment CD'?
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When the given rectangle is rotated 90° around origin point, you obtain the same rectangle, but instead of a horizonatl rectangle as before, you get a vertical rectangle with height CD' and width A'D'.
The length of the segment CD' is 6 units
The graph of y = x 2 has been translated 7 units to the left. The equation of the resulting parabola is _____.y = (x - 7) 2y = (x + 7) 2y = x 2 - 7y = x 2 + 7
Answers
The translation of a function to the left or to the right is a horizontal translation. Horizontal translation can be defined as the movement toward the left or right of the graph of a function by the given units. It should be noted that the shape of the function remains the same. The horizontal translation is also known as the movement/shifting of the graph along the x-axis. For any base function f(x), the horizontal translation by a value k can be given as
[tex]f(x)=f(x\pm k)[/tex]If the function is shifted to the right, the translation function would be
[tex]f(x)=f(x-k)[/tex]If the function is shifted to the left, the translation would be
[tex]f(x)=f(x+k)[/tex]If the graph of y = x² has been translated 7 units to the left. The equation of the resulting parabola would be
[tex]y=(x+7)^2[/tex]Hence the equation of the resulting parabola is (x+7)²
Can you help me solve this? And step by step please?
Answers
Given the sequence:
1/2, 3/4, 9/8, 27/16, ..........
We are to find the recursive formular
A recursive geometric formular has a pattern:
An = An - 1 * r
Where r is the common ratio. But before we write the formular, we need to look for the value of r.
This r value has to be the same between each consecutive number in the series.
Sinces it's geometric, r is multiplied in. To get from 1/2 to 3/2 we find the r value in this way:
x/2 = 3/4 where x/2 is the same as 1/2 x.
Cross multiply to get 4x = 6 and x = 3/2.
That means that if r is 3/2, then we can multiply every term in that sequence by 3/2 to get the next term in line.
3/4 times 32 is 9/8. So, r = 3/2 and the formulat is:
An = An - 1 * 3/2
Therefore, the crrect optio is B.
I really sure what to do for this question some help would be greatly appreciated
Answers
Given the Domain and the Range of the relation, you need to remember that the Domain is the set of all input values (x-values), and the Range is the set of all the output values (y-values).
Therefore, knowing the input values and the corresponding output values indicated in the Diagram, you can write the following ordered pairs:
[tex](1,9),(4,10),(10,3)[/tex]Notice that they have this form:
[tex](x,y)[/tex]Where "x" is the x-coordinate of the point, and "y" is the y-coordinate.
Therefore, you need to plot all the points on the Coordinate Plane in order to express the relation as a graph.
Hence, the answer is:
how do I calculate the area of a partial circle?
Answers
A part of a circle is called an arc and an arc is named according to its angle.
1. 2х^2 * 3x^3y * 3x^3y=1. 2х^2 * 3x^3*y * 3x^3*y=
Answers
Given the expressions
[tex]\begin{gathered} (A).2x^2\cdot3x^3\cdot y\cdot3x^3\cdot y= \\ (B).2x^2\cdot3x^{3y}\cdot3x^{3y}= \end{gathered}[/tex]First: we group and multiply the numbers
[tex]\begin{gathered} (A).2x^2\cdot3x^3\cdot y\cdot3x^3\cdot y=(2\cdot3\cdot3)\cdot x^2\cdot x^3\cdot y\cdot x^3\cdot y=18x^2\cdot x^3\cdot y\cdot x^3\cdot y \\ (B).2x^2\cdot3x^{3y}\cdot3x^{3y}=(2\cdot3\cdot3)x^2\cdot x^{3y}\cdot x^{3y}=18x^2\cdot x^{3y}\cdot x^{3y} \end{gathered}[/tex]Now we have the expressions
[tex]\begin{gathered} (A).18x^2\cdot x^3\cdot y\cdot x^3\cdot y \\ (B).18x^2\cdot x^{3y}\cdot x^{3y} \end{gathered}[/tex]Second: we multiply the expressionswith the same base adding its exponents
[tex]\begin{gathered} (A).18x^{2+3+3}\cdot y^{1+1}=18x^8y^2 \\ (B).18x^{2+3y+3y}=18x^{6y+2} \end{gathered}[/tex]the center of the circle is at O. determine the measure of angle ABC
Answers
If the center of the circle is at O.then the measure of angle ABC is 28 degree
The measure of angle ABC can be calculated by using central angle theorem
What is central angle theorem
The Central Angle Theorem states that the central angle from two chosen points A and B on the circle is always twice the inscribed angle from those two points ie if the angle inscribes at the circumference is x, then the angle at the center is 2x.
The angle ABC = 1/2 angle AOC
the angle ABC = 1/2 x 56
the angle ABC is 28
Therefore, if the center of the circle is at O.then the measure of angle ABC is 28 degree
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A physical education teacher divides the class into teams of 5 to play floor hockey. There are atotal of 4 teams. How many students, s, are in the class? Solve the equation 8 + 5 = 4 to find thenumber of students.
Answers
we know that
the number of students (s) is equal to the number of teams, multiplied by the number of students in each team
so
s=4*5
s=20
answer is 20 students
Question #5The table shows four relations.RelationRelation 2Relation 3Rolation 4-2-5-3Y-4-4-2-1- 11312372Which relations represent functions?ARelation 1 and Relation 3BRelation 2 and Relation 4СRelation 3 and Relation 2DRelation 4 and Relation 1
Answers
The RELATION 1 and 3 represent a function
Rationale
There are no x value with several y values.
For a relation to be a function, there should only one y value fot each x
estimate the product by rounding to the nearest 10: 28×56×76
Answers
EXPLANATION
Given the operation:
28------> rounded to 30
56-------> rounded to 50
76 ------> rounded to 80
Now, we can mentally calculate that:
3x5= 15 so 30x50 = 1500 (two zeros)
15x8 = 120 so,
1500x80 = 120,000
The answer is 144,000.
what is the mean? 66, 594, 69, or 74what is the median? 74, 66, 69, or 75what is the mode? 74, 90, 21, or 66what is the range? 69, 66, 74, or 594
Answers
We have the distribution;
74, 90, 21, 68, 62, 84, 34, 87,74.
Let's arrange this from ascending to descending order, we obtain;
[tex]21,34,62,68,74,74,84,87,90[/tex]i. The mean or average of this distribution is
[tex]\begin{gathered} \frac{21+34+62+68+74+74+84+87+90}{9}=\frac{594}{9} \\ \operatorname{mean}=66 \end{gathered}[/tex]ii. The median is the central value, in this distribution, there are 9 values, so the median value is the 5th value.
[tex]\operatorname{median}=74[/tex]iii. The mode is the value with the highest frequency, this is the most occurring value, in this distribution;
[tex]\text{mode}=74[/tex]iv. The range is the difference between the highest and lowest values, this is;
[tex]\begin{gathered} 90-21=69 \\ \text{Range}=69 \end{gathered}[/tex]
I need help checking to make sure my work is correct. Start with the basic function f(x) = 2x. If you have an initial value of 1, then you end up with the following iterations:f(1) = 2 x 1 = 2f^2 (1) = 2 x 2 x 1 = 4f^3 (1) = 2 x 2 x 2 x 1 = 8The question Part 1: If you continue the pattern, what do you expect would happen to the numbers as the number of iterations grows? Check your result by conducting at least 10 iterations. I put: f^4 (1) = 2 x 2 x 2 x 2 x 1 = 16f^5 (1) = 2 x 2 x 2 x 2 x 2 x 1 = 32f^6 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 1 = 64f^7 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 128f^8 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 256f^9 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 512f^10 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 1024Part 2: Repeat the process with an initial value of -1. What happens as the number of iterations grows?
Answers
Given: The function below:
[tex]f(x)=2x[/tex]To Determine: The interation with initial value of 1
When the initial value is 1, it means that x = 1
If x =1, we can determine f(1) by the substituting for x in the function as shown below:
[tex]\begin{gathered} f(x)=2x \\ x=1 \\ f(1)=2(1)=2\times1=2 \end{gathered}[/tex][tex]f^2(1)=2^2\times1=2\times2\times1=4[/tex]Part 1:
It can be observed that as the number of iterations grow, the number increase in powers of 2
This can be modelled as
[tex]f^n=2^n\times1=2^n[/tex][tex]f^{10}=2^{10}\times1=1024[/tex]Part 2:
If we repeat the process with an initial value of -1. As the number of iterations grows, the number can be modelled as
[tex]\begin{gathered} f^{-n}=2^{-n}\times1 \\ f^{-1}=2^{-1}\times1=\frac{1}{2}\times1=\frac{1}{2} \\ \text{For initial value of -2, we would have} \\ f^{-2}=2^{-2}\times1=\frac{1}{2^2}\times1=\frac{1}{4} \end{gathered}[/tex]So, as the initial value decreases, it can be observed by the above calculations that the number would be decreasing by the the reciprocal of the power of 2.
what are the coordinates of the vertex for x^2+ 5x - 24 = 0
Answers
Solution:
We are required to find the coordinates of the vertex for x^2+ 5x - 24 = 0
[tex]The\text{ x-coordinate of the vertex is x=}\frac{-b}{2a}[/tex][tex]\begin{gathered} For\text{ x}^2+5x-24=0 \\ a=1 \\ b=5 \\ x=-\frac{5}{2(1)} \\ x=-\frac{5}{2} \\ x=-2.5 \end{gathered}[/tex]To get the y coordinate, substitute x = -5/2 into the equation
[tex]\begin{gathered} \begin{equation*} \text{x}^2+5x-24=0 \end{equation*} \\ =(\frac{-5}{2})^2+5(\frac{-5}{2})-24 \\ \\ =\frac{25}{4}-\frac{25}{2}-\frac{24}{1} \\ =\frac{25-50-96}{4} \\ \\ =\frac{-121}{4} \\ \\ =-30.25 \end{gathered}[/tex]Hence, the coordinate of the vertex is (-2.5, -30.25)
You went to the mall to buy a sweater that was 30% off and you had an additional 20% off coupon. The cashier took the 20% off first and then the 30% off of the reduced amount second. The manager said "No, you are supposed to take the 30% off first and then the 20% off the reduced amount second. Would it matter which way this was done? Why or why not?
Answers
Explanation
let's check every case,
Step 1
A)The cashier took the 20% off first and then the 30% off of the reduced amount second.
let x represents the original price
to find the 20% we can use
[tex]\begin{gathered} new\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ new\text{ price= x*\lparen}\frac{100-20}{100}=x*(\frac{80}{100})=0.8x \\ new\text{ price =}0.8c \end{gathered}[/tex]then,the 30 % of the reduced amount, so
[tex]\begin{gathered} final\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ final\text{ price= \lparen0.8x\rparen *\lparen}\frac{100-30}{100}=(0.8x)*(\frac{70}{100})=(0.8x)(0.7)=0.56x \\ final\text{ price =0.56x} \end{gathered}[/tex]Step 2
B)The manager said "No, you are supposed to take the 30% off first and then the 20% off the reduced amount second
so
i) 30 of the first
[tex]\begin{gathered} new\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ new\text{ price= x*\lparen}\frac{100-30}{100})=x*(\frac{70}{100})=0.7x \\ new\text{ price =}0.7c \end{gathered}[/tex]then, 20 % off the reduced amount
[tex]\begin{gathered} final\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ final\text{ price= \lparen0.7x\rparen *\lparen}\frac{100-20}{100}=(0.7x)*(\frac{80}{100})=(0.7x)(0.8)=0.56x \\ final\text{ price =0.56x} \end{gathered}[/tex]Step 3
so, we can conclude in both cases the final price will be the same, becuase we have a triple product
[tex]\begin{gathered} x*0.8*0.7=x*0.7*0.8 \\ 0.56x=0.56x \end{gathered}[/tex]so, the answer is
it does not matter which way the calculation is done, because the order does not affect the product
I hope this helps you
F (x) +5 x-2 Someone pls help me I’m crying
Answers
Given the function:
[tex]f(x)=2x^2+5\sqrt[]{x-2}[/tex]to find f(3), we have to make x = 3 and substitute on the function, to get the following:
[tex]\begin{gathered} f(3)=2(3)^2+5\sqrt[]{3-2}=2(9)+5\sqrt[]{1}=18+5=23 \\ \end{gathered}[/tex]therefore, f(3)=23
At a New Car Dealership, a particularmodel comes in 4 different trim levels(CX, DX, EX, and Si). The same modelcomes in 5 different colors (Night Black,Pearl White, Evening Blue, Sandy Red,and Forest Green). The model of car alsohas 3 different interior options (GreyCloth, Tan Cloth, Black Leather). Howmany different versions of this model canbe created from these options?
Answers
solution
diferent trim levels = 4
different colors = 5
different interior options = 3
then:
[tex]4\cdot5\cdot3=60[/tex]answer: 60 different versions of this model
Consider this prism. Enter the volume of the rectangular prism, in cubic centimeters. 3 3/4, 3 1/3, 2 1/2.
Answers
Solution
For this case we have the following dimensions:
x = 3 3/4 = 15/4
y= 3 1/3 = 10/3
z= 2 1/2 = 5/2
Then we can find the volume with the following formula:
[tex]V=x\cdot y\cdot z=\frac{15}{4}\cdot\frac{10}{3}\cdot\frac{5}{2}=\frac{125}{4}ft^3[/tex]Then we can convert to cm^3 like this:
[tex]\frac{125}{4}ft^3\cdot\frac{(30.48\operatorname{cm})^3}{1ft^3}=884901.46\operatorname{cm}^3[/tex]Can you please solve this equation and please explain to me ^step-by-step^ (this is my homework)
Answers
In the equation
[tex]0.07(6t-4)=0.42(t-1)+0.14[/tex]to solve for t, we first expand both sides of the equation.
[tex]0.42t-0.28=0.42t-0.42+0.14[/tex]We subtract 0.42t from both sides to get
[tex]-0.28=0.42+0.14[/tex]The right side does not equal the left side of the equation; therefore, this equation has no solution and choice C is correct.
The local newspaper charges $34.80 for an 8-week subscription. Paige buys an 8-week subscription. How much does it cost her each week?
Answers
Answer:
$4.35
Step-by-step explanation:
8 weeks = $34.80
1 week = x
Cross-multiply
$34.80/8
=$4.35
So, for each week, Paige will pay $4.35
$(4.35 × 8 = 34.8)
Priya rewrites the expression 8 − 24 as 8( − 3). Han rewrites 8 − 24 as2(4 − 12). Are Priya's and Han's expressions each equivalent to 8 − 24? Explain your reasoning.
Answers
The given expression is
[tex]8y-24[/tex]Priya rewrite the expression as
[tex]8(y-3)[/tex]Expanding priya's expression gives
[tex]\begin{gathered} 8(y-3)=8\times y-8\times3 \\ 8(y-3)=8y-24 \end{gathered}[/tex]Hence Priya's expression is equivalent to 8y - 24
Han's rewrite the expression as
[tex]2(4y-12)[/tex]Expanding Han's expression gives
[tex]\begin{gathered} 2(4y-12)=2\times4y-2\times12 \\ 2(4y-12)=8y-24 \end{gathered}[/tex]Hence, Han's expression is equivalent to 8y - 24
Which of the numbers 12, 13, or 14 is the solution of 106 = 118 - x?
Answers
The given expression is
[tex]106=118-x[/tex]First, we add x on each side
[tex]\begin{gathered} 106+x=118-x+x \\ 106+x=118 \end{gathered}[/tex]Then, we subtract 106 from each side
[tex]\begin{gathered} 106-106+x=118-106 \\ x=12 \end{gathered}[/tex]what number do you need to add/subtract/multiply/divide each side by in order to solve the problem below?[tex] \frac{5}{6} = - \frac{2}{3} x[/tex]
Answers
The equation is,
[tex]\frac{5}{6}=-\frac{2}{3}\cdot x[/tex]The equation can be solved if on right side there is only variable with any number in multiplication. So equation can be solved as,
[tex]\begin{gathered} \frac{5}{6}\cdot\frac{-3}{2}=-\frac{2}{3}x\cdot\frac{-3}{2} \\ x=-\frac{5}{4} \end{gathered}[/tex]So to eliminate -2/3
The table below shows the thickness of coins. Coin Thickness quarter i millimeters 12 millimeters dime nickel millimeters penny 13 millimeters Hailey stacks a dime on top of a penny. She estimates the thickness of the two coins to be less than 3 millimeters. Write a symbol (, or =) in the box to make the statement true. Then use the statement to tell whether Hailey's estimate is correct. 12 + 12 + 1 Is Hailey's estimate correct?
Answers
A dime has a thickness of 1 7/20 mm and a penny has 1 1/2 mm.
Stacking both coins, we will have :
[tex]1\frac{1}{2}+1\frac{7}{20}[/tex]and we have the inequality :
[tex]1\frac{1}{2}+1\frac{7}{20}\boxed{\text{ }}1\frac{1}{2}+1\frac{1}{2}[/tex]Note that 1 7/20 is less than 1 1/2, so the inequality symbol is "<"
[tex]1\frac{1}{2}+1\frac{7}{20}<1\frac{1}{2}+1\frac{1}{2}[/tex]since 1 1/2 + 1 1/2 is equal to 3mm
Therefore, the thickness of stacking coins is less than 3mm
Hailey's estimate is correct (Yes)
Express 4√90 in simplest radical form.
Answers
ANSWER
[tex]\text{12}\sqrt[]{10}[/tex]EXPLANATION
We want to find the simplest radical form of 4√90.
To do this, we have to reduce the number in the square root in factor form and then reduce it with the square root.
We have:
[tex]\begin{gathered} 4\sqrt[]{90} \\ \Rightarrow\text{ 4 }\cdot\text{ }\sqrt[]{\text{9 }\cdot\text{ 10}}\text{ = 4 }\cdot\text{ }\sqrt[]{3\cdot\text{ 3 }\cdot\text{ 10}} \\ \Rightarrow\text{ 4 }\cdot\text{ 3 }\cdot\text{ }\sqrt[]{10} \\ \Rightarrow\text{ 12}\sqrt[]{10} \end{gathered}[/tex]That is the simplest radical form.
g(0) 10 Cabin Rental Cost ($) У 70 60 50 + (0,57] ) 40 30 10 1 (0.15) 0 1 2 3 4 5 6 7 8 9 10 Number of Days
Answers
f(x) = x +57
g(x) =7x+15
The solution is (7,64). To rent the cabin for 7 days cost $64
1) Let's examine the graph. We can see two linear equations.
Picking two points for f(t) = (7,64) and (0,57) and for g(t) (0,15) and (7,64) let's find out their respectives slopes:
2) For f(t) , let's plug into the slope-intercept formula, plugging one point:
(0,57)
y=mx+b
57=0x +b
57= b
So the rule for the function is, in terms of f(x) = x +57
(0,15)
y=mx +b
15=0x +b
15 =b
So the rule for the function g(t) , in terms of g(x) is g(x) =7x+15
Interpreting the solution:
The solution to this Linear System of Equations is the common point (7,64).
So filling in the blanks we have:
The solution is (7,64). To rent the cabin for 7 days cost $64