Find the missing side length and angles of ABC given that m A = 41°, b = 4, and c = 10.
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To solve this question, we would use cosine rule which is given as
[tex]a^2=b^2+c^2-2bc\cos A[/tex]Our values have been defined for us and we will proceed to evaluate
[tex]\begin{gathered} a^2=4^2+10^2-2(4)(10)\cos 41 \\ a^2=16+100-80\cos 41 \\ a^2=116-60.376 \\ a^2=55.624 \\ \text{take the square root of both sides} \\ a=\sqrt[]{55.624} \\ a=7.458\approx7.5 \end{gathered}[/tex]From the calculations above, the value of the missing side a is 7.5 units
To find angle B,
we can use sine rule
[tex]\begin{gathered} \frac{a}{\sin A}=\frac{b}{\sin B} \\ \frac{7.5}{\sin 41}=\frac{4}{\sin B} \\ \sin B=\frac{4\times\sin 41}{7.5} \\ \sin B=0.3498 \\ B=\sin ^{-1}0.3498 \\ B=20.5^0 \end{gathered}[/tex]We can still approach C with sine rule or sum of angle in a triangle
[tex]\begin{gathered} A+B+C=180 \\ 41+20.5+C=180 \\ c=118.5^0 \end{gathered}[/tex]From the calculations above, the value of a = 7.5 , B = 22⁰ and C = 118.5⁰ respectively which is option B
Related Questions
-3.9-3.99-3.999-4-4.001-4.01-4.10.420.4020.4002-41.5039991.53991.89try valueclear tableDNEundefinedlim f(2)=lim f(2)=2-)-4+lim f (30)f(-4)-4
Answers
In order to determine the limit of f(x) when x tends to -4 from the right (4^+), we need to look in the table the value that f(x) is approaching when x goes from -3.9 to -3.99 to -3.999.
From the table we can see that this value is 0.4.
Then, to determine the limit of f(x) when x tends to -4 from the left (4^-), we need to look in the table the value that f(x) is approaching when x goes from -4.1 to -4.01 to -4.001.
From the table we can see that this value is 1.5.
Since the limit from the left is different from the limit from the right, the limit when x tends to -4 is undefined.
Finally, the value of f(-4) is the value of f(x) when x = -4. From the table, we can see that this value is -4.
△GHI~△WVU.51010IHG122UVWWhat is the similarity ratio of △GHI to △WVU?Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
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Answer: 5
To get the similarity ratio, we must know that for the given triangles:
[tex]\frac{IG}{UW}=\frac{GH}{WV}=\frac{HI}{VU}[/tex]From the given, we know that:
UW = 2
WV = 2
VU = 1
IG = 10
GH = 10
HI = 5
Substitute these to the given equation and we will get:
[tex]\begin{gathered} \frac{IG}{UW}=\frac{GH}{WV}=\frac{HI}{VU} \\ \frac{10}{2}=\frac{10}{2}=\frac{5}{1} \\ 5=5=5 \end{gathered}[/tex]With this, we have the similarity ratio of ΔGHI to ΔWVU is 5
For each system through the best description of a solution if applicable give the solution
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System A
[tex]\begin{gathered} -x+5y-5=0 \\ x-5y=5 \end{gathered}[/tex]solve the second equation for x
[tex]x=5+5y[/tex]replace in the first equation
[tex]\begin{gathered} -(5+5y)+5y-5=0 \\ -5-5y+5y-5=0 \\ -10=0;\text{FALSE} \end{gathered}[/tex]The system has no solution.
System B
[tex]\begin{gathered} -X+2Y=8 \\ X-2Y=-8 \end{gathered}[/tex]solve the second equation for x
[tex]x=-8+2y[/tex]replace in the first equation
[tex]\begin{gathered} -(-8+2y)+2y=8 \\ 8-2y+2y=8 \\ 8=8 \end{gathered}[/tex]The system has infinitely many solutions, they must satisfy the following equation:
[tex]\begin{gathered} -x+2y=8 \\ 2y=8+x \\ y=\frac{8}{2}+\frac{x}{2} \\ y=\frac{x}{2}+4 \end{gathered}[/tex]Solve the equation algebraically. x2 +6x+9=25
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We must solve for x the following equation:
[tex]x^2+6x+9=25.[/tex]1) We pass the +25 on the right to left as -25:
[tex]\begin{gathered} x^2+6x+9-25=0, \\ x^2+6x-16=0. \end{gathered}[/tex]2) Now, we can rewrite the equation in the following form:
[tex]x\cdot x+8\cdot x-2\cdot x-2\cdot8=0.[/tex]3) Factoring the last expression, we have:
[tex]x\cdot(x+8)-2\cdot(x+8)=0.[/tex]Factoring the (x+8) in each term:
[tex](x-2)\cdot(x+8)=0.[/tex]4) By replacing x = 2 or x = -8 in the last expression, we see that the equation is satisfied. So the solutions of the equation are:
[tex]\begin{gathered} x=2, \\ x=-8. \end{gathered}[/tex]Answer
The solutions are:
• x = 2
,• x = -8
2. The length of Sally's garden is 4 meters greater than 3 times the width. Theperimeter of her garden is 72 meters. Find the dimensions of Sally's garden.The garden has a width of 8 and a length of 28.
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L = length
W = width
L = 4 + 3*W
The perimeter of a rectangle is the sum of its sides: 2L + 2W. Since it's 72, we have:
2L + 2W = 72
Now, to solve for L and W, the dimensions of the garden, we can use the first equation (L = 4 + 3*W) into the second one (2L + 2W = 72):
2L + 2W = 72
2 * (4 + 3*W) + 2W = 72
2 * 4 + 2 * 3W + 2W = 72
8 + 6W + 2W = 72
8W = 72 - 8
8W = 64
W = 64/8 = 8
Then we can use this result to find L:
L = 4 + 3W = 4 + 3 * 8 = 4 + 24 = 28
Therefore, the garden has a width of 8 and a length of 28.
Write a word problem that the bar model in problem 2 could represent.
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An example of a problem for the given diagram:
You go to a store to buy the school supplies you will need for the next term. There are boxes of 7 pencils each, and you decide to buy 5 of those boxes. How many pencils do you end up buying?
If Mason made 20 free throws, how many free throws did he attempt in all?
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Answer:
what is the shooting percentage?
What value of x would make lines land m parallel?5050°t55°75xº55m105
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If l and m are parallel, then ∠1 must measure 55°.
The addition of the angles of a triangle is equal to 180°, in consequence,
Find the values of the variables so that the figure is aparallelogram.
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Given the following question:
[tex]\begin{gathered} \text{ The property of a }parallelogram \\ A\text{ + B = 180} \\ B\text{ + C = 180} \\ 64\text{ + }116\text{ = 180} \\ 116+64=180 \\ y=116 \\ x=64 \end{gathered}[/tex]y = 116
x = 64
2) The ratio of trucks to cars on the freeway is 5 to 8. If thereare 440 cars on the freeway, how many trucks are there?
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If the ratio of trucks to trucks is 5 to 8,
then we can use proportions to solve for the number of truck (unknown "x"):
5 / 8 = x / 440
we solve for x by multiplying: by 440 both sides
x = 440 * 5 / 8
x = 275
There are 275 trucks on the freeway.
x^2-18x-57=6 solve each equation by completing the square
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x=-3
x=21
Find the distance from P to l. Line l contains points (2, 4) and (5, 1). Point P has coordinates (1, 1).
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First we need to find the equation of the line l passing through the points (2, 4) and (5, 1).
The equation of a line is expressed as y = mx+c
m is the slope
c is the intercept
m = y2-y1/x2-x1
m = 1-4/5-2
m = -3/3
m = -1
Get the intercept
Substitute any point (2, 4) and the slope m = -3 into the expression y = mx + c
4 = -3(2)+c
4 = -6 + c
c = 4+6
c = 10
The equation of line l is y = -3x+10
Next is to find the equation of the line w perpendicular to the line l, through P(1, 1).
Since the line w is perpendicular to lin
Given the following data: {3, 7, 8, 2, 4, 11, 7, 5, 9, 6),a. What is the median? (remember to put the data in order first)
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what is the ratio of sin b
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we have that
sin(B)=56/65 -----> by opposite side angle B divided by the hypotenuse
I need help on this. and there's two answers that's right but I don't know
Answers
Answer
Options B and C are correct.
(5⁸/5⁴) = 625
(5²)² = 625
Explanation
We need to first know that
625 = 5⁴
So, the options that the laws of indices allow us to reduce to 5⁴
Option A
(5⁻²/5²) = 5⁻²⁻² = 5⁻⁴ = (1/5⁴) = (1/625)
This option is not correct.
Option B
(5⁸/5⁴) = 5⁸⁻⁴ = 5⁴ = 625
This option is correct.
Option C
(5²)² = 5⁴ = 625
This option is correct.
Option D
(5⁴) (5⁻²) = 5⁴⁻² = 5² = 25
This option is not correct.
Hope this Helps!!!
Suppose that our section of MAT 012 has 23 students, and the other two sections of MAT 012 have a total of 44 students. What percent of all the students taking MAT012 are in our section of MAT 012?
Answers
Explanation
We can deduce from the information that MAT 012 has 3 sections, namely:
Our section, and two other sections
Then, we can also infer that MAT012 has a total of:
[tex]23+44=67\text{ students}[/tex]Our task will be to get the percentage of our section taking MAT 102
Since our section has 23
Then we can calculate the answer as
[tex]\frac{23}{67}\times100=34.33\text{ \%}[/tex]Thus, the answer is 34.33%
suppose each cube in this right rectangular prism is a 1/2-in unit cube
Answers
Answer:
The length of each cube is given below as
[tex]l=\frac{1}{2}in[/tex]Concept:
To figure out the dimension of the prism, we will calculate the number of cubes to make the length,width and height and multiply by 1/2
To figure out the length of the prism,
we will multiply 1/2in by 5
[tex]\begin{gathered} l=\frac{1}{2}in\times5 \\ l=2.5in \end{gathered}[/tex]To figure out the width of the prism,
we will multiply 1/2in by 4
[tex]\begin{gathered} w=\frac{1}{2}in\times4 \\ w=2in \end{gathered}[/tex]To figure out the height of the prism,
we will multiply 1/2 in by 3
[tex]\begin{gathered} h=\frac{1}{2}in\times3 \\ h=\frac{3}{2}in=1.5in \end{gathered}[/tex]Hence,
The dimensions of the prism are
Length = 2.5in
Width = 2in
Height = 1.5 in
2.5in by 2in by 1.5in
Part B:
To figure out the volume of the prism, we will use the formula below
[tex]\begin{gathered} V_{prism}=base\text{ area}\times height \\ V_{prism}=l\times w\times h \\ l=2.5in,w=2in,h=1.5in \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} V_{pr\imaginaryI sm}=l\times w\times h \\ V_{pr\mathrm{i}sm}=2.5in\times2in\times1.5in \\ V_{pr\mathrm{i}sm}=7.5in^3 \end{gathered}[/tex]Alternatively, we will calculate below by calculate the volume of each cube and then multiply by the total number of cubes
[tex]\begin{gathered} volume\text{ of each cube=} \\ =l^3=(\frac{1}{2})^3=\frac{1}{8}in^3 \\ The\text{ total number of cubes =} \\ =5\times4\times3 \\ =60cubes \\ Volume\text{ of the prism } \\ =\frac{1}{8}in^3\times60 \\ =7.5in^3 \end{gathered}[/tex]Hence,
The volume of the prism is = 7.5in³
If 6 times a certain number is added to 8, the result is 32.Which of the following equations could be used to solve the problem?O6(x+8)=326 x=8+326 x+8 = 326 x= 32
Answers
Answer: 6x + 8 = 32
Explanation:
Let x represent the number
6 times the number = 6 * x = 6x
If we add 6x to 8, it becomes
6x + 8
Given that the result is 32, the equation could be used to solve the problem is
6x + 8 = 32
please help me solve. The answer I have is in yellow. They are wrong.
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Let's simplify the radicals:
[tex]\begin{gathered} \sqrt[]{30}\cdot\sqrt[]{5}=\sqrt[]{30\cdot5} \\ =\sqrt[]{150} \\ =\sqrt[]{25\cdot6} \\ =\sqrt[]{25}\sqrt[]{6} \\ =5\sqrt[]{6} \end{gathered}[/tex]Question 31 of 50 2 Points An assumption about a population parameter that is verified based on the results of sample data is a/an OA. statistical hypothesis OB. assumption OC. presumptive statement OD. prediction
Answers
From the question, it is:
An assumption about a population parameter that is verified based on the real results of sample data is a/an Statistical Hypothesis.
Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution.
Therefore, the correct options is A, which is Statistical Hypothesis.
Help on question on math precalculus Question states-Which interval(s) is the function decreasing?Group of answer choicesBetween 1.5 and 4.5Between -3 and -1.5Between 7 and 9Between -1.5 and 4.5
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We have a function of which we only know the graph.
We have to find in which intervals the function is decreasing.
We know that a function is decreasing in some interval when, for any xb > xa in the interval, we have f(xa) < f(xb).
This means that when x increases, f(x) decreases.
We can see this intervals in the graph as:
We assume each division represents one unit of x. Between divisions, we can only approximate the values.
Then, we identify all the segments in the graph where f(x) has a negative slope, meaning it is decreasing.
We have the segments: [-3, -1.5), (1,5, 4.5) and (7,9].
Answer:
The right options are:
Between 1.5 and 4.5
Between -3 and -1.5
Between 7 and 9
Write an equation of the line perpendicular to the line –4x + 3y = –15 and passes through the point (–8, –13)
Answers
4y = -3x - 76
Explanations:The given equation is:
-4x + 3y = -15
Make y the subject of the formula to express the equation in the form
y = mx + c
[tex]\begin{gathered} -4x\text{ + 3y = -15} \\ 3y\text{ = 4x - 15} \\ y\text{ = }\frac{4}{3}x\text{ - }\frac{15}{3} \\ y\text{ = }\frac{4}{3}x\text{ - 5} \end{gathered}[/tex]Comparing the equation with y = mx + c
the slope, m = 4/3
the y-intercept, c = -5
The equation perpendicular to the equation y = mx + c is:
[tex]y-y_1\text{ = }\frac{-1}{m}(x-x_1)[/tex]The line passes through the point (-8, -13). That is, x₁ = -8, y₁ = -13
Substitute m = 4/3, x₁ = -8, y₁ = -13 into the equation above
[tex]\begin{gathered} y\text{ - (-13) = }\frac{-1}{\frac{4}{3}}(x\text{ - (-8))} \\ y\text{ + 13 = }\frac{-3}{4}(x\text{ + 8)} \\ y\text{ + 13 = }\frac{-3}{4}x\text{ - 6} \\ y\text{ = }\frac{-3}{4}x\text{ - 6 - 13} \\ y\text{ = }\frac{-3}{4}x\text{ - 19} \\ 4y\text{ = -3x - }76 \end{gathered}[/tex]What is the solution to the equation below? 3x = x + 10 O A. x = 10 B. x = 0 C. X = 5 D. No Solutions
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Hence, the correct option is C: x=5
the item to the trashcan. Click the trashcan to clear all your answers.
Factor completely, then place the factors in The proper location on the grid.3y2 +7y+4
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We are asked to factor in the following expression:
[tex]3y^2+7y+4[/tex]To do that we will multiply by 3/3:
[tex]3y^2+7y+4=\frac{3(3y^2+7y+4)}{3}[/tex]Now, we use the distributive property on the numerator:
[tex]\frac{3(3y^2+7y+4)}{3}=\frac{9y^2+7(3y)+12}{3}[/tex]Now we factor in the numerator on the right side in the following form:
[tex]\frac{9y^2+7(3y)+12}{3}=\frac{(3y+\cdot)(3y+\cdot)}{3}[/tex]Now, in the spaces, we need to find 2 numbers whose product is 12 and their algebraic sum is 7. Those numbers are 4 and 3, since:
[tex]\begin{gathered} 4\times3=12 \\ 4+3=7 \end{gathered}[/tex]Substituting the numbers we get:
[tex]\frac{(3y+4)(3y+3)}{3}[/tex]Now we take 3 as a common factor on the parenthesis on the right:
[tex]\frac{(3y+4)(3y+3)}{3}=\frac{(3y+4)3(y+1)}{3}[/tex]Now we cancel out the 3:
[tex]\frac{(3y+4)3(y+1)}{3}=(3y+4)(y+1)[/tex]Therefore, the factored form of the expression is (3y + 4)(y + 1).
The relation described in the following diagram is function. A. True B. False
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Answer:
False
Explanation:
A relation is a function each term of the first set is related to only one term of the second set. In this case, 1 is related to 5 and to 10, so it is not a function.
Therefore, the answer is
False
2. When we are in a situation where we have a proportional relationship between two quantities, what information do we need to find an equation?
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Answer:
If two quantites have a proportional relatio
Graph each equation rewrite in slope intercept form first if necessary -8+6x=4y
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slope intercept form of the required graph:
-8 + 6x = 4y
y = 3/2x - 2
Can you pls help me with this question thank you
Answers
To solve this question, follow the steps below.
Step 01: Substitute j and k by its corresponding values.
j = 6
k = 0.5
Then,
[tex]\begin{gathered} 3.6j-2k \\ 3.6\cdot6-2\cdot0.5 \\ \end{gathered}[/tex]Step 02: Solve the multiplications.
[tex]21.6-1[/tex]Step 03: Solve the subtraction.
[tex]20.6[/tex]Answer: b. 20.6.
I’m circle P with m ∠NRQ=42, find the angle measure of minor arc NQ
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Here we must apply the following rule:
[tex]arc\text{ }NQ=2\cdot m\angle NRQ[/tex]Since m ∠NRQ = 42°, we have:
[tex]arc\text{ }NQ=2\cdot42=84\degree[/tex]6. An odometer shows that a car has traveled 56,000 miles by January 1, 2020. The car travels 14,000 miles each year. Write an equation that represents the number y of miles on the car's odometer x years after 2020.
Answers
Answer:
y=14000x
Step-by-step explanation:
x represents years after 2020 and y is the number of miles
The required equation for the distance travelled versus number of years after 2020 is given as y = 14000x + 56000.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
The given problem can be solved as follows,
Suppose the year 2020 represents x = 0.
The distance travelled per year can be taken as the slope of the linear equation.
This implies that slope = 14000.
And, the distance travelled by January 1, 2020 is 56000.
It implies that for x = 0, y = 56000.
The slope-point form of a linear equation is given as y = mx + c.
Substitute the corresponding values in the above equation to obtain,
y = 14000x + c
At x = 0, y = 56000
=> 56000 = 14000 × 0 + c
=> c = 56000
Now, the equation can be written as,
y = 14000x + 56000
Hence, the required equation for number of miles and years for the car is given as y = 14000x + 56000.
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