Answers
Hello, in this question we will use the "Sinus Theorem".
The general formula of the Sine Theorem is as follows;
[tex]A=\frac{1}{2}.a.b.sin(C)[/tex]We are given the length of the two sides and the sine value of the angle of the unknown side. We also know the area of the triangle. Let's substitute the required values in this formula to get the result.
[tex]A=\frac{1}{2} (x+2)(2x-3)(sin45^o)[/tex][tex]4\sqrt{2}=\frac{1}{2}(x+2)(2x-3)(\frac{1}{\sqrt{2} } )[/tex][tex]16=(x+2)(2x-3)[/tex][tex]16=2x^2+x-6[/tex][tex]0=2x^2+x-22[/tex]In the last step, we are left with a quadratic equation with one unknown. To solve this equation, we need to calculate the discriminant value.
[tex]Discriminant=b^2-4ac[/tex]There are only two roots of a quadratic equation with one unknown.
[tex]x_{1}=\frac{-b-\sqrt{Discriminant} }{2a}[/tex][tex]x_{2}=\frac{-b+\sqrt{Discriminant} }{2a}[/tex]Thus our x values;
[tex]x_{1}=\frac{-1-\sqrt{177} }{4}[/tex][tex]x_{2}=\frac{-1+\sqrt{177} }{4}[/tex]We cannot accept the first root [tex]x_1[/tex]. Because length cannot be a negative value.
Ans = [tex]x_{2}=\frac{-1+\sqrt{177} }{4}=3.076[/tex]
Related Questions
WRITE AN EQUATION TO DESCRIBE THE RELATIONSHIP BETWEEN J AND Mj | 4 | 12 | 20m | 3 | 9 | 15
Answers
First, we can use the points (4,3) and (20,15) to find the slope of the line:
[tex]\begin{gathered} s=\frac{m_2─m_1}{j_2─j_1}=\frac{15─3}{20─4}=\frac{12}{16}=\frac{3}{4} \\ s=\frac{3}{4} \end{gathered}[/tex]Now we can find the relation function using the point (4,3) and the slope s=3/4
[tex]\begin{gathered} m─m_1=s(j─j_1) \\ \Rightarrow m─3=\frac{3}{4}(j─4)=\frac{3}{4}j─(\frac{12}{4})=\frac{3}{4}j─3 \\ m=\frac{3}{4}j \end{gathered}[/tex]therefore, the equation to describe the relationship between J and M is m=3/4j
(-4k - 1) - (-6k - 6)
Answers
Answer:
2k + 5
Step-by-step explanation:
Since this is a subtraction problem, you need to change it to an addition problem. When you do this, you also need to change the sign of each term in the second set of parentheses.
(-4k - 1) - (-6k - 6)
(-4k - 1) + (6k + 6)
Remove the parentheses and add like terms.
-4k - 1 + 6k + 6
2k +5
2K+5
The new figure that is produced in a transformation is called the
Answers
Let:
[tex]\begin{gathered} P=(x1,y1)=(-3,4) \\ P^{\prime}=(x2,y2)=(4,0) \end{gathered}[/tex][tex]\begin{gathered} x1+a=x2 \\ -3+a=4 \\ so\colon \\ a=4+3 \\ a=7 \\ ---- \\ y1+b=y2 \\ 4+b=0 \\ b=-4 \end{gathered}[/tex]Therefore:
[tex](x,y)\to(x+7,y-4)[/tex]PLSSSSS
WILL MARK BRAINLIEST!!!
SIMPLEEE
(Yr7)
Answers
Answer:
Step-by-step explanation:
the answer I have given below
kind regards
Determine the intervals on which the function is increasing, decreasing, and constant.
A) Increasing on (- 5, - 3) and (2, 5) Decreasing on (- 3, 0) Constant on (0, 2) B) Increasing on (- 3, - 1) Decreasing on (- 5, - 2) and (2, 4) Constant on (- 1, 2) C) Increasing on (- 3, 1) ; Decreasing on (- 5, - 3) and (0, 5) ; Constant on (1, 2) D ) Increasing on (- 3, 0) Decreasing on (- 5, - 3) and (2, 5); Constant on (0, 2)
Answers
The intervals on which the function is increasing, decreasing and constant are (-5,-3) and (2,5) on increasing (-3,0) on decreasing and (0,2) on constant.
What is intervals?
An interval in math is the measured in terms of the numbers. An interval to includes all the numbers that come between two of particular numbers. This is the range includes all of the realistic numbers between those two of numbers. Real numbers are the any kind of number you can definitely think of.
Sol-by showing in the figure the function is increasing on the (-3,0)
Decreasing on (-5,-3) and (2,5)
Constant on (0,2)
Thus, the correct option is A
To know more about intervals click-
https://brainly.com/question/1503051
#SPJ13
a box is constructed out of two different types of metal. the metal for the top and bottom, which are both square, costs 1/ft2 and the metal for teh sides costs 2 ft find the dimensions that minimize cost if the box has a volume of 20 ft 3
Answers
The cost function of the box is C(x) = 2. x² + 160/x and the dimension that lead to the minimum cost is length = ∛40 ft., width = ∛40 ft., height = ∛5 ft.
Let:
x = the bottom's side length
h = the height of the box
Then, the surface area of top and bottom:
A1 = 2. x²
The surface area of vertical sides:
A2 = 4 x. h
The cost function is:
C(x) = 2. x² . 1 + 4 x. h . 2
C(x) = 2. x² + 8 x. h
The volume of the box is:
V = x² . h
20 = x² . h
h = 20 / x²
Substitute h = 20 / x² into the cost function:
C(x) = 2. x² + 8 x. h
C(x) = 2. x² + 8 x. 20 / x²
C(x) = 2. x² + 160/x
At the minimum point, the derivative of a function is equal to zero. Hence,
C'(x) = 4x -160 / x² = 0
x³ = 40
x = ∛40
Substitute x = ∛40 to find the height:
h = 20 / x²
= 2 . 10 / (∛4² . ∛10²)
= ∛10 / ∛2 = ∛5
Learn more about the minimum point here
https://brainly.com/question/19157654
#SPJ4
I need help 9th grade math
Answers
Answer:
D
Step-by-step explanation:
A hiker descended 450 feet down to an elevation of 2300 feet. Which equation models this scenario?
Answers
The equation models this scenario regarding the hiker is x - 450 = 2300.
Whet is elevation?Elevation is simply used to illustrate the height above the sea level.
In this case, the hiker descended 450 feet down to an elevation of 2300 feet.
The equation that can model the scenario will be x - 450 = 2300
where x = Initial elevation
Learn more about elevation on:
brainly.com/question/88158
#SPJ1
Multiply and write in standard form: 10x + 3)(2x - 1) Show all work
Answers
Explanation
[tex](10x+3)(2x+1)[/tex]Step 1
apply distributive property
[tex]\begin{gathered} (10x+3)(2x+1)=(10x\cdot2x)+(10x\cdot1)+(3\cdot2x)+(3\cdot1) \\ (10x+3)(2x+1)=20x^2+10x+6x+3 \end{gathered}[/tex]Step 2
add similar terms and order
[tex]\begin{gathered} (10x+3)(2x+1)=20x^2+10x+6x+3 \\ (10x+3)(2x+1)=20x^2+16x+3 \\ \text{the standard form is} \\ ax^2+bx+c,so \\ ax^2+bx+c\Rightarrow20x^2+16x+3 \end{gathered}[/tex]so, the answer is
[tex]20x^2+16x+3[/tex]I hope this helps you
according to the chart, approximately how many times more likely is a 16-year-old driver to crash with two passengers as opposed to with no passengers?
Answers
About twice as likely is a 16-year-old driver to crash with two passengers as opposed to with no passengers.A 16 or 17-year-old driver has a higher risk of dying every mile they drive compared to operating a vehicle alone. increases by 44% when one of the passengers is under the age of 21. while transporting two passengers who are under 21 in doubles.
Are 16 year olds more likely to crash?Teenagers between the ages of 16 and 19 had the highest crash risk of any age group. Teen drivers in this age range have a roughly three times higher risk of being in a fatal collision per mile traveled than drivers who are at least 20 years old.According to CDC research, there are a few main factors that increase the likelihood of young drivers being in auto accidents: insufficient experience Due in part to their inability to identify and avoid road dangers, teen drivers have a fatal crash risk that is three times higher than that of older drivers.To learn more about crash with two passengers refer to:
https://brainly.com/question/26728739
#SPJ1
16-year-old driver to crash with two passengers as opposed to with no passengers is about twice as likely.
Are 16 year old's more likely to crash?Teenagers between the ages of 16 and 19 had the highest crash risk of any age group. Teen drivers in this age range have a roughly three times higher risk of being in a fatal collision per mile traveled than drivers who are at least 20 years old.According to CDC research, there are a few main factors that increase the likelihood of young drivers being in auto accidents: insufficient experience Due in part to their inability to identify and avoid road dangers, teen drivers have a fatal crash risk that is three times higher than that of older drivers.The complete question is,
According to the chart, approximately how many times more likely is a 16-year-old driver to crash with two passengers as opposed to with no passengers?
just as likely
about twice as likely
about three times more likely
about four times more likely
To learn more about crash with two passengers refer to:
brainly.com/question/26728739
#SPJ1
The slope of line ℓ
is greater than 0 and less than 1. Write an inequality for the slope of a line perpendicular to ℓ
.
Answers
By properties of perpendicular lines and algebra properties, the slope of the line perpendicular to line ℓ is represented by m' > 1.
How to represent an inequality associated with a line perpendicular to another line
Let m be the slope of a line, in accordance with analytic geometry, the slope of line perpendicular to the first one is equal to m' = - 1 / m. The statement can be summarized by the following inequality:
0 < m < 1
Then, by algebra properties for inequalities we find that that slope for the perpendicular line is:
0 < m · m⁻¹ < m⁻¹
0 < 1 < m⁻¹
1 < m⁻¹
- m⁻¹ > 1
- 1 / m > 1
m' > 1
The slope of the line perpendicular to line ℓ is represented by m' > 1.
To learn more on perpendicular lines: https://brainly.com/question/2096532
#SPJ1
a school nurse can give 25 eye tests in a two-hour period. how long will it take the nurse to give eye tests to all 600 stuents in her school.
Answers
24•2 = 48
48 hours for all 600 students
I need help with these problems ASAP.
Answers
The following cases are described:
The rational function is (f / g) (x) = x - 6, whose domain is all the real numbers.The rational function is (f / g) (x) = 1 / (x + 2), whose domain is all the real numbers except x = - 2.How to derive a rational function by division of functions and find its domain
Algebraically speaking, rational functions are expressions of the form f(x) = p(x) / q(x), such that q(x) ≠ 0, where p(x) is the numerator and q(x) is the denominator. Rational functions can be found by using the defintion of division between two functions:
(f / g) (x) = f(x) / g(x)
And the domain of (f / g) (x) is every value of x such that g(x) ≠ 0. Now we proceed to find all the required information for each case:
Case 1 - f(x) = x² - 3 · x - 18, g(x) = x + 3
Rule: (f / g) (x) = (x² - 3 · x - 18) / (x + 3)
(f / g) (x) = [(x - 6) · (x + 3)] / (x + 3)
(f / g) (x) = x - 6
Domain: Since the resulting expression is a linear function, then the domain of (f / g) (x) is all the real numbers.
Case 2 - f(x) = x - 3, g(x) = x² - x - 6
Rule: (f / g) (x) = (x - 3) / (x² - x - 6)
(f / g) (x) = (x - 3) / [(x - 3) · (x + 2)]
(f / g) (x) = 1 / (x + 2)
Domain: The domain of the rational function is any real number except x = - 2.
To learn more on rational functions: https://brainly.com/question/8177326
#SPJ1
Tom bought 10 cans of Coca cola drink at a cost of USD26.00. How much he will need to pay for 36 cans of Coca Cola?
(20 Points) Working Step
Answers
Tom will need to pay $93.60 for 36 cans of Coca-Cola.
Linear ExpressionA linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=3x+2.
The question gives:
Tom bought 10 cans of Coca-cola drink at a cost of USD26.00. Here you can convert this text into an algebraic expression, see:
10x = 26, where x represents the unit cost.
You can find x, solving the previous algebraic expression. Thus,
10x=26
x=26/10
x=2.6
So, 1 can of Coca-Cola costs $2.60.
For knowing the cost total for 36 cans of Coca-Cola, you need to multiply 36 units by the unit cost ($2.6). See below:
36*2.6= $93.60
Learn more about the algebraic expression here:
brainly.com/question/2164351
#SPJ1
Tara's family raises honey bees and sells the honey at the farmers' market. to get ready for market day, tara fills 28 equal sized jars with honey. she brings a total of 14 cups of honey to sell at the farmers' market. use an equation to find the amount of honey each jar holds. to write a fraction, use a slash ( / ) to separate the numerator and denominator.
Answers
The amount of honey each jar holds is 1/2 cup by jar
To solve this exercise we have to perform a mathematical operation of division with fractions:
Information about the problem:
Jars filled = 28 jarsCups brought = 14 cupsTo find the amount of honey each jar holds we state the following equation:
Amount of honey by jar = Cups brought / Jars filled
Amount of honey by jar = 14 cups /28 jar
Simplifying to its minimum expression, we have:
Amount of honey by jar = 7 cups / 14 jar
Amount of honey by jar = 1 cup / 2 jar
Amount of honey by jar = 1/2 cup by jar
What is a fraction?Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.
Learn more about fraction at: brainly.com/question/11562149
#SPJ4
Students in a fitness class each completed a one-mile
Which statements are true about a histogram with one-
walk or run. The list shows the time it took each person
minute increments representing the data? Select three
to complete the mile. Each time is rounded to the
options.
nearest half-minute.
5.5, 6, 7, 10, 7.5, 8, 9.5, 9, 8.5, 8, 7, 7.5, 6, 6.5, 5.5
O A histogram will show that the mean time iS
approximately equal to the median time of 7.5
minutes.
O The histogram will have a shape that is left-skewed.
O The histogram will show that the mean time is greater iS
than the median time of 7.4 minutes.
O The shape of the histogram can be approximated with
a normal curve.
0 The histogram will show that most of the data is
centered between 6 minutes and 9 minutes.
Answers
In linear equation, The histogram will show that most of the data is centered between 6 minutes and 9 minutes.
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.5.5+6+7+10+7.5+8+9.5+9+8.5+8+7+7.5+6+6.5+5.5=111.5
Since there are 15 values,
their mean is 111.5/15=7.43 which is very close to the mean.
A)A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes
D)The shape of the histogram can be approximated with a normal curve.
E)The histogram will show that most of the data is centered between 6 minutes and 9 minutes.
Learn more about linear equation
brainly.com/question/11897796
#SPJ13
How can I work out the size of angle y?
Answers
Answer:
180 degrees converted is 3.14159 i think
Step-by-step explanation:
Answer:
< y = 17 degrees.
Step-by-step explanation:
x + y = 180 - 112 = 68 (as there are 180 degrees in a triangle)
Also, x = 3y, so substituting for x in the first equation:
3y + y = 68
4y = 68
y = 17.
So,
x = 3*17 = 51,
Karyn proofreads 15 pages in 2 hours for $40. What is her proofreading rate in pages per hour? How much does she earn per hour?
Answers
The proofreading rate of Karyn in pages per hour is $20 per 7.5 pages per hour , and she earn $20 per hour .
In the question ,
it is given that
Karyn proofreads ⇒15 pages in 2 hours for $40
Karyn in 2 hour proofreads 15 pages ,
So, in 1 hour She will proofread = 15/2= 7.5 pages
and will get $40/2 = $20 for 1 hour ,
hence ,her rate in pages per hour is $20 per 7.5 pages per hour .
In 2 hour Karyn earns $40
So , in 1 hour Karyn will earn $40/2 = $20
hence , she earn $20 per hour .
Therefore , the proofreading rate of Karyn in pages per hour is $20 per 7.5 pages per hour , and she earn $20 per hour .
Learn more about Division here
https://brainly.com/question/729512
#SPJ1
Hey!
New question 4 today
Nadia is walking a 3.4-mile trail. She stops to take a break after walking 1.6 miles. Which explains whether the distance Nadia already walked is greater than, less than, or equal to the distance she has left to walk?
!PLEASE!
Don't give wrong answers. (its not very nice)
Only use one of the answer options. (other answers are wrong)
Answers
Based on the distance walked by Nadia when she took her break, the statement that explains the distance already walked is C. The distance Nadia already walked is less because 3.4 - 1.6 = 1.8, and 1.6 < 1.8.
How to find the distance?Nadia had already walked 1.6 miles by the time she took her break. This means that the distance she was still left to walk in the mile trail was:
= 3.4 - 1.6
= 1.8 miles
The distance that Nadia had already walked was 1.6 miles and yet she was left to walk 1.8 miles.
We can therefore conclude that the distance that Nadia already walked is less than the distance still to be walked.
Find out more on distance at https://brainly.com/question/28881917
#SPJ1
The distance Nadia already walked is less because 3.4 - 1.6 = 1.8, and 1.6 < 1.8 which is the correct answer would be an option (C).
What is the distance?Distance is calculated as the product of a person's movement and time.
Nadia took a rest after covering 1.6 miles of walking.
This indicates that she had the following distance to cover on the mile trail:
⇒ 3.4 - 1.6 = 1.8 miles
Nadia had already walked 1.6 miles, but she still had another 1.8 miles to go.
Therefore, the distance Nadia has already traveled is less than the distance that needs to be covered.
Hence, the correct answer would be an option (C).
Learn more about the distance here:
brainly.com/question/13269893
#SPJ1
Determine if the table below is proportional?
Answers
The table represent a direct proportional relation.
How to determine if a table represents a proportional relation
In this question we find a table with four pairs of elements that have to be tested with respect to the direct proportional formula, which is defined below:
y = k · x
Where:
x - Independent variable.y - Dependent variable.k - Constant of proportionality.The table represents a direct proportional relation if and only if there is only one constant of proportionality:
k₁k₁ = 12 / 3
k₁ = 4
k₂k₂ = 20 / 5
k₂ = 4
k₃k₃ = 8 / 2
k₃ = 4
k₄k₄ = 32 / 8
k₄ = 4
As k₁ = k₂ = k₃ = k₄, the table represent a proportional relationship.
To learn more on direct proportional relationships: https://brainly.com/question/28628342
#SPJ1
Using the information found in these tables which of the following statements is true
Please helpppp
Answers
PLEASE ASAP HELP MEEEEThe longer leg of a right triangle is 3 inches longer than the shorter leg. The hypotenuse is 6 inches longer than the shorter leg. Find the side lengths of thetriangle.Length of the shorter leg:inchesLength of the longer leg:inchesinchesLength of the hypotenuse:
Answers
In order to find the values of the sides of the triangle you take into account the relation between sides and hypotenuse.
h: hypotenuse
c1: shorter leg
c2: longer leg
Longer leg c2 is 3 inches longer than c1:
c2 = c1 + 3
hypotenuse h is 6 inches longer than c1:
h = c1 + 6
The formula for the calculation of the hypotenuse is:
h² = c1² + c2²
you replace for h and c2 in terms of c1:
(c1 + 6)² = c1² + (c1 + 3)²
You solve the previous equation for c1:
c1² + 12c1 + 36 = c1² + c1² + 6c1 + 9
c1² - 6c1 - 27 = 0
the roots of the previous equation are:
(c1 - 9 )(c1 + 3) = 0
c1 = 9
c1 = -3
You take the positive number because there is no length of sides with negative values.
Then, c2 and h are:
c2 = c1 + 3 = 9 + 3 = 12
h = c1 + 6 = 9 + 6 = 15
Hence, shorter leg is 9 inches, longer leg 12 inches and hypotenuse 15 inches
2. What is the slope-intercept form of 9x + 3y = 15?
y = 3x - 5
y = 3x + 5
y=-3x - 5
y=-3x+5
Answers
Answer:
y=3x+5
Step-by-step explanation:
Julia has a mask collection consisting of 255 masks she keeps on the wall and 45 she keeps in a display case. What percentage of Julias mask collection does she keep on her wall?
Answers
We are told that Julia keeps 255 masks on the wall and 45 on the display case, this means in total the number of masks she has is
[tex]255+45=300\text{masks}[/tex]The number of masks Julia keeps on the wall is 255 masks; therefore, the percentage of fo masks on the wall is
[tex]\frac{255}{300}\times100[/tex][tex]=85.\text{ }[/tex]Hence, Julia keeps 85% of her mask collection on her wall.
Given the polynomial f(x)=x⁴+3x³-3x²-x, which of the following is true?
a) (x+1) is a factor since f(-1)=0.
b) (x-1) is a factor since f(-1)=0.
c) (x+1) is a factor since f(1)=0.
d) (x-1) is a factor since f(1)=0.
Answers
Help help please please help help I need help 30 POINTS
Answers
Line of symmetry is basically a line in the middle or somewhere else that dictates where a shape would be symmetrical
Two companies are competing for a contract to make the programs for middle school gymnastics meets. Nadia’s Printing charges a $19.99 fee for printing and $0.25 for each program printed. Simone’s Stylish Print charges a $29.99 fee for printing and $0.10 for each program printed. For the most recent meet, Nadia’s Printing charged more than Simone’s Stylish Print.
Which inequality models this situation?
Answers
Answer:
the second answer
Step-by-step explanation:
Select all ratios equivalent to 13:14
52:56. 39:42. 3:4
Answers
Answer:
52:56 and 39:42
Step-by-step explanation:
The ratios equivalent to 13:14 are:
52:56
39:42
3:4 is not equivalent to 13:14 because 3 is not a multiple of 13.
Tell whether the given situation is an example of Direct Variation or Inverse Variation. Write DV if it is a Direct Variation and IV for Inverse Variation. (NEED THE ANSWER ASAP)7. The height of a person and his weight
Answers
Given,
The statement is "The height of a person and his weight".
Required/
Identify the statement is inverse or direct variation.
As the height of the person increase then its their weight is also increased.
Similarly,
The height of the person decrease then its their weight is also decreased.
Hence, it is direct variation.
[tex]3 {}^{2} + ( - 4 {}^{2} ) + 5 {}^{2} [/tex]I'm confused on that can you help me please?
Answers
We have to replace the values in the equation
[tex]x^2+y^2+z^2=(3)^2+(-4)^2+(5)^2=9+16+25=50[/tex]Since the square of a negative number is a positive number, (-4)^2 = +16