Using the cosine rule, the measure of the triangles is a = 51, b = 21, c = 68, A = 30.37°, B = 12.02° and C = 137.61°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Cosine rule is given as:
a² = b² + c² - 2bc * cosA
Given that a = 51, b = 21, c = 68, hence:
51² = 21² + 68² - 2(21)(68) * cosA
A = 30.37°
21² = 51² + 68² - 2(51)(68) * cosB
B = 12.02°
68² = 21² + 51² - 2(21)(51) * cosC
C = 137.61°
Using the cosine rule, the measure of the triangles is a = 51, b = 21, c = 68, A = 30.37°, B = 12.02° and C = 137.61°
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
The profit from a business is
described by the function
P(x) = -5x² + 30x + 8, where x
is the number of items made,
in thousands, and P(x) is the
profit in dollars. How many
items will maximize the profit?
First of all we will understand the question!!
The question is saying that you are given a function and you have to find the value of x which will give the maximum profit... Lets solve it by finding the extrema using the vertex
[tex] \rm \: p(x) = - 5 {x}^{2} + 30x + 8[/tex]
Identify the coefficients a and b of the quadratic function[tex] \rm \: p(x) = { - 5x}^{2} + 30x + 8 \\ \rm \: a = - 5 \: and \: b \: = 30[/tex]
Since a<0, the function has the maximum value at x, calculated by substituting a and b into x=-b/2a[tex] \rm \: x = \frac{30}{ 2 \times (- 5)} [/tex]
Solve the equation for x[tex] \rm \: x = 3[/tex]
The maximum of the quadratic function is at x=3Mr. Mason paints his fence on Monday, Tuesday, Wednesday, and Thursday. It takes him a total of 6 2/4 hours to paint his fence. Write a digit in each box to show how many hours he could have painted each day.
A fraction is a way to describe a part of a whole. The number of hours that Mr Mason painted each day is 1.625 hours.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The total number of hours that Mr Mason took to paint the fence is 6 2/4 hours, while the number of days taken by him is 4 hours. Therefore, the number of hours for which Mr Mason painted each day can be written as,
= (6 ²/₄)/4
= (26/4)/4
= 26/16
= 1.625 hours a day
Hence, the number of hours that Mr Mason painted each day is 1.625 hours.
Learn more about Fraction:
https://brainly.com/question/1301963
#SPJ1
Describe the error in solving the equation -2x^2+9x=4 using the Quadratic Formula.
Answer:
The roots are 0.5 and 4.
Step-by-step explanation:
-2x^2+9x=4
Rearrange:
-2x^2 + 9x - 4 = 0
x = [-b +/- √(b)^2 - 4ac)] / 2a
Using this quadratic formula the solution is:
x = [-9 +/- √(9)^2 - 4*(-2)*(-4)] / (2*-2)
= (-9 +/- √49) / -4
= 9/4 +/- (-7/4)
= 9/4 - 7/4 = 0.5
and 9/4 + 7/4 = 4
If f(x)=3x-2 and g(x)=2x+1,find (f+g)(x)
Answer:
f(x) + g(x) = 3x - 2 + 2x + 1
(f + g)(x) = 5x - 1
The great pyramid of giza has a square base. the length of each side of the base is approximately 230 meters. the height of the pyramid is approximately 147 meters. using these dimensions, what is the volume, in cubic meters, of the pyramid?
Answer:
2,592,100 m³
Step-by-step explanation:
The volume of the pyramid can be found by using the given dimensions in the formula for the volume of a square pyramid.
__
formulaV = 1/3s²h
where s is the side length of the square base, and h is the height.
applicationUsing the given dimensions, s = 230 m, h = 147 m, we find the volume to be ...
V = 1/3(230 m)²(147 m) = 2,592,100 m³
The volume of the pyramid is 2,592,100 cubic meters.
Which equation can be simplified to find the inverse of y=x^2-7
write a polynomial that represents the length of the rectangle
help please !!
Answer:
[tex]\textsf{Length}=0.8x^2-0.7x+0.7\quad \sf units[/tex]
Step-by-step explanation:
Area of a rectangle = width × length
Therefore, to find the length of the rectangle, we need to divide the area by the width.
Using long division:
[tex]\large\begin{array}{r}0.8x^2-0.7x+0.7\phantom{)} \\x+0.5{\overline{\smash{\big)}\,0.8x^3-0.3x^2+0.35x+0.35\phantom{)}}}\\-~\phantom{(}\underline{(0.8x^3+0.4x^2)\phantom{-b))))))))))))))}}\\0-0.7x^2+0.35x+0.35\phantom{)}\\ \underline{-~\phantom{()}(-0.7x^2-0.35x)\phantom{-b)))))}}\\ 0.7x+0.35\phantom{)}\\\underline{-~\phantom{()}(0.7x-0.35)}\\ 0\phantom{)}\end{array}[/tex]
Therefore, the length of the rectangle is:
[tex]0.8x^2-0.7x+0.7[/tex]
Ari said there are three possible outcomes when you
spin this spinner twice: two reds, a yellow and a red,
or two yellows.
So, the probability of getting two yellows is 1/3
Do you agree or disagree? Explain your thinking
Please answer fast :(
========================================================
Reason:
Ari hasn't considered the case of "red and yellow" which is almost identical to "yellow and red".
It helps to lay out a two by two table. Along the rows and columns, you'll have "red" and "yellow". See below.
Then inside the table are the list of all outcomes in the form (x,y) where x is the horizontal component along the columns, and y is the vertical component along the rows.
Example: if x = red and y = red, then we have the outcome (x,y) = (red, red)
As the table shows, we have 4 outcomes. Therefore the probability of getting two yellows is 1/4
Technically the (red, yellow) = (yellow, red) since ultimately order doesn't matter in this case. For some probability problems, order will matter. But again, order doesn't matter here and it means that we can treat these two situations the same. So I can see why Ari thinks there are only three outcomes.
--------------------------------
Here's another way to look at it:
The probability of landing on yellow is 1/2 assuming red and yellow are equally likely.
This means the probability of two yellow in a row is (1/2)*(1/2) = 1/4
Each is spin is independent of any other.
Market research shows that 30% of consumers are likely to purchase an electronic tablet for younger children under age 10. However, only 2% of consumers are likely to buy a laptop for children under the age of 10. On the other hand, for children ages 10 – 17, 50% of consumers are likely to buy a tablet and 40% are likely to buy a laptop. If a family has a five-year-old son and a 13-year-old daughter, what is the probability of both children receiving a tablet?
Answer:
see the attachment photo!
Don’t know how to solve.
Answer:
$122.88
Step-by-step explanation:
the phone decreases by 20% each year , that is
(100 - 20)% = 80% = [tex]\frac{80}{100}[/tex] = 0.8
the phone reduces by a factor of 0.8 each year , then after 4 years
value = $300 × [tex](0.8)^{4}[/tex] = $122.88
What is the next fraction in this sequence? Simplify your answer.
13/23, 1/2, 10/23, 17/46,
...
Submit
Answer:
7/23
Step-by-step explanation:
Each answer is 1.5/23 less than the previous
17/46 - 1.5/23 = 17/46 - 3/46 = 14/46 = 7/23
The measures of all of the interior angles of a triangle are in the extended ratio 1 : 2 : 3. The value of the smallest angle is:
Answer:
30 degrees
Explanation:
Let the ratio's be in x, 2x, 3x
Total Interior Angle of a triangle sum ups to 180°
x + 2x + 3x = 180°6x = 180°x = 180°/6 = 30°
The smallest angle which is x is 30°
20 POINTS
Write the slope intercept form of each equation of the line. Use a fraction for slope if needed.
Parallel to y=−3/2x+1, through (0, -4)
Answer:
the answer to this question is c=-4
-7x + 13 > 41 what is the answer
Answer:
x < -4
Step-by-step explanation:
-7x>28
7x<-28
x<-4
please give brainliest!
hope this helps :)
(2,-9) and (-3,6) in slope intercept form
Answer:
2 - 9 - 36
= - 43
Step-by-step explanation:
(hope it's Help)
What is the area of the triangle formed from 0,-1), (0.4), and
(4,-1)?
OA. 20 square units
B. 5 square units
O C. 40 square units
O D. 10 square units
Answer:
D. 10 square units
Step-by-step explanation:
The area of a triangle is given by the formula ...
A = 1/2bh
__
This triangle has a base of 4 units and a height of 5 units. (These dimensions can be counted from the graph, or found by subtracting coordinate values.) Its area is ...
A = 1/2(4 units)(5 units) = 10 square units
_____
Additional comment
The first two coordinates lie on the line x=0. The length of that segment is the difference of the y-values: 4 -(-1) = 5.
The first and last coordinates lie on the line y=-1. The length of that segment is the difference of the x-values: 4 -0 = 4.
Which expression is equivalent to startfraction startroot 10 endroot over rootindex 4 startroot 8 endroot?
The expression that is equivalent to √10 / (4√8) is given as √5 / 8
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the equation:
√10 / (4√8)
Simplifying:
= √10 / (4√(4 * 2))
= √10 / (8√2)
= √5 / 8
The expression that is equivalent to √10 / (4√8) is given as √5 / 8
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
what is the perimeter of the triangle
A submarine travels 19 degrees west of north. What is its compass heading? PLS HELP WILL GIVE BRAINLIEST
Answer:
NNW(North-northwest)
The required compass heading of the submarine is 341 degrees.
To find the compass heading of the submarine, we need to determine the angle it makes in the north direction, clockwise.
Since the submarine is traveling 19 degrees west of north, the compass heading can be calculated as follows:
Compass Heading = 360 degrees - (Angle west of North)
Compass Heading = 360 degrees - 19 degrees
Compass Heading = 341 degrees
So, the compass heading of the submarine is 341 degrees.
Learn more about compass here:
https://brainly.com/question/29095249
#SPJ4
In class 8 A, there are 20 students, 55% students are present on Wednesday. Find out how many people are present that day? How many people are absent on that day?
Answer:
11 students are present and 9 are absent.
During a game of golf, Kayley hits her ball out of a sand trap. The equation h = t? + 4t -
21 models the height of the golf ball in feet in relation to the number of t seconds since it was hit. Kayley solved the quadratic by factoring: .
a. How many seconds does it take for her ball to reach the green?
b. How do we know the 2nd value isn't also a solution?
A quadratic equation is in the form of ax²+bx+c. It took 3seconds for the golf ball to reach the green.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
A.) The time that the ball takes to reach the green can be found by equation the equation against zero. As the ball will have 0 height when it will be on the green,
t²+4t-21=0
t²+7t-3t-21=0
t(t+7)-3(t+7)=0
(t+7)(t-3)=0
t = -7, 3
Hence, it took 3seconds for the golf ball to reach the green.
B.) Since the time can not be negative the second value is wrong.
Learn more about Quadratic Equations:
https://brainly.com/question/2263981
#SPJ1
-2 (3d - 5d²) simplify
Answer: =-6d+10d^2
Step-by-step explanation:
what is the square root of x divided by the square root of 2 equal
Answer:
[tex]\sqrt{\frac{x}{2} }[/tex]
Key:
• [tex]\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{x}}{\sqrt{2}}\\[/tex]
[tex]\frac{\sqrt{x}}{\sqrt{2}}=\sqrt{\frac{x}{2}}\\[/tex]
[tex]=\sqrt{\frac{x}{2}}[/tex]
Members of a soccer team raised $1511 to go to a tournament. They rented a bus for $933.50 and budgeted $38.50 per player for meals. Determine the number of players the team can bring to the tournament.
hurry pls
The number of players in the team would be 15 which can bring to the tournament.
A soccer squad collected $1511 to attend a competition. They spent $933.50 on a bus rental and $38.50 for each player on food.
What is a numerical expression?A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
Let the number of players would be x
As per the given information, the required solution would be as:
Total budget = (per player meal)(x players) + bus rent
1511 = 38.50x + 933.50
Rearrange the terms and solve for x
1511 - 933.50 = 38.50x
577.50 = 38.50 x
Divide both sides by 38.50 into above equation,
x = 15
Therefore, the number of players in the team would be 15 which can bring to the tournament.
To learn more about numerical expression click here :
https://brainly.com/question/6037813
#SPJ2
Could anyone give me the answer to this question?
Answer:
36
Step-by-step explanation:
[tex]\angle AOC[/tex] is made up of s + r, and since r is [tex]\frac{3}{5}[/tex] of [tex]\angle AOC[/tex] we know r must be the remaining [tex]\frac{2}{5}[/tex] of [tex]\angle AOC[/tex].
We can solve for [tex]\angle AOC[/tex] by using this equation:
[tex]\frac{2}{5}\angle AOC = 24\\(\frac{2}{5}\angle AOC)\frac{5}{2} = (24)\frac{5}{2}\\ \boxed{\angle AOC = 60}[/tex]
1. 2 fifths of [tex]\angle AOC[/tex] is 24
2. multiply both sides by [tex]\frac{5}{2}[/tex] to isolate [tex]\angle AOC[/tex]
3. [tex]\angle AOC[/tex] is 60°
We can now solve for r
[tex]r = \frac{3}{5}\angle AOC\\r = \frac{3}{5}(60)\\\boxed{r = 36}[/tex]
1. the equation the problem gave us
2. substitute [tex]\angle AOC[/tex] for 60 (we solved for it before)
3. [tex]r[/tex] is 36°
Select the correct answer.
The Cohen family started their wheat farm in 1995. The equation models the number of bushels of wheat they produced each year, where t
is the number of years since 1995.
C(t) = 7,000+500 In(t+1)
The Mason family also started their wheat farm in 1995. The graph models the number of bushels of wheat they produced each year, where t
is the number of years since 1995.
M(1)
12,000
8,000
4,000
-24-168
16 24
4,000
-8,000+
12,000
Which statement is true about the quantity of wheat the two farms will produce as the years pass?
OA The wheat production of both farms will continue to increase each year without bound.
OB. The Cohen farm's wheat production will continue to increase each year without bound, while the Mason farm's wheat
production will approach a stable amount.
OC. The Mason farm's wheat production will continue to increase each year without bound, while the Cohen farm's wheat
production will approach a stable amount.
O D.
The wheat production of both farms will approach a stable amount as the years pass.
The wheat production of both farms will approach a stable amount as the years pass.
What is an exponential function?
An exponential function is one that is steadily increasing or decreasing. We can see that in this case there is a positive sign indicating an increase.
Thus, from the graph, we can see that, the wheat production of both farms will approach a stable amount as the years pass.
Learn more about exponential function:https://brainly.com/question/11487261
#SPJ1
The hypotenuse of a right triangle measures 17 cm and one of its legs measures 13 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Step-by-step explanation:
13^2 + x^2 = 17^2
169 + x^2 = 289
289 - 169 = 120
x^2 = 120
[tex] \sqrt{120} = 10.9544511501[/tex]
x = 11.0
how do you find the breadth of the area in a square
Answer:
A = l x b
Step-by-step explanation:
Area = length x breath
So find the area and length and work it out by dividing area by length.
1 stick butter is equivalent to _____ ounces.
Answer:
4 ounces
Step-by-step explanation:
Answer:
1 stick butter is equivalent to __4___ ounces.
Step-by-step explanation:
1 stick of butter is equal to 4 ounces
Question 5 of 10
What is the surface area of the cube below?
OA. 20 units²
B. 8 units²
C. 24 units²
OD. 12 units²
SUBMIT
Answer:
S=6a^2
S=6×2^2
S=6×4=24
The right answer is C
Answer:
24 units²
Explanation:
The surface area of cube is 6(side)²
Here given:
a = 2
The surface area:
= 6(2)^2
= 6(4)
= 24