Answer: ~96.83°
Step-by-step explanation:
1) It's obvious that the largest angle is the opposite to the largest side.
▪︎ QR = 18 (the largest side)
=> <QPR is the largest angle
2) Cosine Rule:
▪︎ QR^2 = QP^2 + PR^2 - 2*QP*PR*cos(QPR)
▪︎ 18*18 = 13*13 + 11*11 - 2*13*11*cos(QPR)
▪︎ 324 = 169 + 121 - 286*cos(QPR)
▪︎ 34 = -286*cos(QPR)
▪︎ cos(QPR) = -34/286
▪︎ <QPR = arccos(-34/286) = 96.827...°
Find the roots of:
[tex]1.\ &2x^3-7x^2+8x-3=0\\ 2. \ & x^3-x^2-4=0\\ 3. \ &6x^3+7x^2-9x+2=0 \end{align*}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \ 2x^3-7x^2+8x-3=0 } \end{gathered}$}[/tex]
Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:
| 2 -7 8 -3
1 | 2 -5 3
| 2 -5 3 0
1 | 2 -3
2 -3 0
So the factorization is (x-1)² (2x-3)=0. So:
[tex]\bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2} }[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \ x^3-x^2-4=0 } \end{gathered}$}[/tex]
Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:
| 1 -1 0 -4
2 | 2 2
1 2 2 0
So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.
[tex]\bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{3) \ 6x^3+7x^2-9x+2=0 } \end{gathered}$}[/tex]
Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:
| 6 7 9 2
-2 | -12 10 -2
6 -5 1 0
So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:
[tex]\bf{ x_{2, 3}&=\dfrac{5\pm \sqrt{(5)^2-4(6)(1)}}{2(6)}=\dfrac{5\pm \sqrt{25-24}}{12}=\dfrac{5\pm 1}{12} }}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{matrix} x_1=-2&\ \ \ \ \ \ x_{2}=\dfrac{6}{12} \qquad &\ \ \ x_3=\dfrac{4}{12}\\ &\ \ \ x_2=\dfrac{1}{2} \qquad &x_3=\dfrac{1}{3} \end{matrix} \end{gathered}$}[/tex]
please help me asap urgent grade 11 math
Answer:
choose option 1
Step-by-step explanation:
option one is going to take a longer time to pay off but option 2's annual fees are going to make you spend at least $200 more dollars than option 1
If 50% of all federal inmates are serving time for extortion and a random sample of 16 federal inmates is selected, then what is the expected number of inmates serving time for extortion? A)
18 B)12 C) 9 D) 8
Part 1: Come up with and describe two scenarios: one that models a direct variation situation and one that models an inverse variation situation. Do not state explicitly which scenario is which, but provide at least four data pairs for each situation. Your classmates will have to determine which of the scenarios is a direct variation and which is an inverse variation, and the value of k for each.
Answer:
1. I went to a store four days in a row and only bought chocolate bars each day. All chocolate bars were the same and cost the same. On the first day, I bought 2 chocolate bars for $2.38. On the second day I bought 1 chocolate bar for $1.19. On the third day, I bought 10 chocolate bars for $11.90. On the fourth day, I bough 4 chocolate bars for $4.76.
2. A sink is full. It contains 20 gallons of water. The stopper is removed and water starts draining out. One minute after the stopper is removed, the volume of water in the sink is 18 gallons. Two minutes after the stopper is removed, the volume of water in the sink is 16 gallons. Four minutes after the stopper is removed, the volume of water in the sink is 12 gallons. Ten minutes after the stopper is removed, the sink is empty.
Triangle 1 has an angle that measures 26 ° and an angle that measures 53 ° .Triangle 2 has an angle that measures 26 ° and an angle that measures a ° where a≠53 °.
Based on the information, Frank claims that triangle 1 and triangle 2 cannot be similar.
What value of a will refute Frank's claim?
a=_____
Answer:
101 degrees
Step-by-step explanation:
The third angle in the first triangle would be 180 - (26+53) = 101 degrees
the angle in triangle 2 could be the 101 degree one
5. Which equation can be used to solve for x in the following diagram?
(3x+12)°
२०
A. 3x = 180+X
B. (3x+12) + x = 90
C. (3x+12) + x = 180
D. (3x+12) = x
Answer:
C
Step-by-step explanation:
the 2 angles form a linear pair and sum to 180° , that is
3x + 12 + x = 180
Saif is building a rectangular pen for his dog. the dimensions are 15 units long and 7 units wide. saif is building a second pen that is 75% the length of the original and 125% the width of the original. write an equation to determine the length of the second pen. what is the length of the second pen? . .
The length of the second pen is 11.25 units.
What is a Rectangle ?A rectangle is a polygon with four sides , the opposite sides are parallel and equal .
it is given in the question that
Saif is building a rectangular pen for his dog. the dimensions are 15 units long and 7 units wide
length new = 75% length initial
Length new = (75/100) * 15
Length new = 0.75 * 15
Length new = 11.25 units
The length of the second pen is 11.25 units.
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A ball is thrown from an initial height of 2 feet with an initial upward velocity of 35ft/s. The ball's height h (in feet) after t seconds is given by the following.
The values for time is 1.361 and 0.828.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0. with a ≠ 0 .
Given: h=-16t²+35t+2
so if the height is going to be 20ft,
20 = 2+35t-16t²
16t²-35t18=0
Solve the above quadratic equation
x= -b±√b²-4ac/2a
a=16, b=-5, c=18
x=[-(-35)±√(-35)²-4*16*18]/2*16
x= [35±√73]/32
x= 35+√73/32 and x= 35-√73/32
x=1.361 and 0.828.
Hence, the values for time is 1.361 and 0.828.
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find the slope between the following coordinates. (6,4)&(6,-2)
Answer:
slope is undefined
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6, 4 ) and (x₂, y₂ ) = (6, - 2 )
m = [tex]\frac{-2-4}{6-6}[/tex] = [tex]\frac{-6}{0}[/tex]
division by zero is undefined, therefore the slope of the vertical line is undefined.
When dante was born, his grandparents deposited $10,000 into a special college fund that paid 4% annual interest, compounded monthly. how old was dante when the balance in the account reached$13,000? round your answer to the nearest tenth of a year.
Using compound interest, it is found that Dante was 6.6 years old when the balance in the account reached $13,000.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.In this problem, we have that the parameters are given as follows:
A(t) = 13000, A(0) = 10000, r = 0.04, n = 12.
Hence the time in years is found as follows:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]13000 = 10000\left(1 + \frac{0.04}{12}\right)^{12t}[/tex]
[tex](1.0033)^{12t} = 1.3[/tex]
[tex]\log{(1.0033)^{12t}} = \log{1.3}[/tex]
[tex]12t\log{1.0033} = \log{1.3}[/tex]
[tex]t = \frac{\log{1.3}}{12\log{1.0033}}[/tex]
t = 6.6
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Whats the equation of the line that passes through the points (-8,4) and (0,22)
Answer:
d
Step-by-step explanation:
your answer to your question is D
For melions birthday she wanted to make fruit punch that had 2 1/2 gallons of orange juice, 4 quarts of cranberry juice, and 3 quarts of apple juice. how much did she make in all?
Answer:
4.25 gallons of juice
Step-by-step explanation:
4 quarts = 1 gallon
3 quarts = 3/4 gallon
2 1/2 + 1 + 3/4 = 3 2/4 + 3/4 = 3 5/4 = 4 1/4
4 1/4 = 4.25
give brainliest please
hope this helps :)
General Sherman, a tree located in Sequoia National Park, stands 275 feet tall. To see the top of the tree,
Carlos looks up at a 19° angle of elevation. If Carlos is 6 feet tall, how far is he from the base of the tree to the
nearest foot?
By using trigonometric relations, we will see that the distance between Carlos and the tree is:
D = 781.23 ft
How far is Carlos for the base of the tree?We can model this with a right triangle. We know that Carlos is 6ft tall, and the height of the tree is 275ft.
Then one of the cathetus of the triangle is equal to:
275ft - 6ft = 269ft.
That cathetus is the opposite cathetus to the angle of 19° (the elevation angle). And the adjacent cathetus is the distance between Carlos and the tree.
Then we can use the relation:
tan(a) = (opposite cathetus)/(adjacent cathetus).
Where:
a = 19°opposite cathetus = 269ftadjacent cathetus = D.Replacing that, we get:
tan(19°) = 269ft/D
Solving for D, we get:
D = 269ft/tan(19°) = 781.2ft
So we conclude that Carlos is at 781.23 ft of the tree.
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Find f(-2) for f(x) = 3.2.
O A. 2/1
OB.
36
O C. -36
OD. -12
3/4
Answer:
3/4 (A)
Step-by-step explanation:
replace x with -2 in the function
3 · 2^-2 = 3 · 0.25
3 · 0.25 = 0.75
0.75 = 3/4
A line passes through the points (6, 8) and (4, 2). What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y=3x-10
Step-by-step explanation:
Slope: (y2-y1)/(x2-x1)
(2-8)/(4-6)
slope= -6/-2 = 3
Point: (6,8)
Slope-intercept: y-y1=m(x-x1)
y-8=3(x-6)
y-8=3x-18
y=3x-10
Inspired by the works of Neil Dawson and Bert Flugelman, Kassidy drafts a design for a modern sculpture celebrating education. The sculpture is to be created from sheets of tempered spring steel, it will be hollow, and the supporting cone will not include a base.
Calculate the amount of steel Kassidy will need to create the sculpture if the base of the sculpture is 4-feet tall and has a 2-foot diameter.
Inspired by the works of Neil Dawson and Bert Flugelman, Kassidy drafts a design for a modern sculpture, the amount of steel Kassidy will need is mathematically given as
SA=16.094711 ft^2
What is the amount of steel Kassidy will need to create the sculpture if the base of the sculpture is 4-feet tall and has a 2-foot diameter.?Generally, the equation for the surface area of a cone is mathematically given as
SA=πr(rπ+√(h^2+r^2))
Therefore
SA=πr(rπ+√(h^2+r^2))
SA=π*1(1+√(4^2+1^2))
SA=16.094711 ft^2
In conclusion, the amount of steel Kassidy will need is
SA=16.094711 ft^2
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Which graph shows the information in the table?
Calories in Salad Dressing
Number of Ounces of Salad Dressing
Total Calories
2
300
3
450
4
600
5
750
On a coordinate plane, the x-axis is labeled ounces of salad dressing and the y-axis is labeled Total calories. A line goes through points (2, 300) and (4, 600).
On a coordinate plane, the x-axis is labeled ounces of salad dressing and the y-axis is labeled Total calories. A line goes through points (300, 2) and (600, 4).
On a coordinate plane, the x-axis is labeled ounces of salad dressing and the y-axis is labeled Total calories. A line goes through points (1, 200) and (2, 300).
On a coordinate plane, the x-axis is labeled ounces of salad dressing and the y-axis is labeled Total calories. A line goes through points (200, 1) and (300, 2).
The graph that shows the information on the table is On a coordinate plane, the x-axis is labeled ounces of salad dressing and the y-axis is labeled Total calories. A line goes through points (2, 300) and (4, 600).
How can the information on the table be represented?The independent variable is the number of ounces of salad dressing which means that it will be shown on the x axis.
The total calories is the dependent variable which means that it will be on the y axis.
The line drawn will pass through the points on the table of (2,300) and (4 ,600) so option A is correct.
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i need help finding out the answer
Answer:
D) 5.7 cmStep-by-step explanation:
Let the shorter sides be x.
Given:Isosceles and acute triangle.Longer side is 8 cm.To find:The length of the shorter sides, rounded to the nearest tenth.Solution:The angle at common vertex of congruent sides is less than 90°, since it is acute triangle.
It means the other congruent angles are greater than 45°, according to angle sum theorem.
The vertical bisector divides the triangle in half, with base 8/2 = 4 cm and hypotenuse x.
It gives us the inequality:
4/x < cos 45° ⇒ x > 4 / cos 45° = 5.656 x ≥ 5.7 cmCorrect choice is D
The sum of 3 times one number, x, and 6 times a second number, y, is 111. If the sum of the two numbers is 27, find the two numbers.
Enter a system of equations to represent the situation, then solve the system.
Step-by-step explanation:
using elimination method because this is a simultaneous equation
3×x+6×y=111
x+y=27
1×[3x+6y=111]
3×[x+y=27]
3x+6y=111—equation 1
3x+3y=81—equation 2
substrate equation 1 from equation 2
3y=30
divide both sides by 3
y=10
substitute 10 for y in equation 1
3x+6y=111
3x+6(10)=111
3x+60=111
3x=111-60
3x=51
divide both sides by 3
x=17
Part b
what is the area of the target that earns at least 30 points on a throw?
select the correct from the drop-down menu.
the area is ____ square inches.
a) 16
b) 49
c) 121
d) 144
Which rule describes the relationship between the x- and y-coordinates in the following table?
Y
1
6
4
15
6
21
Choose 1 answer:
A
Multiply by 6 to get y.
B
Multiply by 3. Then add 3 to the result to get y.
8
Answer: B
Step-by-step explanation:
We will test the options and see if they apply to the given values.
[A] ✗
1 * 6 = 6 ✓
4 * 6 ≠ 15✗
[B] ✓
1 * 3 = 3, 3 + 3 = 6 ✓
4 * 3 = 12, 12 + 3 = 15 ✓
6 * 3 = 18, 18 + 3 = 21 ✓
[C] ✗
1 * 8 = 8, 8 - 2 = 6 ✓
4 * 8 = 32, 32 - 2 = 30, 30 ≠ 15 ✗
find the 5th term of the GP is 48 and it 8th term is 384. find the first term and the common
Answer:
[tex]\text{1st term} = 3\\\\\text{Common ratio} = 2[/tex]
Step by step explanation:
[tex]\text{Given that,}\\\\\text{5th term} = ar^{5-1} = ar^4 = 48~~~~~~~~...(i)\\ \\\text{8th term} = ar^{8-1} = ar^7 = 384~~~~~~~...(ii)\\\\\text{1st term,}~ a = ?\\\\\text{Common ratio,}~ r = ?\\\\(ii) \div (i):\\\\~~~~~~\dfrac{ar^7}{ar^4}=\dfrac{384}{48}\\\\\implies r^{7-4} = 8\\\\\implies r^3 = 8\\\\\implies r^3 = 2^3\\\\\implies r =2\\\\\text{Substitute r = 2 in eq (i):}\\\\~~~~~~a\cdot 2^4 = 48\\\\\implies 16a =48\\\\\implies a = \dfrac{48}{16}\\\\\implies a = 3\\[/tex]
The time in seconds, t, it takes for a specific object being dropped from a particular height in feet above sea level, h, to reach the ground can be found by the radical function t equals one fourth times radical h period At what height should you drop an object in order for it to reach the ground in 16 seconds?
Answer:
B.) 4,096 feet
Step-by-step explanation:
You were given a time, and time in the equation is represented by "t". To find the height, represented by "h", you just need to plug the given value in for "t" and simplify to find "h".
t = (1/4)√x <--- Original equation
16 = (1/4)√x <--- Plug 16 in "t"
64 = √x <--- Divide both sides by (1/4)
4,096 ft = x <--- Square both sides
The object reach the ground in 16 seconds, you should drop it from a height of 4096 feet.
The equation is t=1/4 √x , where t is time in seconds and x is height in feet. To determine the height x at which an object should be dropped to reach the ground in 16 seconds, you can plug in the value of t=16 into the equation:
16 = 1/4 √x
Simplify the equation by multiplying both sides by 4:
4⋅16= √x
64= √x
Now, square both sides to isolate x:
64²=x
4096 = x
Therefore, to have the object reach the ground in 16 seconds, you should drop it from a height of 4096 feet.
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X-2y=-3 to standard form
Please help
Why is this not an equilateral triangle?
The given shape in the image is not an equilateral triangle.
What is an equilateral triangle?The triangle with all three sides equal and all the angles equal is called an equilateral triangle.
In the given figure we can see a triangle this triangle is not an equilateral triangle because the figure is formed between a square grid now if you see closely the base of the triangle can not be equal to the two sides of the triangle.
Because these two sides are the hypotenuse for the remaining right-angle triangle. So the base of the highlighted triangle can not be equal to the other two sides of the triangle.
Therefore given shape in the image is not an equilateral triangle.
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In the diagram below FG is parallel to CD. EF=6.9, FC=6.4, And GD= 5.1. Find the length of EF. Round your answer to the nearest 10th if necessary.
The length of EF which lie on line EC is 8.66 units.
What is parallel lines?Parallel lines are the lines that do not intersect or meet each other at any point in a plane. They are always parallel and are at equidistant from each other. Parallel lines are non-intersecting lines.
Here, EG = 6.9 , FC = 6.4, GD = 5.1
Also. FG || CD
By Basic Proportionality Theorem,
[tex]\frac{EF}{FC} = \frac{EG}{GD}[/tex]
[tex]EF = \frac{EG . FC}{GD}[/tex]
EF = (6.9 X 6.4) / 5.1
EF = 8.66 units
Thus, The length of EF which lie on line EC is 8.66 units.
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Hi, can you help me with this probability question?
I'd really appreciate some workings out too :)
Thanks,
the probability of getting a black one given that in the first draw we got a black one is P = 1/2 = 0.5
How to find the probability?
We will assume that all the beads have the same probability of being randomly selected.
Then the probability of picking a black bead is equal to the quotient between the number of black beads and the total number of beads.
Originally, there are 4 black ones and 3 red ones ( a total of 7).
We want to get the probability of getting a black one given that in the first draw we got a black one.
If in the first draw we got a black one, then now there are 3 blacks and 3 reds (a total of 6 beads).
So the probability of getting another black one is:
P = 3/6 = 1/2 = 0.5
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Please help! 30 points!
Answer:
it would be a vertical shift of 5 down
Step-by-step explanation:
I'm learning the same thing rn and that's right
A dishwasher was advertised at $640 with a further $175 for installation. Calculate the total purchase and installation costs if the cost of the dishwasher (excluding installation) is reduced by 18% due to minor scratching.
Answer:
$699.80
Step-by-step explanation:
$640 - 18% = 524.80
(640x18)/100 = 115.20
640-115.20 = 524.80
524.80+175 = 699.80
Answer:
$699.80
Step-by-step explanation:
640(18%)
640 x 18
100
reduce fraction
640 x 9
50
simplify
64 x 9
5
576
5. or 115 1
5. of 115.20
640 - 115.20 = 524.80 (dishwasher)
524.80 + 175 = 699.80 (total including installation)
c) Find the percentage of the instructors who are with the case based strategies (out of the subtotal).
pls help