Answer:
[tex]\sin(\alpha+\beta) = -0.153[/tex]
Step-by-step explanation:
Let determine the angles behind each trigonometric expression:
[tex]\cos \alpha = -\frac{8}{17}[/tex]
[tex]\alpha = \cos^{-1}\left(-\frac{8}{17} \right)[/tex]
Given that [tex]180^{\circ}< \alpha < 270^{\circ}[/tex], the value of [tex]\alpha[/tex] is:
[tex]\alpha \approx 241.928^{\circ}[/tex]
[tex]\sin \beta = -\frac{4}{5}[/tex]
[tex]\beta = \sin^{-1}\left(-\frac{4}{5} \right)[/tex]
Given that [tex]270^{\circ}< \beta <360^{\circ}[/tex], the value of [tex]\beta[/tex] is:
[tex]\beta \approx 306.870^{\circ}[/tex]
The sine function of the sum of angles can be determined by the following identity:
[tex]\sin(\alpha + \beta)=\sin \alpha \cdot \cos \beta + \sin \beta \cdot \cos \alpha[/tex]
If [tex]\alpha \approx 241.928^{\circ}[/tex] and [tex]\beta \approx 306.870^{\circ}[/tex], then:
[tex]\sin (241.928^{\circ}+306.870^{\circ}) = (\sin 241.928^{\circ}) \cdot (\cos 306.870^{\circ}) + (\sin 306.870^{\circ})\cdot (\cos 241.928^{\circ})[/tex][tex]\sin(241.928^{\circ}+306.870^{\circ}) = -0.153[/tex]
I need help ASAP!! If you know what you’re doing go ahead and answer but if you don’t, don’t even bother thanks
Answer:
133.97 cm³
Step-by-step explanation:
The volume of a cone is given by:
[tex]V = \frac13 \pi r^2h[/tex]
r is half the diameter, so 4 cm
h is 8 cm
So:
V= 1/3 * 3.14 * 16 * 8 ≈ 133.97 cm³
Find the area of the composite shape... WILL MARK BRAINIEST
Answer:
324.5m^2
Step-by-step explanation:
To find the area of the composite shape, divide the shape into 3 known shapes and calculate their areas.
SO, here we divide the shape into 2 triangles and 1 rectangle.
Area of rectangle = 15 x 8 = 120m^2
Area of triangle 1 = 1/2 x 7 x 15 = 52.5m^2
Area of triangle 2 = 1/2 x 9 x 8 = 4 x 9 = 32cm^2
Now, the sum of these areas = area of composite shape = 32 + 52.5 + 120 = 204.5m^2
Hope this helps.
Please mark brainiest
Good Luck
Answer: 52.5 + 36 + 120 = 208.5
208.5 m is your answer.
Step-by-step explanation: To come to this, first you have to break the composite shape into the three different shapes that you see. 2 rectangles and a triangle. From there, you simply solve the area for each individual shape and then add them together as shown in the answer.
Patty buys a new car and gets it appraised every few years. After owning the car for 3 years, it’s value is $15,000. After owning the car for 5 years, it’s value is $9,000. What is the constant of proportionality in this inverse variation?
Answer: $3,000 per year
Step-by-step explanation: 15,000 divided by 9,000 is 6,000, 5 minus 3 is 2 6,000 divided by 2 equals 3,000.
Work out the mean for the data set below: 1, 2, 1, 2, 2, 5 Give your answer as a fraction.
Answer:
13/6 or 2 and 1/6
Step-by-step explanation:
The mean (or average) is the sum of all elements divided by the amount of elements. In this case that would be (1 + 2 + 1 + 2 + 2 + 5) / 6 = 13 / 6 or 2 1/6
After 2.4 hours Jenny had traveled 216 miles. If she travels at a constant speed, how far will she have traveled after 4 hours
Answer:bruh
Step-by-step explanation:
I couldn’t even tell u
Simplify the expression in the following photo.
Answer:
0
Step-by-step explanation:
If we factor out √5a from the numerator we have √5a * (√4 - √9 + √1) / √5a. √5a cancels out so we are left with √4 - √9 + √1 which equals 2 - 3 + 1 = 0.
Anyone know the answer to this one ?
Answer: B) y = 2 · 3ˣ
Step-by-step explanation:
We can see that (2, 18) is a point on the graph.
Plug it into the equations to see which one make a true statement.
A) y = 1 · 3ˣ
18 = 1 · 3²
18 = 1 · 9
18 ≠ 9
B) y = 2 · 3ˣ
18 = 2 · 3²
18 = 2 · 9
18 = 18 This works!
C) y = 3 · 2ˣ
18 = 3 · 2²
18 = 3 · 4
18 ≠ 12
D) y = 4 · 3ˣ
18 = 4 · 3²
18 = 4 · 9
18 ≠ 36
In how many ways can 2 juniors and 2 seniors be selected from a group of 8 juniors and 6 seniors?
Answer:
Step-by-step explanation:
8c2×6c2=((8×7)/2)×((6×5)/2)=28×15=420
Calculate the measure of arc AG if a=20 and b=10
Answer:
90°
Step-by-step explanation:
∆GFD is an isosceles right triangle, so angle FDG is 45°. Segment DF bisects angle EDG, so that angle is 90°.
Arc AG is the other half of the semicircle AGE that includes 90° arc GE.
So, arc AG is 90°.
__
Comment on the problem
"a" and "b" are irrelevant to arc AG. They come into play for arc CE.
Please answer this question now
Answer:
17.3
Step-by-step explanation:
The following data were obtained from the question:
Angle T = 87°
Side T = t
Side V = 14
Side U = 11
The value of t can be obtained by using cosine rule as show below:
t² = u² + v² – 2uv cosT
t² = 11² + 14² – 2×11×14 cos 87°
t² = 121 + 196 – 308 × Cos 87°
t² = 300.88
Take the square root of both side
t = √300.88
t = 17.3
Therefore, the value of t is 17.3
What is the relationship between angles 1 and 2? AB Is parallel to FG AND BC IS TO DE
Answer:
Angles 1 and 2 are supplementary.
Step-by-step explanation:
<BAC is equal to <FGE, because BC and DE are parallel. So <DGF would be 180° minus angle 1. So, they are supplementary.
Mark me brainliest if possible. Thank you.
If α and β are the zeros of the quadratic polynomial f(x) = 3x2–4x + 5, find a polynomialwhose zeros are 2α + 3β and 3α + 2β.
Answer:
[tex]\boxed{\sf \ \ \ 3x^2-20x+37\ \ \ }[/tex]
Step-by-step explanation:
Hello,
a and b are the zeros, we can say that
[tex]f(x)=3(x^2-\dfrac{4}{3}x+\dfrac{5}{3}) = 3(x-a)(x-b)=3(x-(a+b)x+ab)[/tex]
So we can say that
[tex]a+b=\dfrac{4}{3}\\ab=\dfrac{5}{3}[/tex]
Now, we are looking for a polynomial where zeros are 2a+3b and 3a+2b
for instance we can write
[tex](x-2a-3b)(x-3a-2b)=x^2-(2a+3b+3a+2b)x+(2a+3b)(3a+2b)\\= x^2-5(a+b)x+6a^2+6b^2+9ab+4ab[/tex]
and we can notice that
[tex]a^2+b^2=(a+b)^2-2ab[/tex] so
[tex](x-2a-3b)(x-3a-2b)=x^2-5(a+b)x+6[(a+b)2-2ab]+13ab\\= x^2-5(a+b)x+6(a+b)^2+ab[/tex]
it comes
[tex]x^2-5*\dfrac{4}{3}x+6(\dfrac{4}{3})^2+\dfrac{5}{3}[/tex]
multiply by 3
[tex]3x^2-20x+2*16+5=3x^2-20x+37[/tex]
What stamens is converse of p
p: If every fourth card drawn is a spade, then 25% of the cards in a deck would be spades. If 25% of the cards in a deck are spades, then every fourth card drawn would be a spade. If every fourth card drawn isn’t a spade, then 25% of the cards in a deck aren’t spades. If 25% of the cards in a deck aren’t spades, then every fourth card drawn wouldn’t be a spade. If every fourth card drawn isn’t a spade, then 75% of the cards in a deck are spades.
Answer:25
Step-by-step explanation:
Get monkeyd
A drawer contains three red marbles, four green marbles, and five blue marbles. One marble is taken from the drawer and then replaced. Another marble is taken from the drawer. The problem models: a dependent event. independent events.
Answer:
independent events
Step-by-step explanation:
dependent is when the previous event affects the outcome of the next event.
Ex: When I draw a card without replacement at first I will have 52 cards. Once I draw the card, I will have only 51 cards to choose from.
Independent event is when the outcome is not related.
Example like the problem given to you
Please answer now only have two minutes left do it fast
Answer:
work is shown and pictured
If y varies inversely as x, and y = 10 when x = 20,
find x when y = 16.
Answer:
12.5
Step-by-step explanation:
y varies inversely as x.
y = k/x
10 = k/20
200 = k
The constant proportion k is 200.
16 = 200/x
Cross multiply.
200 = 16x
200/16 = x
x = 12.5
Please answer this question now in two minutes
Answer:
y = 2x +10
Step-by-step explanation:
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
__
Comparing this to the given equation, we see that line s has a slope of -1/2. The perpendicular line t will have a slope that is the negative reciprocal of this:
m = -1/(-1/2) = 2
Using the above point-slope form equation, we can write the equation of line t as ...
y -4 = 2(x -(-3))
y = 2x +6 +4 . . . . add 4, simplify
y = 2x +10 . . . . equation of line t
The graph below represents the solution set of which inequality?
Answer:
x < 2
Step-by-step explanation:
The indicated part is left from point 2.
You see an open circle at point (2,0) which means you should exclude the point x = 2 in the inequation.
Now you have enough info to get the right inequality:
x < 2
what is the square root of 0.49
Answer:
0.7
if you multiply 0.7 with 0.7 you get 0.49 so 0.7 is the square root
Hope this helps
Step-by-step explanation:
Answer:
0.7
Step-by-step explanation:
0.49 = 49/100
√(49/100)
√49/√100
7/10
= 0.7
What is the y-intercept of the line whose equation is 2x-3y=-6
Answer:
(0, -2)
Step-by-step explanation:
Step 1: Write equation in slope-intercept form
-3y = 6 - 2x
y = -2 - 2/3x
Step 2: Find y-int
y = -2 -2/3(0)
y = -2
(0, -2)
4. How else can the ratio 4/5 be written?
O A.4:5
O B.5:4
O C.54
O D..2
Answer:
Answer is option a) 4:5
Step-by-step explanation:
[tex]the \: ratio \: \frac{4}{5} can \: \\ also \: be \: written \: as \: 4 : 5[/tex]
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
What formula tells the cost, in dollars, if
chocolate chip cookies are $1.50/dozen and
lemon frosteds are $ 1.00/dozen? Let c =
number of dozens of chocolate chip cookies; L=
number of dozens of lemon frosteds; T = total
charge.
Answer:
T = $1.50C + $1.00L
Step-by-step explanation:
Chocolate chip cookies - $1.50/dozen
C: # of dozens of chocolate chip cookies
↓
$1.50C
Lemon Frosteds - $1.00/dozen
L: # of dozens of lemon frosteds
↓
$1.00L
T(total) = $1.50C + $1.00L
Hope that helps.
Consider the numbers p
= 2.78 × 10^11 and q = 3.12 × 10^-3
Calculate 3 radical p/q.
Give your full calculator display.
Answer:
44664.59503
Step-by-step explanation:
Hello,
In this question, you're asked to find the radical of a number. However in mathematics, the radical of a number simply means "√" and not directly square root of that number, its could be the cube root "³√" or even the fourth root "⁴√".
In this case, we're asked to find the 3 radical of p/q which means 3√(p/q)
P = 2.78×10¹¹
Q = 3.12×10⁻³
p / q = 2.78×10¹¹ / 3.12×10⁻³
p / q = 8.91×10¹³
The 3 radical = 3√(8.91×10¹³)
3√(p/q) = 44664.59503
the lowest number is 11 the range is 13 and the median is 17 what are the 3 numbers
Answer:
11, 17, and 28.
Step-by-step explanation:
[tex]x, y, z\\[/tex]
Lowest number is [tex]x[/tex]
Median is [tex]y[/tex]
Highest number is [tex]z[/tex]
[tex]x=11\\y=17\\\\z-x=17\\z-11=17\\z-11+11=17+11\\z=28\\\\x=11\\y=17\\z=28\\\\11, 17, 28[/tex]
The three numbers are 11 , 17 and 24
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first number be = a
Let the second number be = b
Let the third number be = c
And , the lowest number is 11
So , the value of a = 11
The median is 17
So , the value of the middle number b = 17
Now , the range of the three numbers = 13
So , the maximum value - minimum value = 13
Substituting the values in the equation for range , we get
c - a = 13
c - 11 = 13
Adding 11 on both sides , we get
c = 11 + 13
c = 24
Therefore , the value of a = 11 , b = 17 and c = 24
Hence , The three numbers are 11 , 17 and 24
To learn more about equations click :
https://brainly.com/question/10413253
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ASAP The rectangle below has been enlarged by a scale of 3.5. A rectangle with a length of 8 and width of 6. [Not drawn to scale] What is the area of the enlarged rectangle?
Answer:
588 units^2
Step-by-step explanation:
To find the area of the enlarged rectangle, first find the length and width of the enlarged rectangle.
This is 3.5 multiplied by their original measures:
Length = 3.5 x 8 = 28
Width = 3.5 x 6 = 21
Now, area =. LxW = 588 units^2
Hope this helps
Answer:
588 units squared
Step-by-step explanation:
We have a rectangle that has dimensions 8 units by 6 units.
From the problem, we know that this rectangle has been enlarged by a scale of 3.5. Essentially, to obtain the dimensions of the new, bigger rectangle, we multiply the current length (8 units) by 3.5 and the current width (6 units) by 3.5:
new length = 8 * 3.5 = 28 units
new width = 6 * 3.5 = 21 units
Given this, we can now calculate the area.
The area of a rectangle is denoted by A = lw, where l is the length and w is the width.
Here, the length is l = 28 and the width is w = 21. Plug these in:
A = lw
A = 28 * 21 = 588
The answer is thus 588 units squared.
~ an aesthetics lover
I need help pls A certain university in the United States has a student enrollment of 19,100. Mr. Hill knows the percentage of students that are male and the percentage of students that are female. Suppose a student reaches in the bag and randomly selects nine red chips and eleven yellow chips. Based on this sample, what is a good estimate for the number of enrolled university students that are male?
Answer:
About 8595 students
Step-by-step explanation:
If approximately 9/20 of the students are male, multiplying this by the total number of students enrolled will give a good approximation of the total number of enrolled males. 9/20 * 19100=8595. Hope this helps!
Answer:
8595
Step-by-step explanation:
9/11 is the ratio of male to female
9/20 of students are male and 11/20 are female
If total number is 19100,
then male= 19100*9/20= 8595
Which of the following expressions is equivalent to -10? Which of the following expressions is equivalent to -10?
-7 + 3
-3 - 7
3 - 7
7 - 3
Answer:
-3-7
Step-by-step explanation:
-3-7=10
Answer:
-3 - 7.
Step-by-step explanation:
-3 - 7 = -10.
Which best describes the relationship between the line that passes through the points (9, –1) and (11, 3) and the line that passes through the points (–6, –4) and (–4, 0)?
Answer:
They are parallel
Step-by-step explanation:
You can tell that they are parallel because if you find the slope of it, you can see that they both have a slope of 2.
Hope this is the answer you were looking for. :)
Please help me.. very appreciated if you do
1 Answer:
D
2 Answer:
B
Step-by-step explanation:
-x ≤ -3all we should do here is multiply both sides by -1 and switch the sign ≤ since we multiplied by a negative number
-x ≤ -3 x ≥ 3x is equal or greater than 3 so 3 is included
3 will be represented by a clored dot
so the graph is D
-6- x ≤ -3again multiply by -1 to get rid of the - signs and switch ≤ by ≥ since it's a negative number
-6 -x ≤ -3 6+x ≥ 3 substract 6 from both sides x+6-6 ≥ 3-6 x ≥ -3x is equal or greater than -3 so -3 is included
the graph is b since there is a dot in -3
Which value of x from the set {4, 5, 6, 7), makes this equation true?
4(8 - x) = 8
OA.
4
B.
5
OC. 6
OD.
7
Hey there! :)
Answer:
C. x = 6.
Step-by-step explanation:
Given:
4(8 - x) = 8
Solve for x. Distribute:
32 - 4x = 8
Subtract 32 from both sides:
-4x = -24
Divide both sides by -4:
-4x/(-4) = -24/(-4)
x = 6.