Answer:
31°,59°
Step-by-step explanation:
csc (2x+9)=sec(3x+26)
1/sin(2x+9)=1/cos (3x+26)
sin (2x+9)=cos(3x+26)
cos (90-2x-9)=cos(3x+26)
90=3x+26+2x+9
5x+35=90
5x=90-35=55
x=55/5=11
2x+9=2×11+9=31°
3x+26=3×11+26=59°
In a game for 24 groups, the average number of children was 16. When one more group of children was formed to join in the game, the average number of children became 18. The number of boys to girls who had just joined in the game was in the ratio 5:6. If there were 220 boys at first, how many more boys than girls were in the end?
Answer:
50 boys
Step-by-step explanation:
The number of groups = 24
The average number of children = 16
The new average number of children when one group is added = 18
The ratio of boys to girls in the group that just joined = 5:6
The initial number of boys = 220
Let the initial number of children
The initial total number of children = 24 × 16 = 384
The initial number of girls = 384 - 220 = 164
The final number of children = 25 × 18 = 450
The number of children in the group that joined in the game = 450 - 384 = 66
The ratio of boys to girls in the group = 5:6
Therefore, we get;
The number of boys = 66 × 5/11 = 30
The number of girls = 66 - 30 = 36
The number of boys at the end = 220 + 30 = 250
The number of girls at the end = 164 + 36 = 200
The number of more boys than girls at the end = 250 - 200 = 50
The number of more boys than girls at the end = 50 boys
Find the midpoint of the line segment with these endpoints: (-4,3), (-1,5)
In which quadrant is the midpoint?
Answer:
(-5/2, 4)
Second quadrant
Step-by-step explanation:
Mathematically, we can calculate the midpoint using the formula;
(x,y) = (x1 + x2)/2, (y1 + y2/2
We have;
(x,y) = (-4-1)/2, (3+5)/2
(x,y) = (-5/2, 4)
to get the quadrant, as we can see, this is negative x and positive y and that makes it the 2nd quadrant
PLEASE HELP MEE 1616,
What is the value of f in the equation 7f-1=6
Answer:
f=1
Step-by-step explanation:
Answer:
Then vaule of f is 1
Step-by-step explanation:
The vaule of f is 1 because 7 x 1 = 7 - 1 =6
Solve for x. x-6 8x + 24
Answer:
x = 18
Step-by-step explanation:
The 2 angles lie on a straight line and sum to 180° , then
x - 6 + 8x + 24 = 180
9x + 18 = 180 ( subtract 18 from both sides )
9x = 162 ( divide both sides by 9 )
x = 18
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND :}}}[/tex]
The value of [tex]x[/tex].
[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { x\:=\:18}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
We know that,
[tex]\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]
➪ [tex]x[/tex] - 6 + 8[tex]x[/tex] + 24 = 180°
➪ 9[tex]x[/tex] + 18 = 180°
➪ 9[tex]x[/tex] = 180° - 18
➪ 9[tex]x[/tex] = 162
➪ [tex]x[/tex] = [tex]\frac{162}{9}[/tex]
➪ [tex]x[/tex] = 18
Therefore, the value of [tex]x[/tex] is 18.
Now, the two angles are:-
( [tex]x[/tex] - 6 ) = ( 18 - 6 ) = 12°( 8[tex]x[/tex] + 24 ) = ( 8 x 18 + 24 ) = 144 + 24 = 168°[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]
✒ 12° + 168° = 180°
✒ 180° = 180°
✒ L. H. S. = R. H. S.
[tex]\sf\blue{Hence\:verified.}[/tex]
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]
A biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts one hundred bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Assuming exponential growth, what is the growth constant "k" for the bacteria? (Round k to two decimal places.) find the
number of bacteria after 13 hours
Answer:
k=.25068
Step-by-step explanation:
450 = 100 [tex]e^{6k}[/tex]
4.5 = [tex]e^{6k}[/tex]
ln(4.5) = 6k
k= ln(4.5)/6
k=.25068
The number of bacteria after 13 hours will be 2579.
What is an exponential expression?Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."
Given that a biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts one hundred bacteria into what he has determined to be a favourable growth medium. Six hours later, he measures 450 bacteria.
The bacteria after 13 hours will be calculated as,
[tex]N=100(e)^{13\times 0.25)[/tex]
[tex]N = 100\times e^{3.25}[/tex]
N = 2579.
Therefore, the number of bacteria after 13 hours will be 2579.
To know more about an exponential expression follow
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let A=(1,2,3,4,5)which of the following sets are equal to A?
1.=(4,1,2,3,5)
2.=(1,2,3,4,5,6)
3.(x:x is interger & xsquare ≤ 25)
4.(x:x is a positive integer and x ≤5)
5.(x:x is a whole number and ≤ 5)
Answer:
1. (4,1,2,3,5)
Step-by-step explanation:
Since all the members of set A are present in "1"
A walking path across a park is represented by the equation y = -3x - 6. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-3, 3). Identify the
equation that represents the new path.
Answer:
y = 1/3 x +4
Step-by-step explanation:
m = 1/3
3 = 1/3(-3) + b
3 = -1 +b
b=4
Solve the system by substitution.
y = -5x
y= -7x – 14
Answer:
x = -7 y = 35
Step-by-step explanation:
-5x = -7x - 14
2x = -14
x = -7
y = -5(-7)
y = 35
gregory wants to buy a new video game system priced at $179.00. if the sales tax is 6%, what is the total amount he will pay for the video game system
Answer:
$189.74
Step-by-step explanation:
Since the sales tax is 6%,
179x0.06=10.74
Add to the starting price, 179.00+10.74=189.74!
I hope this helped!
A triangle with the coordinates X(3, 2), Y(5, -1), and Z(-2,3) is reflected across both the x- and y-axes. The coordinates after both reflections are X'( ), Y'( ), and Z'( ).
Answer:
X'(-3, -2), Y'(-5, 1), and Z'(2, -3)
Prove that A - B = A-(A n B) using a Venn diagram
Step-by-step explanation:
my answer is an image above
Solving equations:
(a) 5x - 9 = 3x + 3
(b) x + 6 = 34 - x
Answer:
a) 5x - 9 = 3x + 3
5x - 3x = 3 + 9
2x = 12
x = 12 / 2
x = 6
b) x + 6 = 34 - x
x + x = 34 - 6
2x = 28
x = 28 / 2
x = 14
[tex] \: (a)5x - 9 = 3x + 3 \\ 5x - 9 - 3x = 3 \\ 2x - 9 = 3 \\ 2x = 3 + 9 \\ 2x = 12 \\ x = \frac{12}{2} \\ x = 6 \\ (b) \: x + 6 = 34 - x \\ x + 6 + x = 34 \\ 2x + 6 = 34 \\ 2x = 34 - 6 \\ 2x = 28 \\ x = \frac{28}{2} \\ x = 14[/tex]
HOPE IT HELPS!!!I NEED BRAINLIEST ✌️ PLZWhich of the following regression equations best fits the data shown below?
Answer:
the answer is A
Step-by-step explanation:
sorry if im worng
The value of a car has decreases by 5% each year. Sophie bought a car two years ago for £10000 work out the value now .
Answer:
£9000
Step-by-step explanation:
= £10 000× 5 ×2
100
= 1000
= £10 000-1000
= £9000
What is the measure of ZR?
8
8
P
R.
A. 32°
B. 40°
O
C. Cannot be determined
D. 64°
Answer:
option A
Step-by-step explanation:
since the two sides of the triangle are equal the given triangle is an isosceles triangle.
Base angles of an isosceles triangle are equal.
angle P = angle R
32 degree = angle R
The measure of <QRP = 32 degree.
What is an Isosceles Triangle?An isosceles triangle is one with two sides that are the same size and a third side that is a different size.
According to the isosceles triangle theorem, if two sides of a triangle are congruent, the angles across from those sides are likewise congruent.
We have,
A triangle whose two sides are 8 unit each and an angle 32.
As, we know a triangle whose two sides are equal is said to be isosceles triangle.
So, the given triangle is isosceles.
Now, angle opposite to equal sides are also equal.
so, <QPR = <QRP = 32 degree
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What type of solutions will a quadratic equation have when the discrimination b^2 - 4ac in the quadratic formula is negative? (plz give explanations)
a - two nonreal solutions
b - one real solution
c - two real solutions
d - no solutions
Answer:
Step-by-step explanation:
The discriminant comes from the quadratic formula. We use the discriminant to determine, before factoring, what types of solutions we can expect when we do factor. In the quadratic formula, the discriminant is under a square root sign. If the number under a square root sign is negative (meaning the discriminant is negative), we will not have real number solutions because you can't have a negative number under a square root. So a is your choice.
Answer:
a
Step-by-step explanation:
Does anyone know the answer to this question ?
Answer:
12/25 = 48/100 = .48 = 48%
Step-by-step explanation:
Worth 10 pts
Plssssssssssssssssss help
Will give brainliest
Answer: [tex]2\sqrt{2}+\sqrt{3}\\\\[/tex]
a = 2 and b = 1
=======================================================
Explanation:
Set the expression equal to the given form we want. Then square both sides so we get rid of the outer-most square root
[tex]\sqrt{11+4\sqrt{6}} = a\sqrt{2}+b\sqrt{3}\\\\\left(\sqrt{11+4\sqrt{6}}\right)^2 = \left(a\sqrt{2}+b\sqrt{3}\right)^2\\\\11+4\sqrt{6} = \left(a\sqrt{2}\right)^2+2*a\sqrt{2}*b\sqrt{3}+\left(b\sqrt{3}\right)^2\\\\11+4\sqrt{6} = 2a^2+2ab\sqrt{2*3}+3b^2\\\\11+4\sqrt{6} = 2a^2+3b^2+2ab\sqrt{6}\\\\[/tex]
In the third line, I used the rule that (x+y)^2 = x^2+2xy+y^2
-------------------
At this point, we equate the non-radical and radical terms to get this system of equations
[tex]\begin{cases}11 = 2a^2+3b^2\\ 4\sqrt{6} = 2ab\sqrt{6}\end{cases}[/tex]
The second equation turns into 4 = 2ab when we divide both sides by sqrt(6)
Then 4 = 2ab turns into ab = 2 after dividing both sides by 2.
We're told that a,b are rational numbers. Let's assume that they are integers (which is a subset of the rational numbers).
If so, then we have these four possibilities
a = 2, b = 1a = -2, b = -1a = 1, b = 2a = -1, b = -2If a,b are negative, then you'll find that [tex]a\sqrt{2}+b\sqrt{3}[/tex] overall is negative. But this contradicts that [tex]\sqrt{11+4\sqrt{6}}[/tex] is positive. So a,b must be positive.
Let's assume that a = 1 and b = 2. If so, then,
2a^2+3b^2 = 2(1)^2+3(2)^2 = 14
but we want that result to be 11 instead.
Let's try a = 2 and b = 1
2a^2+3b^2 = 2(2)^2+3(1)^2 = 11
which works out perfectly.
Therefore,
[tex]\sqrt{11+4\sqrt{6}} = 2\sqrt{2}+\sqrt{3}\\\\[/tex]
---------------------------------
Checking the answer:
Use a calculator to find that
[tex]\sqrt{11+4\sqrt{6}} \approx 4.5604779\\\\2\sqrt{2}+\sqrt{3} \approx 4.5604779\\\\[/tex]
both have the same decimal approximation, so this is a fairly informal way to confirm the answer.
Another thing you can do is to take advantage of the idea that if x = y, then x-y = 0
So if you want to see if two things are equal, you subtract them. You should get exactly 0 or something very small (pretty much equal to 0).
If the circumference is 56cm find the area of the circle
Answer:
The First answer
Step-by-step explanation:
56 divided by 2 is the radius which is 28 and that squared times pi is 2464
solve it : -
[tex] \sqrt{18 \times 2} [/tex]
________
Answer:
6
Step-by-step explanation:
sqrt(36)
sqrt(6^2)
6
Answer:
6
Step-by-step explanation:
18 * 2 = 64
√64 = 6
6
2
Add
3
+
7. Simplify the answer and write as a mixed number.
.
Question Help: Video
Submit Question
Answer:
1 11/21
Step-by-step explanation:
Use common denominator of 3 * 7 = 21
2/3 * 7/7 = 14/21
6/7 * 3/3 = 18/21
-------------------------
14/21 + 18/21 = 32/21
Reduce
32/21 = 1 11/21
Answer: 1 11/21
Step-by-step explanation:
Data: 2/3+6/7=x
Step one, Find the common denominator
(2/3)x7(for each number)=14/21
(6/7)x3(for each number)=18/21
Reason: To add fractions, you always have to find the common denominator(so you can make the denominator the same for each fraction). The common denominator of 3 and 7 is 21 and since what you do to the bottom has to be done to the top, you multiply 2 by 7 and 6 by 3 to end up with 14/21 and 18/21.
Step two, add
14/21+18/21=32/21=1 11/21
Reason: Since we have our common denominators, we just have to add and, with fractions, you only add the top(numerator) and not the bottom(denominator) you end up with 32/14 but when made into a mixed fraction(by dividing the bottom into the top and leaving the remainder on the top) you get 1 11/21 which can't be simplified.
So since it can't be simplified, it's your answer
I hope this helps!
Math help please show work I will mark Brainlist if correct
Answer:
Step-by-step explanation:
(1).
(a). 1 m ≈ 3.28 ft.
128 m ≈ 419.84 ft.
(b). 1 yd. ≈ 0.0009144 km
3910 yd. ≈ 3.58 km
(2). 1 m ≈ 0.0006214 mi.
10 000 m ≈ 6.2 mi.
A triangle has side length 3,8 and 9. Find the angle measurement for the angle cross from the side with length of 8.
Answer:
The angle measurement is 61.218°
Step-by-step explanation:
I used a triangle calculator
In a sale of 30% discount, the selling price of a LED TV was AED 4200. Calculate the price of TV before sale.
Answer:
3000
Step-by-step explanation:
30%×100=3000
then the profit is=
4200-3000=1200
What is the fractional equivalent of the repeating decimal 0.3
Answer: 0.3 repeating as a fraction is equal to 1/3explanation:
34. Find the mean for the following data X F 10 3 12 5 14 4 16 5 18 3
A theater has 56 rows of seats. If there are 13 seats in the first row, 18 in the 2nd row, 23 in the 3rd row. How many seats are there in total
Answer:
8428
Step-by-step explanation:
According to the Question,
Given, A theater has 56 rows of seats. If there are 13 seats in the first row, 18 in the 2nd row, 23 in the 3rd row.We have a number sequence 13, 18, 23, ...
We can say that this is an arithmetic sequence because of the common difference 'd', is equal to 5, and the first term 'a1' is equal to 13.The formula for the sum of an arithmetic sequence with n terms is given is [tex]S_n= \frac{n}{2} [2a_1+(n-1)d]S[/tex] .Substitute the given values into the equation to solve for the sum of the 56 rows of seats.
[tex]S_56= \frac{56}{2}[2(13)+(56-1)(5)]\\S_{56}=28\left[26+275\right]\\S_{56}=28\left[301\right]\\S_{56}=8428[/tex]
Therefore, there are 8428 seats in all.
Someone help
Please with the one I have circled everyone keeps saying it’s 15 but it’s incorrect when I put it in please help
Answer:
w
Step-by-step explanation:
Monday = 4
Tuesday = 1/3 w (where w is the miles walked on Wednesday)
Wednesday = w
Total = 24
4 + 1/3 w + w = 24
Combine like terms
4 + 4/3 w = 24
Subtract 4 from each side
4/3 w = 20
Multiply each side by 3/4
w = 20 *3/4
w = 15
In the equation when we start, we need to put the variable, not the solution
At the end we have the solution
Determine the intercepts of the line.
y
=
11
x
+
6
Answer:
intercepts are (-6/11 , 0) and ( 6,0 )
PLZ HELP WILL GIVE BRAINLY IF RIGHT!!!
-2(x-4)=4x+2x+8
Answer:
x = 0
Step-by-step explanation:
-2(x-4)=4x+2x+8
Distribute
-2x +8 =4x+2x+8
Combine like terms
-2x+8 =6x+8
Add 2x to each side
-2x+2x+8 =6x+2x+8
8 = 8x+8
Subtract 8 from each side
8-8 = 8x+8-8
0 = 8x
Divide by 8
0=x
Answer:
x = 0
Step-by-step explanation:
-2(x-4) = 4x+2x+8
-2x+8 = 6x+8
8-8 = 6x+2x
0 = 8x
x = 0
Hope this will help and if so, then please mark me as brainliest.