Answer:
The cost of an adult ticket is $12.50
Step-by-step explanation:
The given information are;
The cost of two adult tickets and three children tickets = $43.00
The cost of one adult ticket and one child ticket = $18.50
Whereby the cost of an adult ticket is represented by x and the cost of a child's ticket is represented by y, we get the following two simultaneous equations;
2·x + 3·y = 43.00...(1)
x + y = 18.5...(2)
(ii) Multiplying equation (2) by 2 and subtracting the result from equation (1) gives;
2·x + 3·y - 2×(x + y) = 43 - 2×18.5 = 6
2·x - 2·x + 3·y - 2·y = 0 + y = 6
∴ y = 6
The cost of each the children ticket = $6.00
From equation (2), where y = 6, we get;
x + y = 18.5
∴ x + 6 = 18.5
x = 18.5 - 6 = 12.5
The cost of an adult ticket, x = $12.50.
Circle the equation of a straight line that does not intersect the curve y = x2
(1 m
y = 5
X=-3
y = 2x - 5
y= -3x + 1
Answer:
[tex] \boxed{y = 2x\: – \: 5} [/tex]
2
Solve the equation log, (3t+9) - log, 21 =1
Answer:
67
Step-by-step explanation:
log(3t+9)-log21 = 1
Applying, the law of logarithm,
log(3t+9)/21 = 1
converting the log into index
(3t+9)/21 = 10
solving for t
3t+9 = 21×10
3t+9 = 210
3t = 210-9
3t = 201
t = 201/3
t = 67
A tortoise moves forward 15 meters in one hour. It turns around and crawls 10 meters in the
next hour. Finally, in the third hour, it turns around again and crawls 8 more meters. How
much did the tortoise walk in total in 3 hours?
Answer:
Below.
Step-by-step explanation:
15+10+8=33.
Answer:
13 meters
Step-by-step explanation:
It went 15 meters, but then it went back 10 meters.
[tex]15-10=5[/tex]
Then it went 8 more meters.
[tex]5+8=13[/tex]
Hope this helped! Please mark brainliest :)
which of the following are identities? check all that apply.
A. (sinx + cosx)^2= 1+sin2x
B. sin6x=2 sin3x cos3x
C. sin3x/sinxcosx = 4cosx - secx
D. sin3x-sinx/cos3x+cosx = tanx
Answer: (a), (b), (c), and (d)
Step-by-step explanation:
Check the options
[tex](a)\\\Rightarrow [\sin x+\cos x]^2=\sin ^2x+\cos ^2x+2\sin x\cos x\\\Rightarrow [\sin x+\cos x]^2=1+2\sin x\cos x\\\Rightarrow \Rightarrow [\sin x+\cos x]^2=1+\sin 2x[/tex]
[tex](b)\\\Rightarrow \sin (6x)=\sin 2(3x)\\\Rightarrow \sin 2(3x)=2\sin (3x)\cos (3x)[/tex]
[tex](c)\\\Rightarrow \dfrac{\sin 3x}{\sin x\cos x}=\dfrac{3\sin x-4\sin ^3x}{\sin x\cos x}\\\\\Rightarrow 3\sec x-4\sin ^2x\sec x\\\Rightarrow 3\sec x-4[1-\cos ^2x]\sec x\\\Rightarrow 3\sec x-4\sec x+4\cos x\\\Rightarrow 4\cos x-\sec x[/tex]
[tex](d)\\\Rightarrow \dfrac{\sin 3x-\sin x}{\cos 3x+\cos x}=\dfrac{2\cos [\frac{3x+x}{2}] \sin [\frac{3x-x}{2}]}{2\cos [\frac{3x+x}{2}]\cos [\frac{3x-x}{2}]}\\\\\Rightarrow \dfrac{2\cos 2x\sin x}{2\cos 2x\cos x}=\dfrac{\sin x}{\cos x}\\\\\Rightarrow \tan x[/tex]
Thus, all the identities are correct.
A. Not an identity
B. An identity
C. Not an identity
D. An identity
To check whether each expression is an identity, we need to verify if the equation holds true for all values of the variable x. If it is true for all values of x, then it is an identity. Let's check each option:
A. [tex]\((\sin x + \cos x)^2 = 1 + \sin 2x\)[/tex]
To check if this is an identity, let's expand the left-hand side (LHS):
[tex]\((\sin x + \cos x)^2 = \sin^2 x + 2\sin x \cos x + \cos^2 x\)[/tex]
Now, we can use the trigonometric identity [tex]\(\sin^2 x + \cos^2 x = 1\)[/tex] to simplify the LHS:
[tex]\(\sin^2 x + 2\sin x \cos x + \cos^2 x = 1 + 2\sin x \cos x\)[/tex]
The simplified LHS is not equal to the right-hand side (RHS) 1 + sin 2x since it is missing the sin 2x term. Therefore, option A is not an identity.
B. [tex]\(\sin 6x = 2 \sin 3x \cos 3x\)[/tex]
To check if this is an identity, we can use the double-angle identity for sine:[tex]\(\sin 2\theta = 2\sin \theta \cos \theta\)[/tex]
Let [tex]\(2\theta = 6x\)[/tex], which means [tex]\(\theta = 3x\):[/tex]
[tex]\(\sin 6x = 2 \sin 3x \cos 3x\)[/tex]
The equation holds true with the double-angle identity, so option B is an identity.
C. [tex]\(\frac{\sin 3x}{\sin x \cos x} = 4\cos x - \sec x\)[/tex]
To check if this is an identity, we can simplify the right-hand side (RHS) using trigonometric identities.
Recall that [tex]\(\sec x = \frac{1}{\cos x}\):[/tex]
[tex]\(4\cos x - \sec x = 4\cos x - \frac{1}{\cos x} = \frac{4\cos^2 x - 1}{\cos x}\)[/tex]
Now, using the double-angle identity for sine, [tex]\(\sin 2\theta = 2\sin \theta \cos \theta\),[/tex] let [tex]\(\theta = x\):[/tex]
[tex]\(\sin 2x = 2\sin x \cos x\)[/tex]
Multiply both sides by 2: [tex]\(2\sin x \cos x = \sin 2x\)[/tex]
Now, the left-hand side (LHS) becomes:
[tex]\(\frac{\sin 3x}{\sin x \cos x} = \frac{\sin 2x}{\sin x \cos x}\)[/tex]
Using the double-angle identity for sine again, let [tex]\(2\theta = 2x\):[/tex]
[tex]\(\frac{\sin 2x}{\sin x \cos x} = \frac{2\sin x \cos x}{\sin x \cos x} = 2\)[/tex]
So, the LHS is 2, which is not equal to the RHS [tex]\(\frac{4\cos^2 x - 1}{\cos x}\)[/tex]. Therefore, option C is not an identity.
D. [tex]\(\frac{\sin 3x - \sin x}{\cos 3x + \cos x} = \tan x\)[/tex]
To check if this is an identity, we can use the sum-to-product trigonometric identities:
[tex]\(\sin A - \sin B = 2\sin \frac{A-B}{2} \cos \frac{A+B}{2}\)\(\cos A + \cos B = 2\cos \frac{A+B}{2} \cos \frac{A-B}{2}\)[/tex]
Let A = 3x and B = x:
[tex]\(\sin 3x - \sin x = 2\sin x \cos 2x\)\(\cos 3x + \cos x = 2\cos 2x \cos x\)[/tex]
Now, we can rewrite the expression:
[tex]\(\frac{\sin 3x - \sin x}{\cos 3x + \cos x} = \frac{2\sin x \cos 2x}{2\cos 2x \cos x} = \frac{\sin x}{\cos x} = \tan x\)[/tex]
The equation holds true, so option D is an identity.
To know more about identity:
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HELP ME !
Please!
Which of the following tables represents a function?
Find the equation of the line that
is perpendicular to y = -4x + 3
and contains the point (8, 1).
Answer:
x-4y=8
Step-by-step explanation:
y=mx+c comparing with given eq
we get slope(m1)=-4
since both are prependicular
m1×m2=-1
-4×m2=-1
m2=1÷4
eq:-y-y1=m2 (x-x1)
y-1=(1÷4)(x-8)
x-4y=4
Find the difference of the polynomials given below and classify it in terms of degree and number of terms.
Answer:
4th degree polynomial with 4 terms
Step-by-step explanation:
Given:
3n²(n²+ 4n - 5) - (2n² - n⁴ + 3)
Open parenthesis
= 3n⁴ + 12n³ - 15n² - 2n² + n⁴ - 3
Collect like terms
= 3n⁴ + n⁴ + 12n³ - 15n² - 2n² - 3
= 4n⁴ + 12n³ - 17n² - 3
Number 1 term is 4n²
Number 2 term is 12n³
Number 3 term is -17n³
Number 4 term is -3
The highest degree of the polynomial is 4th degree
Therefore,
The difference in 3n²(n²+ 4n - 5) - (2n² - n⁴ + 3) is
4th degree polynomial with 4 terms
Answer:
4th degree polynomial with 4 terms
Step-by-step explanation:
W=VI. Make V the subject of formula
Answer:
hope that is helpful
Step-by-step explanation:
W= VI
W= VI
I. I
V= W
I
Answer:
V = [tex]\frac{W}{I}[/tex]
Step-by-step explanation:
Given
W = VI ( isolate V by dividing both sides by I )
[tex]\frac{W}{I}[/tex] = V
Hey there I need some assistance need on this problem. What do I mean by checkpoints and how am I supposed to find the y-intercept and the slope from the given values?
Slope Formula: y2 - y1 / x2 - x1
(m and slope represent the same quantity)
m = 1 - - 5 / -4 - 0
m = 1 + 5 / -4
m = 6 / -4
m = -3/2
Now that we know the slope, we can plug the slope and one of our points into slope-intercept form (y = mx + b) and solve for b. I will be using the point (-4,1).
y = -3/2x + b
1 = -3/2(-4) + b
1 = 6 + b
b = -5
In point form, the y-intercept is (0, -5).
Therefore, to get the equation all we need to do is plug in our slope and b-value to slope-intercept form.
Equation: y = -3/2 x - 5
To check the point (-6, -14) we plug it into our equation and see if the two sides are equal.
-14 = -3/2(-6) - 5
-14 = 9 - 5
-14 = 4
-14 does not equal 4, therefore the point is NOT on the line.
Hope this helps!
What is the difference between calculating the area and calculating the perimeter of a rectangle?
Answer:
For perimeter you add up the side lengths to get the perimeter but for area you multiply the length times width (L x W )to get area.
Step-by-step explanation:
find the period of the graph shown below
Answer:
Step-by-step explanation:
The period of a trig function tells you how much space is taken up by one "up-down-up" of the graph, which is a revolution. Because half of this graph takes place in a span of 2π, then the whole graph will span 4π.
In ΔTUV, the measure of ∠V=90°, UT = 65, VU = 56, and TV = 33. What ratio represents the cosine of ∠T?
Answer: The ratio that represents the cosine of ∠T is [tex]\frac{56}{65}[/tex]
Step-by-step explanation:
We are given:
UV = 56 units
VT = 33 units
UT = 65 units
∠V = 90°
Cosine of an angle is equal to the ratio of base and the hypotenuse of the triangle. ΔTUV is drawn in the image below.
[tex]\cos \theta=\frac{\text{base}}{\text{hypotenuse}}[/tex]
Base of the triangle is UV and the hypotenuse of the triangle is TU
Putting values in above equation, we get:
[tex]\cos \theta=\frac{UV}{TU}=\frac{56}{65}[/tex]
Hence, the ratio that represents the cosine of ∠T is [tex]\frac{56}{65}[/tex]
Plz help me.
I WILL GIVE BRAINLY
Answer:
p = T - a - b
Step-by-step explanation:
T = a + p + b
p = T - a - b
The given equation has been solved in the table. Step Statement 1 1 –7n + 11 = -10 2. -7n + 11 – 11 = -10 – 11 3 -7n = -21 4 = = =21 .In -7 -21 __7 5 n = 3 Use the table to complete each statement. In step 2, the In step 4, the property of equality was applied. property of equality was applied.
Answer:
In step 2, the subtraction property of equality was applied
In step 4, the division property of equality was applied
Step-by-step explanation:
For a project in his Geometry class, Tyler uses a mirror on the ground to measure the height of his school building. He walks a distance of 14.65 meters from his school, then places a mirror on flat on the ground, marked with an X at the center. He then steps 0.8 meters to the other side of the mirror, until he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.15 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.
Answer:
The height of the school building is approximately 21.06 meters
Step-by-step explanation:
The method of Geometry Tyler is using to determine the height of his school building is through the property that similar triangles have a common ratio of corresponding their sides
The given parameters for the triangle formed by Tyler and the mirror are;
The distance from Tyler's eyes to the ground = 1.15 meters
The horizontal distance between Tyler and the mirror at X = 0.8 m
The parameters of the triangle formed by the height, h, of the school building and the mirror at X are;
The horizontal distance between the school building and the mirror = 14.65 m
The height of the school building = h
Therefore, we have;
[tex]\dfrac{The \ distance \ from \ Tyler's \ eyes \ to \ the \ ground}{The \ height \ of the \ school \ building} =\dfrac{Tyler's \ horizontal \ distance \ from \ mirror }{The \ building \ to \ mirror \ horizontal \ distance }[/tex]Therefore;
[tex]\dfrac{1.15 \, m}{h} = \dfrac{0.8 \ m}{14.65 \ m}[/tex]
[tex]h = \dfrac{1.15 \, m \times 14.65 \, m }{0.8 \, m} = 21.059375 \ m[/tex]
The height of the school building h to the nearest hundredth meter ≈ 21.06 m.
A circular garden is surrounded by a circular path of 7m width.If the area of path is 770m²,find the area of the garden without path.
help me this question ⁉️
Answer:
Answer:
Radius of the circular garden
= 210 sq
=105m
Radius of the region covering the garden and the path =105m+7m
=112m
Area of the region between two concentric circles
with radius of outer circle R, and inner circle r =π(R sq−r sq)
Hence, the area of the path
=π(112sq−105 sq)= 7/22
(12544−11025)
= 33418/7
=4774m sq
HOPE THIS WILL HELP YOU MATE
There is $1.90 in a jar filled with
quarters, dimes, and nickels.
There are 2 more quarters than
dimes and there are 2 more
nickels than quarters.
How many of each coin are there?
Answer:
7 nickels, 5 quarters, 3 dimes
Step-by-step explanation:
7 nickels= 35 cents
5 quarters= $1.25
3 dimes= 30 cents
35+ 1.25+ 30= $1.90
Hope this helps!
Plz mark Brainliest if u can :)
Plz help. How to convert this standard notation to scientific notation 549,755,813,888.
Answer:
To change a number from scientific notation to standard form, move the decimal point to the left (if the exponent of ten is a negative number), or to the right (if the exponent is positive). You should move the point as many times as the exponent indicates. Do not write the power of ten anymore
A house plan Is drawn to a scale 1cm to 2m. What is the length of a window 2.5cm long on the plan?
1cm = 2m
=> 1cm = 200cm
2.5cm = 2.5 × 200cm = 500 cm = 5m
So, the length of window is 500cm or 5m.
I want to know the Answers
Step-by-step explanation:
this is the correct answer you wanted to know
please mark brainliest
Solve the equation and enter the value of x below. 3(x+11) + 5= 68
[tex]\boxed{ \sf{Answer}} [/tex]
[tex]3(x + 11) + 5 = 68 \\ 3x + 33 + 5 = 68 \\ 3x + 38 = 68 \\ 3x = 68 - 38 \\ 3x = 30 \\ x = \frac{30}{3} \\ x = 10[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
[tex]3(x + 11) + 5 = 68 \\ 3 \times x + 3 \times 11 + 5 = 68 \\ 3x + 33 + 5 = 68 \\ 3x + 33= 68 - 5 \\ 3x + 33= 63 \\ 3x = 63 - 33 \\ 3x = 30 \\ x = \frac{30}{3} \\ x = 10[/tex]
PLEASE HELP! Which of the following ordered pairs is a solution to the given system of equations?
A. (12, 8)
B. (3, 5)
C. (-3, 3)
D. (0, 4)
please don’t use this for points.
Answer:
A.............
Step-by-step explanation:
. ..........
Answer:
C. (3,3)
Step-by-step explanation:
When These equations are both graphed the solution for these equations when they intersect is (-3,3)
the base of a right prism is an equilateral triangle each of whose sides measures 4cm.the altitude of the prism measures 5cm.Find the volume of the prism
Answer:
[tex]V=34.64\ cm^3[/tex]
Step-by-step explanation:
Given that,
The side of an equilateral prism = 4 cm
The altitude of the prism = 5 cm
We need to find the volume of the prism. The formula for the volume of a prism is as follows :
[tex]V=A\times h[/tex]
Where
A is the area of equilateral triangle, [tex]A=\dfrac{\sqrt3}{4}a^2[/tex]
So,
[tex]V=\dfrac{\sqrt3}{4}a^2\times h\\\\V=\dfrac{\sqrt3}{4}\times 4^2\times 5\\\\V=34.64\ cm^3[/tex]
So, the volume of the prism is equal to [tex]34.64\ cm^3[/tex].
A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries negative 10, 0, 0, negative 4, negative 6, 0.
Which is a y-intercept of the continuous function in the table?
Hello,
[tex]\begin{array}{c|c|c|}&x&f(x)\\1&-4&-10\\2&-3&0\\3&-2&0\\4&-1&-4\\5&0&-6******\\6&1&0\\\end{array}\\[/tex]
y-intercept is -6
If x=0 then y=-6
plz help me out with the answer and explaination
Answer:
7500 m
Step-by-step explanation:
5500 is the initial height. It increased by 1500, so 5500 + 1500 = 7000. Then it went down 2000 meters, so 7000 - 2000 = 5000. It went up 2500 again. 5000 + 2500 = 7500
Write an
equivalent expression by distributing the
"---"
sign outside the parentheses:
-(3.9d + 10)
Answer of this question
-3.9d-10PLEASE HURRY!! NEED IT ASAP!! WILL MAKE BRAINLIEST
Question 1 of 10
Which choice is equivalent to the expression below when y > or equal to 0?
Answer:
I think B
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
[tex]\sqrt{y^3} +\sqrt{9y^3} -3y\sqrt{y} \\=\sqrt{y^2 *y} +\sqrt{9*y^2*y} -3y\sqrt{y} \\=y\sqrt{y} +3y\sqrt{y} -3y\sqrt{y} \\=y\sqrt{y}[/tex]
if the diagonal of a square is √48 what is the area of a square
Answer:
using Pythagoras' theorem c²=a²+b²
the diagonal is the hypotenuse of one of the triangles formed
let x represent one side of the square
√48²=x²+x²
√48²=2x²
48=2x²
48/2=2x²/2
24=x²
√24=√x²
4.8989794855663561=x
~4.90
Area of the square=side x side
4.90x4.90
24.01units²
help or i will fail my acellus
Answer:
I think it's 155 cm
Step-by-step explanation:
=(5×5×3)+(5×2×4)
= 75+40
= 155 cm2
Maths assignment
y^2-36
Answer:
Since both terms are perfect squares, factor using the difference of squares formula,
a ^2 − b ^2 = ( a + b ) ( a − b )
where
a = y
and
b = 6
( y + 6 ) ( y − 6 )
