Answer:
2 sheep
Step-by-step explanation:
If you have 36 sheep and you sell:
first day 1/2 of them you sold 18
second day 1/3 them you sold 12
On thhe third day 1/9 them you sold 4
Therefore you sold 18 + 12 + 4 = 34
And you still have 2 sheep
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:
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]
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!
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:
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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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
# If two vectors whose direction ratios are 1,2,3 and -k,2,1 are perpendicular to each other then, a) k=7 b) k=4 c) k=3 O d) k=6 me especially since we had be 1 poir 82) I don't know why he turned friends for so long.
Answer:
(a)k=7
Step-by-step explanation:
We are given that
Two vectors whose direction ratios are 1,2,3 and -k,2,1.
Let
[tex]a_1=1,b_1=2,c_1=3[/tex]
[tex]a_2=-k,b_2=2,c_2=1[/tex]
We have to find the value of k.
We are given that two vectors are perpendicular to each other.
We know that two vectors are perpendicular to each other then
[tex]a_1a_2+b_1b_2+c_1c_2=0[/tex]
Substitute the values
[tex]1(-k)+2(2)+3(1)=0[/tex]
[tex]-k+4+3=0[/tex]
[tex]-k+7=0[/tex]
[tex]\implies k=7[/tex]
Hence, option a is correct.
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
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
help!!!!!
Describe the graph of the function. y = VX-6 +2
I NEED HELP ASAP
Answer:
First answer choice: [tex]y=\sqrt{x}[/tex] shifted right 6 units and down 2 units.
Step-by-step explanation:
Graph
Write the following expression in exponential form:
16x16x16x1.6
0416
0164
16x4
O 16+ 4
Answer:
16x16x16x1.6
Step-by-step explanation:
here's your answer hope it helps you
A and B are two similar 2D shapes
A 12cm
B 15cm
The area of the shape A is 200cm^2.
Calculate the area of shape B
Answer: [tex]312.5\ cm^2[/tex]
Step-by-step explanation:
Given
A and B are two similar shape with lengths of 12 cm and 15 cm
A has an area of [tex]200\ cm^2[/tex]
For similar figures, ratio of the square of corresponding length is equal to the ratio of the area
[tex]\Rightarrow \dfrac{200}{A_b}=\dfrac{12^2}{15^2}\\\\\Rightarrow A_b=\dfrac{15^2}{12^2}\times 200\\\\\Rightarrow A_b=312.5\ cm^2[/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
Drag the operator to the correct location on the image.
Which operation results in a binomial?
The correct answer is to drag The Plus sign (+)
What is an Operator?This has to do with the use of symbols to denote mathematical equations such as addition, subtraction, etc.
Hence, we can see that the correct position to put the operator on the image to result in a binomial is to drag the plus sign (+) so that the equations can be solved,.
Read more about operators here:
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Answer:.
Step-by-step explanation:
what is the measure of angle D?
Answer:
57
Step-by-step explanation:
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 :)
Determine the area of the triangle.
223.6 square units
248.7 square units
447.1 square units
458.4 square units
Answer:
223.6 square units. or 223.569 square units
Answer:A
Step-by-step explanation:I took the test
Add (1.3t3 + 0.4t2 – 24t) + (8 – 18t + 0.6t2) For each term in the second polynomial, enter the letter showing where that term should be placed to add the polynomials vertically.
Answer:
[tex](1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2) = 1.3t^3 + t^2 -42t + 8[/tex]
Step-by-step explanation:
Given
[tex](1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2)[/tex]
Required
Solve
We have:
[tex](1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2)[/tex]
Collect like terms
[tex]1.3t^3 + 0.6t^2 + 0.4t^2 - 24t- 18t + 8[/tex]
[tex]1.3t^3 + t^2 -42t + 8[/tex]
So:
[tex](1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2) = 1.3t^3 + t^2 -42t + 8[/tex]
Answer:
look at pic
Step-by-step explanation:
[tex]solve : - \\ \\ ( \sqrt{100 - 64)} [/tex]
Answer:
[tex] \sqrt{100 - 64} \\ = 36 \\ = {6}^{2} [/tex]
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
Write an
equivalent expression by distributing the
"---"
sign outside the parentheses:
-(3.9d + 10)
Answer of this question
-3.9d-10Maths 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 )
HELP ME !
Please!
Which of the following tables represents a function?
I want to know the Answers
Step-by-step explanation:
this is the correct answer you wanted to know
please mark brainliest
If K is the midpoint of JL, JK = 8x + 11 and KL = 14x – 1, find JL.
Answer:
[tex]JL=54[/tex]
Step-by-step explanation:
We are given that K is the midpoint of JL. Using this information, we want to find JL.
By the definition of midpoint, this means that:
[tex]JK=KL[/tex]
Substitute them for their equations:
[tex]8x+11=14x-1[/tex]
Solve for x. Subtract 8x from both sides:
[tex]11=6x-1[/tex]
Add 1 to both sides:
[tex]6x=12[/tex]
And divide both sides by 6. Hence:
[tex]x=2[/tex]
JL is the sum of JK and KL. Hence:
[tex]JK+KL=JL[/tex]
Since JK = KL, substitute either one for the other:
[tex]JK+(JK)=2JK=JL[/tex]
Substitute JK for its equation:
[tex]2(8x+11)=JL[/tex]
Since we know that x = 2:
[tex]2(8(2)+11)=2(16+11)=2(27)=54=JL[/tex]
Thus:
[tex]JL=54[/tex]
write twelve thousand twelve hundred and twelve in numbers
Answer:
12, 120,012
Step-by-step explanation:
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 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.
Plz help me.
I WILL GIVE BRAINLY
Answer:
p = T - a - b
Step-by-step explanation:
T = a + p + b
p = T - a - b
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
