Clare earned a total of $12 for 2 hours of yard work. How many hours in all will it take Clare
to earn $18? Solve using unit rates.
Fast please asap thanks
Answer:
3 hours
Step-by-step explanation:
$12 = 2hours
Find how much Clare was paid for one hour
Total money earned ÷ number of hours = wage per hour
12 ÷ 2 = $6 per hour
set up equation
6x = 18
This equation says 6 dollars an hour × number of hours = $18
To solve for this equation, divide both sides by 6 (this isolates the variable)
6x ÷ 6 = 18 ÷ 6
1x = 3
x = 3
If the infinite curve y = e−4x, x ≥ 0, is rotated about the x-axis, find the area of the resulting surface.
Answer: the area of the resulting surface is π/16 [ 4√(17) + In( 4 + √( 17)) ]
Step-by-step explanation:
Given that;
y = e^(-4x), x ≥ 0
then, dy/dx = -4e^(-4x)
now, √( 1 + (dy/dx)² ) = √( 1 + ( -4e^(-4x))²) = √( 1 + 16e^(-8x)
so the surface area of the surface obtaining by rotating the curve y = e^(-4x) on ( 0, ∞ ) about x-axis is,
S = ₀∫^∞ 2πy √( 1 + (dy/dx)² ) dx
S = ₀∫^∞ 2πe^(-4x) . √( 1 + 16e^(-8x) dx
S = 2π. ₀∫^∞ e^(-4x) . √( 1 + 16e^(-8x) dx
so LET 4e^-4x = u ⇒ -16e^(-4x) dx = du
⇒e^-4x dx = du/ -16
so whenx = 0, then u =4 and when x → ∞ then e^(-4x) → 0 so u →0
therefore
S = 2π ₄∫⁰ √(1 + u²) . du/-16
= π/8 ₀∫⁴ √(1 + u²) . du
= π/8 [ u/2√(1 + u²) + 1/2 In ( u + √( 1 + u²) ]₀⁴
WE MAKE USE OF
∫√( a² + u²) du = u/2√(a² + u²) + a²/2 In ( u + √( a² + u²)) + C
so
= π/8 [ 4/2√(1 + 16) + 1/2 In ( 4 + √( 1 + u16 ]
= π/8 [ 2√(17) + 1/2 In ( 4 + √( 17)) ]
= π/16 [ 4√(17) + In( 4 + √( 17)) ]
therefore the area of the resulting surface is π/16 [ 4√(17) + In( 4 + √( 17)) ]
(1/4)^−2−(5^0⋅2)⋅1^−1
Answer:
14.62 I believe
Step-by-step explanation:
Factor the trinomial and solve
x²-10x+21
Answer:
(x-3)(x-7)
Step-by-step explanation:
All fifth grade students from centerville elementary hiked around lake D. if there are 317 students about how many total miles did they hike
Answer:
317 x 18 = 5706
Mr.Milton had $1200 in his savings account at the beginning of the year. If his account has a balance of $1230 at the end of the year, what percent increase of his balance?
Answer:
2.5%
Step-by-step explanation:
1230-1200 = 30
30÷1200 = 0.025
0.025 x 100 = 2.5
WILL MARK BRAINLIEAT I NEED ANSWER NOWSelect the correct answer.
If the function 5x + y = 1 has the domain {-2, 1,6}, then what is the corresponding range?
O A.
{-9, 6, 31}
B. {9, -6, -31}
C. {-11, 4, 29}
D. {11, -4,-29}
Answer:
D, R: {11, -4, -29}
Step-by-step explanation:
According to the given set of domains, the corresponding range is found by substituting the x values into the equation and solving for y.
i.e {-2} -> 5x + y = 1, -10 + y = 1, y = 11
{1} -> 5x + y = 1, 5 + y = 1, y = -4
{6} -> 5x + y = 1, 30 + y = 1, y = -29
Answer:
The short answer is D
What is the error in this problem?
Find the values of x and y. The diagram is not to scale.
Answer:
51+x-5+y-6=180
x+y=180-51+5+6
X+y=140
Answer x=77 y=63
(those 2 lines with the arrows are perpendicular so their angles are the same 72° and (x-5)=77-5= 72°)
The values of x and y are 77 and 63 respectively.
What is Angle?Angle is defined as the figure formed by two lines or rays which has a common point of intersection where the angle is formed.
Sum of the interior angles of a triangle is supplementary.
That is three angles (y - 6)°, 72° and an unknown angle is supplementary.
We have two parallel lines given and a transversal line intersects the parallel lines.
So the unknown angle of the triangle and the angle 51° are alternate interior angles and are thus equal.
So the third angle of the triangle = 51°
(y - 6) + 72 + 51 = 180
y - 6 + 123 = 180
y + 117 = 180
y = 63
The angles (x - 5)°, 51° and (y - 6)° are supplementary.
(x - 5) + 51 + (y - 6) = 180
x - 5 + 51 + 63 - 6 = 180
x + 103 = 180
x = 77
Hence the value of x is 77 and the value of y is 63.
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please tell me what the domain and range of graphs Part 4
What is the image of the point (-2,4) after a rotation of 270° counterclockwise about the origin?
Answer:
(4, 2) the formula for 270 rotation counterclockwise is (y,-x)
Step-by-step explanation:
A mason is forming a rectangular floor for a storage shed.
The perimeter of the rectangle is 44 feet.
Perimeter is the lengths of the edges added up. And if the shape is a rectangle, there are 4 edges so we divide by 4. 44/4=11. each of the four sides are 11 feet long.
width=11
length=11
area=width*length=121
Which of the following expressions are equivalent to 12x+20? Select all that apply.
A.-2(6x - 10)
B.4(3x+ 20)
C.4(3x + 5)
D.12(x+1 2/3)
E.-2(10 – 6x)
Answer:
C
Step-by-step explanation:
4(3x+5) = 12x+20
Answer:
c
Step-by-step explanation:
A boat is 2000m from a cliff. If the angle of depression from the top of the cliff to the boat is 10 degrees, how tall is the cliff.
Answer:
Let AB is the height of the cliff = H and p is the posit ion of the boat.Angle of depression= angle of elevation= 15 degrees therefore angle APB= 15 degrees tan 15=AB=h/1,000 h=(1,000)*tan 15=(1,000)(0.26794919243112)=268.94919243112 meters or
Simply: 268meters..........Ans
Which graph represents the equation 3x+y=-1?
Answer:
The answer is c
Step-by-step explanation:
I put this into my graphing calculator to solve it. To do this by hand though you need to choose two numbers and enter then for x and that should give you the numbers the you need to plot on your graph.
Hope that help :)
Evaluate: 3² × (-2)³ × 5
Answer:
360Step-by-step explanation:
3^2 × (-2)^3 × 5= 9 × 8 × 5= 72 × 5= 360Thank you ☺️☺️
Which type of government BEST describes the type of government found in
Mesopotamia?
A- Small Kingdoms
B- Independent City-states
C- Large Empires
D- Populated Towns
Please help quick!!
(iv) 123456
3. Find the sum of the place values of 5 in the following numbers:
(0) 3515
(II) 52105
(III) 61655
(iv) 52545
(v) 50005
(VI) 525250
(vil) 55348
(vill) 52756
Answer:
it should be 45,870
Step-by-step explanation:
The square root of 10 lies between what 2 numbers?
A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. The square root of 10 lies between 3 and 4.
What is a number line?A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.
In order to find the square root of 10 lies between which two numbers the approximate value of the root is needed to be calculated.
√10 = 3.162.......
Now, if we plot √10 on the number line its value will lie between 3 and 4.
Hence, The square root of 10 lies between 3 and 4.
Learn more about the Number line:
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Which of the following variable expressions would represent the area of a rectangle if its length was represented by x+5 and its width was represented by x-2?
x[tex]x^{2} +3x+10\\
x^{2} +3x-10\\
x^{2} -10x+3\\
x^{2} -10[/tex]
Answer:
B
Step-by-step explanation:
Remember that the area of a rectangle is given by the formula [tex]A=lw[/tex].
We know that the length is [tex](x+5)[/tex] and the width is [tex](x-2)[/tex]. Therefore, the area will be:
[tex]A=(x+5)(x-2)[/tex]
Expand. Use the Distribute Property. This yields:
[tex]A=(x+5)(x)+(x+5)(-2)[/tex]
Multiply:
[tex]A=(x^2+5x)+(-2x-10)[/tex]
Combine Like Terms:
[tex]A=x^2+(5x-2x)-10\\A=x^2+3x-10[/tex]
Therefore, our answer is B.
Determine the intercepts of the line.
y- intercept (_,_)
x- intercept (_,_)
Answer:
Therefore, the y-intercept is (0,2.5) and x-intercept is (3.5,0) .
Step-by-step explanation:
Intercept means the line touching the axis. As you look at the graph, y-intercept (line touching y-axis) is (0,2.5) and the x-intercept is (3.5,0) .
Take note :
When finding y-intercept, x-coordinate must be 0.
When finding x-intercept, y-coordinate must be 0.
Melissa's flower shop got a shipment of 158 roses. She wants to make bouquets of 6 roses each. How many bouquets can Melissa make?
bouquets
How many roses will she have left over?
It is common in many industrial areas to use a filling machine to fill boxes full of product. This occurs in the food industry as well as other areas in which the product is used in the home, for example, detergent. These machines are not perfect, and indeed they may A, fill to specification, B, underfill, and C, overfill. Generally, the practice of underfilling is that which one hopes to avoid. Let P(B) = 0.002 while P(A) = 0.980.
pls Help brainly I’ll give u brailest
Gracie, Mary, and Nancy each have a small collection of seashells. Gracie has 5 more than times the number of shells Mary has. Nancy has 1 more than times the number of shells Mary has. Gracie and Nancy have the same number of shells. If x is the number of shells Mary has, identify the equation that represents this situation and identify its solution.
the mass of a block is 12g and the volume is 6 ml calculate the density of the block
a.) 0.5 g/ml
b.) 18 g/ml
c.)2 g/ml
d.)72g/ml
Answer:
c.)2 g/ml
Step-by-step explanation:
Given:
Mass of block = 12 g
Volume of block = 6 ml
Required:
Density of the block
SOLUTION:
Density is given as the mass of the block per unit volume.
Thus, density = mass/volume
Density of block = [tex] \frac{12 g}{6 ml} [/tex]
= 2 g/ml.
The answer is c. 2 g/ml.
Which choice correctly shows rounding to the hundredths place?
4.234 + 4.752 + 7.99 right-arrow 4.2 + 4.8 + 8.0
3.825 + 4.792 + 3.0805 right-arrow 3.82 + 4.79 + 3.82
3.824 + 4.765 + 1.732 right-arrow 3.81 + 4.77 + 3.80
3.8765 + 4.824 + 1.733 right-arrow 3.88 + 4.82 + 1.73
Answer:
the last one:))))
Step-by-step explanation:
trust me
Mia has a large bag of sweets. if she shares the sweets equally among 2,3,4,5 or 6 people there will always be one sweet left over. what is the smallest number of sweets there could be in the bag?
Answer:
4
Step-by-step explanation:
are 8x2y and-5yx2 like terms?
“CAN”
PLACE VALUE
How does the 5 in the tens place
compare to the 5 in the ones place?
3,055
The triangles below are congruent. Which of the following statements must be true?
Answer:
BC=FD
Step-by-step explanation:
Answer: I agree it’s BC congruent to FD
Step-by-step explanation:
