Answer:
My friend's mower will take approximately 0.75 h to mow the lawn alone.
Step-by-step explanation:
To solve this problem we can use the idea of average speed and apply to this problem, using the appropriate formula shown below:
[tex]speed = \frac{distance}{time}[/tex]
Where each lawn mower has a speed at which they can mown, the distance is the lawn they're mowing and the time is how long they will take to do it. In the case where my equipment is working alone, its speed "x" can be modeled as below:
[tex]x = \frac{lawn}{1.5}[/tex]
When my friend's mower does the job, its speed "y" can be seen as:
[tex]y = \frac{lawn}{time}[/tex]
When both work together the speed can be seen as:
[tex]x + y = \frac{lawn}{0.5}[/tex]
Applying the first two equations on the second, gives us:
[tex]\frac{lawn}{1.5} + \frac{lawn}{time} = \frac{lawn}{0.5}\\\frac{1}{time} = \frac{1}{0.5} - \frac{1}{1.5}\\\frac{1}{time} = 2 - 0.667\\\frac{1}{time} = 1.333\\1.333*time = 1\\time = \frac{1}{1.333} = 0.75[/tex]
My friend's mower will take approximately 0.75 h to mow the lawn alone.
Please answer this ASAP ❤️
Answer:
4
Step-by-step explanation:
just change the x into -6
-(-6)-2 = 6 - 2 = 4
Answer:
f(x)=-x-2
f(-6)=-(-6)-2
f(-6)=4
Step-by-step explanation:
How do you write this quadratic equation using substitution
Answer:
u^2 +7u -8=0 where u = 3x+2
Step-by-step explanation:
(3x+2)^2 + 7(3x+2) - 8=0
Let 3x+2 = u
u^2 +7u -8=0
The diagonal of a rectangle is 58" the site is 40" and the base is 42" what is the ratio of the diagonal to the base of the rectangle
Answer:
29:21
Step-by-step explanation:
The ratio of the diagonal to the base of the rectangle is 58:42
The ratio can be simplified further.
The simplified ratio is 29:21.
PLEASE HELP, SOLVE THIS PROBLEM AND GIVE ME THE ANSWER!!!
Answer:
11 is the answer
Step-by-step explanation: i hope so cuz my calculations gives this answer
Anybody know this ? Please help :(
Answer:
D
Step-by-step explanation:
5.50. 5.50+0.25= 5.75, 5.75+0.25= 6.00, 6.00+0.25= 6.25, 6.25+0.25= 6.50
Option D is the answer:
5.50, 5.75, 6.00, 6.25, 6.50...
choose all functions below that have a vertex of (4.5,-8)
Answer: Answer: A
Explanation:
Just plug in numbers since you know the unknown values,
x + r = 4 + 5
4 + 5 = 9
Step-by-step explanation:
Important!!!
That is the distance between (-5, 4) and (-1, 4)?
-5 units
-4 units
4 units
5 units
Answer:
4 units
Step-by-step explanation:
Since the y value is the same, we only have to look at the x value
-1 - -5
-1 +5
4
The distance is 4 units
Answer:
4 units
Step-by-step explanation:
if you graph these 2 points, they'll be on the same line of the graph separated by 4 units
Find the values of x and y in triangle ABCD
Answer:
x and y = 66.5
Step-by-step explanation:
180-47=133
133/2=66.5
Elijah uses 2 pints of stain on each table that he makes . How many tables can he paint with 1 gallon of stain ? sets
Answer:
4 sets
Step-by-step explanation:
1 gallon contains 8 pints. It takes 2 pints per table, so we should divide 8 by 2.
By doing this, we get 4, therefore he can stain 4 sets of tables with a gallon of stain.
Brandee makes an hourly wage. In the last pay period, she earned $800 for regular hours and $240 for overtime hours. Her overtime rate of pay is 50% more than her regular rate of pay "r". Write and simplify an expression in terms of "r" that represents the number of hours "h" Brandee worked in the pay period. Show your work.
Step-by-step explanation:
Overtime rate= r+50%= 1.5r
Regular hours= 800/r
Overtime hours= 240/1.5r
Total hours worked
h=800/r+240/1.5rh= 800/r+160/rh=960/rr=960/hThere are 8 times as many males as females on the maths course at university. What fraction of the course are female? Give your answer in its simplest form.
Answer:
⅑
Step-by-step explanation:
Let m represents number of males, and f represents number of females taking the maths course.
Given that number of males (m) taking the maths course is 8 times as much as number of females (f), total number of students taking the maths course (T).
Thus we can represent the information above with the following:
m = no. of males
f = no. of females
T = Total
m = 8f
T = m + f
Thus,
Total = 8f + f = 9f
==>The fraction of the course that are females = No. of females (f) ÷ Total no. of students (T)
= f/9f
Fraction of females in simplified form would be ⅑
2x + 3y = 13
4x - y = -2
Answer:
x=1/2. y=4
Step-by-step explanation:
4(2x+3y=13)=8x+12y=52
2(4x-y=-2)=8x-2y=-4
subtract equation one from equation two to get
14y=56 then u will divide bothe sides by 14. for x u substitute y in equation one
Answer:
x = 1/2 y = 4
Step-by-step explanation:
Equation 1
2x + 3y = 13
Equation 2
4x - y = -2
Multiply equation 2 by 3
12x - 3y = -6
Add equation 1 to 3
14x = 7
x = 7/14
x = 1/2
Substitute x into equation 1
2(1/2) + 3y = 13
3y = 13 -1
3y = 12
y= 12/3
y = 4
x =1/2 y = 4
Hope this helps.
th
Write an explicit formula for An, the nth
term of the sequence 15, 23, 31, ....
Answer:
a₁ = 15 and common difference = 8 so the formula is:
aₙ = 15 + (n - 1) * 8
= 8n + 7
Which of the following equations is the translation 2 units up of the graph of y = |x|?
A. y = |x| - 2
B. y = |x| + 2
C. y = |x + 2|
D. y= |x - 2|
Answer:
its y = |x| + 2
Step-by-step explanation:
Is the following statement true or false? The intersection of a plane and a ray can be a line segment.
Answer:
False
Step-by-step explanation:
Is the following statement true or false?
The intersection of a plane and a ray can be a line segment.
It is false. Correct one is the point.A water balloon is tossed vertically from a window at an initial height (s-sub zero) of 37 feet and with an initial velocity(v-subzero) of 41 feet per second. Answer the following using the fact that h(t)=-16T^2+v-sub zer0t+s sub zero. a) Determine a formula, h)t), for the function that models the height of the water balloon at time t . b)Plot the function in Desmos in an appropriate window. Use the graph to estimate the time the water balloon lands c)Use algebra to find the exact time the water balloon lands. Show your work. No decimals in your answer. d)Determine the exact time the water balloon reaches its highest point and its height at that time. e)4 pts] Compute the average rate of change of on the intervals . Include units on your answers and write a sentence to explain the meaning of the values you found. Arc{1.5,2}____________________________. Explanation: Arc{2,2.5}____________________________. Explanation: årc{2.5,3}____________________________. Explanation:
Answer:
a) h(t) = -16t^2 +41t +37
b) see attached (3.270 seconds)
c) (41+√4049)/32 seconds
d) 1.28125 seconds; 63.265625 feet
e) [1.5, 2]: -15; [2, 2.5]: -31; [2.5, 3]: -47
Step-by-step explanation:
a) The formula and initial values are given. Putting those values into the formula, we get ...
h(t) = -16t^2 +41t +37
__
b) The graph is attached. It shows the t-intercept to be about 3.270 seconds.
__
c) Using the quadratic formula, we can find the landing time as ...
[tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-41\pm\sqrt{41^2-4(-16)(37)}}{2(-16)}\\\\=\dfrac{41\pm\sqrt{4049}}{32}\qquad\text{only $t>0$ is useful}[/tex]
The exact landing time is (41+√4049)/32 seconds.
__
d) The highest point is at t=-b/(2a) = -41/(2(-16)) = 41/32 seconds.
The value of the function at that point is ...
h(41/32) = (-16(41/32) +41)(41/32) +37 = 41^2/64 +37 = 4049/64
The maximum height is 4049/64 = 63.265625 feet.
__
e) For a quadratic function, that average rate of change on an interval is the derivative at the midpoint of the interval. Here, the derivative is ...
h'(t) = -32t +41 . . . in feet per second
Then the average rates of change are ...
arc[1.5, 2] = h'(1.75) = -32·1.75 +41 = -15 ft/s
arc[2, 2.5] = h'(2.25) = -32(2.25) +41 = -31 ft/s
arc[2.5, 3] = h'(2.75) = -32(2.75) +41 = -47 ft/s
These are the average velocity of the water balloon over the given interval(s) in ft/s. Negative indicates downward.
Answer:
(a) h(t) = -16t² + 41t + 37
(b) About 3.3 s
[tex]\large \boxed{\text{(c) }\dfrac{41+ \sqrt{4049}}{32}\text{ s}}[/tex]
(d) -15 ft/s; -31 ft/s; -47 ft/s
Step-by-step explanation:
(a) The function
h(t) = -16t² + v₀t + s₀
v₀ = 41 ft·s⁻¹
s₀ = 37 ft
The function is
h(t) = -16t² + 41t + 37
(b) The graph
See Fig. 1.
It looks like the water balloon lands after about 3.3 s.
(c) Time of landing
h = -16t² + 41t + 37
a = -16; b = 41; c = 37
We can use the quadratic formula to solve the equation:
[tex]h = \dfrac{-b\pm\sqrt{b^2 - 4ac}}{2a} = \dfrac{-b\pm\sqrt{D}}{2a}[/tex]
(i) Evaluate the discriminant D
D = b² - 4ac = 41² - 4(-16) × 37 = 1681 + 2368 = 4049
(ii) Solve for t
[tex]\begin{array}{rcl}h& = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-41\pm\sqrt{4049}}{2(-16)}\\\\ & = & \dfrac{41\pm\sqrt{4049}}{32}\\\\t = \dfrac{41- \sqrt{4049}}{32}&\qquad& t = \dfrac{41+ \sqrt{4049}}{32}\\\\\end{array}\\[/tex]
[tex]\text{The water balloon will land after $\large \boxed{\mathbf{\dfrac{41+ \sqrt{4049}}{32}}\textbf{ s}} $}[/tex]
(d) Time and maximum height
(i) Time
The axis of symmetry (time of maximum height) is at t = -b/(2a)
[tex]t = \dfrac{-41}{2(-16)} = \dfrac{41}{32} = \textbf{1.281 s}[/tex]
(ii) Maximum height
The vertex is at y = h(1.281) = h(t) = -16(1.281)² + 41(1.281) + 37 = 63.27 ft
(e) Average rate of change
(i) Arc{1.5,2}
h(1.5) = 62.5
h(2) = 55
m = (h₂ - h₁)/(t₂ - t₁) = (55 - 62.5)/(2 - 1.5) = -7.5/0.5 = -15 ft/s
The water balloon has started to fall after it has reached peak height, so it is not going very fast
(ii) Arc{2,2.5}
h(2.5) =39.5
m = (39.5 - 55)/(2 - 1.5) = -15.5/0.5 = -31 ft/s
The balloon is in mid-fall, so gravity has caused it to speed up.
(iii) Arc{2.5,3}
h(3) = 16
m = (16 - 39.5)/(2 - 1.5) = -23.5/0.5 = -47 ft/s
The balloon is about to hit the ground, so it is falling at almost its maximum velocity.
Fig. 2 shows the height of the balloon at the above times.
Can someone please help me with this geometry question
Answer:
A. q = 39
Step-by-step explanation:
Since the lines are parallel, their sides will be proportional,
So,
Taking their proportion
=> [tex]\frac{60}{40} = \frac{q}{26}[/tex]
Cross Multiplying
q × 40 = 26 × 60
q = [tex]\frac{1560}{40}[/tex]
q = 39
Multiply 8/11 by the reciprocal of -16/121
Answer: -11/2
Step-by-step explanation:
First, find the reciprocal of -16/121. Which is -121/16 (you can put the negative sign anywhere). Now, you must multiply the two fractions:
[tex]\frac{8}{11} *-\frac{121}{16}[/tex]
You can cross out the terms 8 and 16 because they can be simplified into 1 and 2. And you can cross out 11 and -121 because they can be simplified into 1 and -11:
= [tex]\frac{1}{1} * -\frac{11}{2}[/tex]
Now multiply the numerators together, and multiply the denominators:
= [tex]-\frac{11}{2}[/tex]
solve the equation (X-1) (2x+5)=0
Answer:
x = -5/2
x = 1
Step-by-step explanation:
(x-1) (2x+5) = 0
Divide both sides by (x-1)
2x+5 = 0
Subtract 5 on both sides.
2x = -5
Divide 2 into both sides.
x = -5/2
(x-1) (2x+5) = 0
Divide both sides by (2x+5).
x - 1 = 0
Add 1 to both sides.
x = 1
The volume of the cylinder is 230 cubic units. What is the volume of the
cone? Round to the nearest enth if necessary.
Answer:
Step-by-step explanation:
The formula for determining the volume of a cylinder is expressed as
Volume = πr²h
Where
r represents the radius of the cylinder
h represents the height of the cylinder
π is a constant
The formula for determining the volume of a cone is expressed as
Volume = 1/3πr²h
Where
r represents the radius of the cone
h represents the height of the cone
This means that the volume of the cone is 1/3 × volume of cylinder. Since the volume of the given cylinder is 230 cubic units, then
Volume of cone = 1/3 × 230 = 76.7 cubic units
Based on the given angle measures, which triangle has side length measures that could be correct? A right triangle is shown. The length of the hypotenuse is 16, the base is 8, and the other side is 13.9. The top angle is 60 degrees and the bottom right angle is 30 degrees. A right triangle is shown. The length of the hypotenuse is 13.9, the base is 8, and the other side is 16. The top angle is 60 degrees and the bottom right angle is 30 degrees. A right triangle is shown. The length of the hypotenuse is 13.9, the base is 16, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees. A right triangle is shown. The length of the hypotenuse is 16, the base is 13.9, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees.
Answer:
A right triangle is shown. The length of the hypotenuse is 16, the base is 13.9, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees.
Step-by-step explanation:
The measures of the angles of in a triangle should correspond to the length size of the side opposite each angle in a triangle.
In simple terms, this means that the larger the measure of an angle, the longer the length of the side opposite that angle. Therefore, the smallest measure of an the 3 angles in the triangle should correspond with the shortest length.
Therefore, the triangle with the correct side length would be "A right triangle is shown. The length of the hypotenuse is 16, the base is 13.9, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees." Check the attachment below to see how each side length corresponds with each angle opposite them.
Answer:
D
Step-by-step explanation:
your welcome
The sequence of the differences, 2, 4, 8, 16, 32, … is a geometric sequence with:
Answer:
The first term as 2.
Pattern: Multiply the previous term and 2 to get the next term.
Step-by-step explanation:
The pattern is every term is 2× the previous term.
The sequence of the differences, 2, 4, 8, 16, 32, … is geometric. The pattern is every term is 2 times the previous term.
What is geometric series?The geometric series is a series in which the ratio of two consecutive numbers is constant.
The sequence of the differences, 2, 4, 8, 16, 32, … is geometric.
So, The ratio of two consecutive numbers is constant.
r = 4/2 = 2
r = 8/4 = 2
Thus, The pattern is every term is 2 times the previous term.
Learn more about geometric series;
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On Monday the price of a company’s stock is $30 per share. On Tuesday, the stock price drops $3, on Wednesday it rises $7, on Thursday it rises $3, and on Friday it drops $4. Write a mathematical statement that represents the situation and determine the price at the end of the week.
Answer:
The price at the end of the week is $33.
Step-by-step explanation:
We are given that on Monday the price of a company’s stock is $30 per share. On Tuesday, the stock price drops $3, on Wednesday it rises $7, on Thursday it rises $3, and on Friday it drops $4.
The price of a company’s stock on Monday = $30 per share
So, the mathematical statement that represents the situation is given by;
Price of company’s stock on Monday = $30
On Tuesday, the stock price drops $3, so the price of company’s stock on Tuesday = Price of company’s stock on Monday - Drop in price on Tuesday
= $30 - $3 = $27
On Wednesday, the stock price rises $7, so the price of company’s stock on Wednesday = Price of company’s stock on Tuesday + Rise in price on Wednesday
= $27 + $7 = $34
On Thursday, the stock price rises $3, so the price of company’s stock on Thursday = Price of company’s stock on Wednesday + Rise in price on Thursday
= $34 + $3 = $37
On Friday, the stock price drops $4, so the price of company’s stock on Friday = Price of company’s stock on Thursday - Drop in price on Friday
= $37 - $4 = $33
Hence, the price at the end of the week is $33.
An account pays 7%per year simple interest. In 1 year, the amount in the account is 950. How much is in the account in year 6
Answer:
First year's interest is already given.
There are 5 more payments of interest
= 5 * 0.07 * 950 = 332.5
so amount in the account after 6 years = 950 + 332.5 = 1282.5
Answer:
The answer is 1282.50
Step-by-step explanation:
Can someone answer this question thanks
Answer:
80 = x
Step-by-step explanation:
The base angles are the same if the side lengths are the same
The unmarked angle is 50 degrees
The sum of the angles is a triangle is 180 degrees
180= 50+50+x
180 = 100 +x
180 -100 = 100+x-100
80 = x
Answer:
80°
Step-by-step explanation:
In an isosceles triangle, if the two sides are the same length, then the two angles formed on the base line are equal.
The other angle on the base line is also equal to 50°.
Angles in a triangle add up to 180°.
x° + 50° + 50° = 180°
x° + 100° = 180°
x° = 180° - 100°
x° = 80°
Circumference of circles
Answer:
The circumference formula is 2πr and we know r = 1 so the answer is 2π.
Answer: 6.28 feet
Step-by-step explanation:
The formula for circumference is C= πd Diameter is radius times two. So use a value of π which is usually 3.14 or 3.1416 for practical purposes. Multiply by the diameter. 3.14×2=6.28.
What is the domain of g(x)?
Answer:
-2 ≤x≤5
Step-by-step explanation:
The domain is the inputs
The lowest value of x is -2 and every value of x is valid up to 5
-2 ≤x≤5
Given that ABCD is a rhombus, find the value of x.
Answer:
C
Step-by-step explanation:
The diagonals of a rhombus are perpendicular bisectors of each other.
Thus the angle at the intersection of the diagonals is 90°
The sum of the 3 angles in a triangle = 180°
Sum the angles in the lower triangle and equate to 180, that is
90 + x + x + 40 = 180
2x + 130 = 180 ( subtract 130 from both sides )
2x = 50 ( divide both sides by 2 )
x = 25 → C
The value of x is 25.
What are some of the properties of a rhombus?
All four sides are equal.Diagonals bisect each other at 90°.Given
ABCD is a rhombus,
∠CAD = x°,
∠BDA = (x + 40)°.
Find the equation in x
Let the point where the diagonals intersect be E.
Then, using the property of the rhombus ∠AED = 90°.
We know, in a triangle that the sum of all the three interior angles equals 180°. So, we get,
∠AED + ∠BDA + ∠CAD = 180°
⇒ ∠BDA + ∠CAD = 180° - ∠AED
= 180° - 90° = 90° (∠AED = 90°)
Put the given values of these angles,
(x + 40)° + x° = 90°.
This is the equation to be solved to obtain x.
Solve for x
(x + 40)° + x° = 90°
⇒ (2x)° = 90° - 40° = 50°
⇒ x° = (50 / 2)°
⇒ x = 25.
The required value of x is 25.
Learn more about the properties of a rhombus here
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What is the area of the composite figure? -70 cm2 -100 cm2 -105 cm2 -130 cm2
Make two shapes out of it.
The bottom is a rectangle 14 x 5 = 70 square cm
The top is a triangle 1/2 x 12 x 5 = 30 square cm
Total area = 70 + 30 = 100 square cm
Answer:
100 cm²
Step-by-step explanation:
The composite shape can be cut into two shapes. One triangle and one rectangle. The sum of their areas is the area of the whole composite shape.
The area of the triangle:
b × h × 1/2
(14 - 2) × 5 × 1/2
60 × 1/2
= 30 cm²
The area of the rectangle:
l × w
14 × 5
= 70 cm²
Add the areas of the two shapes.
30 cm² + 70 cm²
= 100 cm²
The area of the composite shape is 100 cm².
apply the distributive property to factor out the greatest common factor for 9+12n I need an expression too
Answer:
3(3+4n)
Step-by-step explanation: