Answer:
x over quantity 2x plus 3 equals 40 over 60
Step-by-step explanation:
Let light clothes=x
Number of dark clothes = 2x + 3,
Dark clothes are 60% of total clothes
Light clothes=100%-60%
=40%
Light clothes / dark clothes = percentage of light clothes / percentage of dark clothes
x / 2x+3 = 40 / 60
x over quantity 2x plus 3 equals 40 over 60
Expression for this situation will be [tex]\frac{x}{2x+3}=\frac{60}{40}[/tex].
Let the number of dark cloths = y
And the number of light cloths = x
"The number of dark cloths is three more than twice the number of light cloths".
Therefore, equation will be,
y = 2x + 3 ----- (1)
"The laundry is 60% dark cloths"
Equation for this statement will be,
y = [tex]\frac{60}{100}(x+y)[/tex]
y = 0.6x + 0.6y
y - 0.6y = 0.6x
0.4y = 0.6x
[tex]\frac{y}{60}=\frac{x}{40}[/tex]
Now substitute the value of y from equation (1),
[tex]\frac{2x+3}{40}=\frac{x}{60}[/tex]
[tex]\frac{2x+3}{x}=\frac{40}{60}[/tex]
[tex]\frac{x}{2x+3}=\frac{60}{40}[/tex]
Therefore, expression for this situation will be [tex]\frac{x}{2x+3}=\frac{60}{40}[/tex].
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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.
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/hsolve 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
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
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
What shape best describes the cross section cut at an angle to the base of a right rectangular prism? Trapezoid Parallelogram Square Rectangle
Answer:
Rectangle.
Step-by-step explanation:
The 2 dimensional section would be a rectangle.
Answer:
rectangle
Step-by-step explanation:
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:
What is the answer ?
Answer:
a rational number
Step-by-step explanation:
a rational number + a rational number will always be a rational number.
In 1995 the USPS approximated that they handled 1.8 x 10^11 pieces of mail. In 2010 the USPS reported that they handled 1.7x10^11 pieces. How many more pieces of mail were handled in 1995 than 2010
Answer:
[tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.
Step-by-step explanation:
We are given that in 1995, the USPS approximated that they handled [tex]1.8 \times 10^{11}[/tex] pieces of mail and in 2010, the USPS reported that they handled [tex]1.7 \times 10^{11}[/tex] pieces.
To find how many more pieces of mail were handled in 1995 than in 2010, we do subtraction of the pieces of mail that were handled in both the years.
Pieces of mail handled in 1995 = [tex]1.8 \times 10^{11}[/tex]
Pieces of mail handled in 2010 = [tex]1.7 \times 10^{11}[/tex]
As it is clear that more pieces of mail were handled in 1995.
So, Pieces of mail handled in 1995 - Pieces of mail handled in 2010 = [tex](1.8 \times 10^{11}) -(1.7 \times 10^{11})[/tex]
= [tex]10^{11} \times (1.8 -1.7)[/tex]
= [tex]10^{11} \times 0.1[/tex] = [tex]1 \times 10^{10}[/tex]
Hence, [tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.
What is the value of X in the given right triangle? WILL GIVE BRAINLIEST!
Answer:
Please mark me brainliest and I hope this helped!
x = 45
Step-by-step explanation:
In this case, we can use the Pythagorean Theorem to figure out the other side of the triangle.
c squared - a squared = b squared
10 squared - 7 squared = b squared
100 - 49 = b squared
51 = b squared
7.14 = b
Now that we know the other side is about 7, we can assume that x is equal to the angle between 10 and 7. So x equals 45.
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]
There 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
Find the equation of a line that passes through the point (3,2) and has a gradient of - 1/3
Leave your answer in the form y=mx + c
Answer:
y = -1/3x +3
Step-by-step explanation:
When given a point and slope, it is convenient to start with a point-slope form of the equation of a line.
y = m(x -h) +k . . . . . line with slope m through point (h, k)
y = (-1/3)(x -3) +2 . . . line with slope -1/3 through point (3, 2)
y = -1/3x +3 . . . . . . . simplified to slope-intercept form
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
Solve the equation 4x2 – 27x – 5 = –10x to the nearest tenth.
Find the value of x.
Answer:
x= 42
Step-by-step explanation:
(2x +1)°= 85° (vert. opp. ∠s)
2x +1= 85
2x= 85 -1 (bring constant to 1 side)
2x= 84 (simplify)
x= 84 ÷2
x= 42
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:
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.
Evaluate xy - y if x=6 and y=-5
Answer:
-25
Step-by-step explanation:
xy - y
Replace 'x' with 6, and 'y' with -5:
[tex]6(-5)-(-5)\\\\-30+5\\\\\boxed{-25}[/tex]
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°
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
Z^5=-7776i
Find the solution of the following equation whose argument is strictly between 270 and 360 degrees
Answer:
Z=+6
Step-by-step explanation:
Z^5=-7776i
Let's note that i I mathematics means negative one i.e
i = -1
So the equation is equal to
Z^5=-*-(7776)
Z^5 = 7776
Z= 5√7776
Since it's a divisible by 6
It's giving us a clue that 6 it's the answer.
Ok let's check the 5th root of 7776 in our calculator.
Z=+6
+6 is the solution to the equation
Z^5=-7776i
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:
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
Evaluate the expression \dfrac{7^2}{x^2-2} x 2 −2 7 2 start fraction, 7, squared, divided by, x, squared, minus, 2, end fraction for x=3x=3x, equals, 3
Answer:
7
Step-by-step explanation:
We want to evaluate the fraction below for x = 3. We will put the value of x to be 3:
[tex]\dfrac{7^2}{x^2-2}\\\\= \dfrac{7^2}{3^2-2}\\\\= \dfrac{49}{9-2}\\\\= \dfrac{49}{7} = 7[/tex]
The answer is 7.
Answer:
7Step-by-step explanation:
goodluck khan academy users
What is the value of the power a if 5^a = 1/125
Answer:
a = -3
Step-by-step explanation:
5^a = 1/125
The fraction 1/125 can be written as a power with base 5.
5^a = 5^(-3)
Cancel the same bases on both sides.
a = -3
Answer:
a = -3.
Step-by-step explanation:
5^a = 1/125
1/125 = 1 / 5^3
= 5^-3
5^a = 5^-3
so a = -3.
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:
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.
expand the following 5( 2x -4 )
Answer:
10x-20
Step-by-step explanation:
5(2x-4)
5x2=10
5x4=20
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.