If 4 teenagers can clean in 6 hours, 1 teenager will take 4x more time
1 teenager will take 24 hours = k
No. of teenagers (p) is proportional to time (t):
p = k/t
3 = 24/t
t = 24/3 = 8 hours
So it will take 8 hours for 3 teenagers to clean a house.
8 hours
Step-by-step explanation:
teenagers. hours
4. 6
3. ?
it is actually direct multiplication where you multiply the upper numbers,4 × 6 ,then divide by the lower value, 3. This gives 24 /3 which gives you 8 .
Simplify 9 3 × 9 2 × 9 4 leaving your answer in index form.
Answer:
804,264
Step-by-step explanation:
Evaluate 93×92×94
We have 1 of the number 93
We have 1 of the number 92
We have 1 of the number 94
Group numbers by powers:
93×92×94 = 93[1]92[1]94[1]
93[1]92[1]94[1] = 804,264
DO,K = (9, 6) (3, 2) The scale factor is___ 1/3 6 3
Based on the dilation, the scale factor of dilation of the point is 1/3
What is dilation?Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.
How to determine the scale factor of dilation?From the question, we have the following parameters
Dilation rule: Do,k
Point = (9, 6)
Image = (3, 2)
As a general rule of dilation, the following are the properties of a scaled copy of another figure
If the scale factor is greater than 1, the side lengths would be greater than the original figureIf the scale factor is less than 1, the side lengths would be less than the original figureThe side lengths may or may not be whole numbersUsing the above as a guide, the scaled factor is calculated as
Scaled factor = Image/Poins
This gives
Scaled factor, k = (3, 2)/(9, 6)
This gives
Scaled factor, k = 1/3
Hence, the scale factor is 1/3
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-23x² + x² - 6x + 10 + 2x²
Answer:
-2(-10x^2 + 3x -5)
Step-by-step explanation:
Combine like terms
Then find the common factor
Answer:
[tex]-20x^{2} -6x+10[/tex]
Step-by-step explanation:
[tex]=-23x^{2} +x^{2} +2x^{2} -6x+10[/tex]
[tex]=-23x^{2} +3x^{2} -6x+10[/tex]
[tex]=-20x^{2} -6x+10[/tex]
Hope this helps
Mr. Lopez travels a distance of 100 miles to work each day, Which of the following graphs best represents the
relationship between the time Mr. Lopez takes to get to
work and the speed at which he drives?
Answer:
Step-by-step explanation:
they left at 12:34
A car traveled at a constant speed. The graph shows how far the car traveled, in miles, during a given amount of time, in hours.
The point is on the graph. Explain what this means in terms of the car.
Is the point on this graph? Explain how you know.\
The point (1, 60). on the graph how's the speed that the car travels.
How to illustrate the value?It should be noted that car traveled at a constant speed. The distance traveled is 210 miles and the time to travel is 3.5 hours.
Therefore, it should be noted that the point (3.5, 120) shows the distance.
The slope of the like which is the speed will be:
= Distance / Time
= 210 / 3.5
= 60 mph
Therefore, it should be noted that the point B(1, 60) lies on the graph.
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how do I write this ?
Answer:
1: -⅔
2: -⅓
Step-by-step explanation:
You plug the number into the Equation.
1:
2 = 3x + 4
-2 = 3x
x = -⅔
2:
3 = 3x + 4
-1 = 3x
x = -⅓
Given the function, [tex]f(x)=-2x-1[/tex] express the value of [tex]\frac{f(x+h)-f(x)}{h}[/tex] in simplest form.
Value of the function [ f(x+ h) - f(x) ] /h in simplest form when f(x) = -2x -1 is equal to -2.
As given,
Given function:
f(x) = -2x -1
Express value of in simplest form:
f( x + h ) = -2 (x + h ) - 1
= -2x -2h -1 ___(1)
Simplify the function by substituting value of f(x +h and f(x),
[f(x + h) - f(x) ] /h
= [ (-2x -2h -1 )- ( -2x -1 ) ] /h
= ( -2x -2h -1 +2x +1 ) /h
= -2h /h
= -2
Therefore, value of the function [ f(x+ h) - f(x) ] /h in simplest form when f(x) = -2x -1 is equal to -2.
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algebra vocabulary question
Answer:
We would describe 7x - 3 > 24 as an inequality
Step-by-step explanation:
The definition of inequality is a relationship between two expressions using one of these inequality symbols:
greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).
Answer:
Inequality
Step-by-step explanation:
Inequalities are never equal just like the question you have
A line is drawn through (-7, 11) and (8,-9). The equation
y-11 = -4/3(x + 7) is written to represent the line. Which
equations also represent the line? Check all that apply.
Answer:
[tex]\textsf{Slope-intercept form}: \quad y=-\dfrac{4}{3}x+\dfrac{5}{3}[/tex]
[tex]\textsf{Standard form}: \quad 4x+3y=5[/tex]
Step-by-step explanation:
Given linear equation:
[tex]y-11=-\dfrac{4}{3}(x+7)[/tex]
The given linear equation is point-slope form.
[tex]\boxed{\begin{minipage}{3.7cm}\underline{Slope-intercept form}\\\\$y=mx+b$\\\\where $m$ is the slope\\ and $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
To write the equation in slope-intercept form, isolate y:
[tex]\implies y-11=-\dfrac{4}{3}(x+7)[/tex]
[tex]\implies y-11=-\dfrac{4}{3}x-\dfrac{28}{3}[/tex]
[tex]\implies y-11+11=-\dfrac{4}{3}x-\dfrac{28}{3}+11[/tex]
[tex]\implies y=-\dfrac{4}{3}x+\dfrac{5}{3}[/tex]
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Standard form}\\\\$Ax+By=C$\\\\where $A, B$ and $C$ are constants and $A$ must be positive.\\\end{minipage}}[/tex]
To write the equation in standard form, eliminate the fraction, bring the terms in x and y to the left of the equation, and the constants to the right:
[tex]\implies y-11=-\dfrac{4}{3}(x+7)[/tex]
[tex]\implies (y-11) \cdot 3=-\dfrac{4}{3}(x+7) \cdot 3[/tex]
[tex]\implies 3y-33=-4(x+7)[/tex]
[tex]\implies 3y-33=-4x-28[/tex]
[tex]\implies 3y-33+4x=-4x-28+4x[/tex]
[tex]\implies 3y-33+4x=-28[/tex]
[tex]\implies 3y-33+4x+33=-28+33[/tex]
[tex]\implies 4x+3y=5[/tex]
A circular pond has a diameter of 15 feet which expression can be used to find the circumference in feet 
The expression used for finding the circumference of the circular pond is; C = 2π(d/2) feet.
What is defined as the circumference?The circumference of the circle, also known as the perimeter of the circle, is the measurement of the circle's boundary. The area of a circle, on the other hand, defines the region it occupies. If we expand a circle and draw a straight line through it, the length of the line is the circumference. It is typically measured in units such as centimeters or meters.For the given question;
Let 'd' be the diameter of the circular pond.
The diameter of the pond = 15 feet.
Let 'C' be the circumference of the circle;
The, the formula for finding the circumference of the circle is;
C = 2π(d/2) feet
For, d = 15 feet
C = 2π(15/2) feet
Take π = 3.14
C = 2×3.14×(15/2) feet
C = 47.1 feet
Thus, the circumference of the circular pond is found as 47.1 feet.
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When an integer is subtracted from 2 times the next consecutive odd integer, the difference is 9. Find the value of the greater integer.
The integer is 5 and the next consecutive odd integer will be 7.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
let the integer be x
then, next consecutive odd integer will be x + 2
Now, according to the question :
integer is subtracted from 2 times the next consecutive odd integeb the difference is 9 means :
2(x+2) - x = 9
2x+ 4-x = 9
x + 4 = 9
x = 5
Therefore, The integer is 5 and the next consecutive odd integer will be 7.
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What is the equation of a line that contains the points (5, 0) and (5,-2)?
Ox=5
Ox=0
Oy=0
Oy=5
Answer:
x=5
you're welcome
Suppose the domain of f is ( -1, 1).
Define the fucnction g by g(x)=f([tex]\frac{x+1}{x-1}[/tex]).
What is the domain of g?
If the domain of f is ( -1, 1), then the function g defined by g(x) = f((x + 1)/(x - 1)) has a domain of; (-2, 0)
What is the domain of the function?The domain of a function refers to the set of all possible intput values that make the function possible.
Now, we are given the function;
g(x) = f((x + 1)/(x - 1))
The domain would be a set of real numbers excluding 1 because at x = 1, the function is undefined.
Since the domain of f(x) is -1 < x < 1 ,
Then the domain of f(x + 1) is -1 < x + 1 < 1 .
domain of -1 < x + 1 < 1 will simplify to -2 < x < 0
Thus, we can say that the domain of f(x + 1) is (-2, 0).
Thus;
g(x) = f(x + 1) and as such, the domain of g(x) is (-2, 0) .
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simplify 2(x - 4) + 9
Answer: 2x + 1
Step-by-step explanation:
We will simplify this expression down to it's lowest terms.
Given:
2(x - 4) + 9
Distribute:
2x - 8 + 9
Combine like terms:
2x + 1
Carol has 1\frac{5}{8} cups of yogurt to make smoothies. Each smoothie uses \frac{1}{3} cup of yogurt.
What is the maximum number of smoothies that Carol can make with yogurt?
Carol can make a maximum of 4 smoothies with the available yoghurt
Cups of yoghurt Carol has for making smoothies = 1 5/8 cups
Yoghurt Carol has in improper fractions = 13/8 cups
Cup of yoghurt used to make smoothie = 1/3 cups
Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
Number of smoothies Carol can make = Total available yoghurt with Carol/Yoghurt used to make a smoothie
= (13/8)/(1/3)
= 39/8
Converting the fraction into a mixed fraction we get: 4 7/8 smoothies
So, she can make 4 cups of smoothie
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i need help on these
Answer:
read below
Step-by-step explanation:
1. $4, five granola bars cost $20. $20/5 = $4
2. 40 miles per hour, travels 100 miles at a constant speed for 40 miles. 100/2.5 = 40 miles
3. 12.5 situps per minute, 50 situps in 4 minutes. 50/4 = 12.5
4. $1.43 per one ounce, 3 ounces cost $4.29. 4.29/3 = $1.43
Select the correct answer. which situation is best met through long-term saving? a. a broken refrigerator b. retirement c. an unexpected car repair d. an unexpected medical bill
The situation best met through long term saving is retirement (Option B).
In many cases, the retirement fund is taken out of the paychecks at your job and is accumulated over years of your service and job till retirement, it is a long-term saving.
The purpose of long-term saving is the type of saving for long term financial goals. The other options are not long-term financial goals rather unexpected expenses. Hence, a situation best fulfilled through long term saving is retirement.
There are several long-term saving accounts use to save for long term financial goals such as retirement, buying a house, children’s education, or similar one-time, long-term expenses.
Hence, the correct answer is retirement – Option B
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What is the slope of a line that goes through the points (1,-5) and (-3, 2)?
O
O
O
7
4
3
3
Answer:
[tex]\sf -\dfrac{7}{4}[/tex]
Step-by-step explanation:
Finding the slope of a line:(1, -5) ⇒ x₁ = 1 ; y₁ = -5
(-3, 2) ⇒ x₂ = -3 ; y₂ = 2
[tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{2-[-5]}{-3-1}\\\\= \dfrac{2+5}{-4}\\\\=\dfrac{7}{-4}\\\\= -\dfrac{7}{4}[/tex]
please helpp i am very confused on finding the answer
Answer:
C. Lines l and m appear to be skew--they are not parallel, and they are not intersecting each other.
Guadalupe quiere saber la longitud de un túnel construido a través de una montaña. Para ello, ella toma las medidas indicadas en la figura a continuación. Utilizar estas medidas para hallar la longitud del túnel.
Llevar a cabo los cálculos intermedios usando al menos cuatro posiciones decimales.
Redondear la respuesta a la décima de metro más cercana.
the 5ft tall person casts a shadow that is 4 ft long. how tall is the flagpole if it 28 foot shadow?
The flagpole is 35ft tall.
How to find the shadow's height?Given,
A 5ft tall person casts a shadow that is 4 ft long.
Flagpole has a 28-foot shadow.
Solution:
Let x be the height of the flagpole.
5/x = 4/28
x = 35ft
The flagpole is 35ft tall.
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A satellite orbiting the earth uses radar to communicate with two control stations on the earth's surface. The satellite's orbit maintains a 10-degree angle of separation between the two stations, as shown in the picture below. Knowing that the earth's radius is 3,963 miles, answer the following questions. Round all answers to the nearest whole number.
TheThe number of miles that a signal sent from Station 1 to the satellite and then to Station 2 will have to travel is; 48,135 miles.
Number of milesDistance from Station 1 to satellite:
tan8.7 = length of longest leg / length of longest leg
tan8.7 = 3963/length of shortest leg
Length of longest leg=3963/tan8.7°
Length of longest leg=3963/0.15302150298
Length of longest leg =25,898 miles
Distance from Station 2 to satellite:
sin 8.7 = length of longest leg / length of hypotenuse
sin 8.7 = 3963/length of hypotenuse
Length of hypotenuse =3963/ sin 8.7
Length of hypotenuse =3963/0.1526082024
Length of hypotenuse=26, 200 miles
Hence,
26, 200 miles - 3,963 =22,237 miles
Total distance:
Total distance = 25,898 miles + 22,237 miles
Total distance = 48,135 miles
Therefore the distance is 48,135 miles.
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The complete question is:
A satellite orbiting the earth uses radar to communicate with two control stations on the earth's surface. The satellite's orbit maintains a 10-degree angle of separation between the two stations, as shown in the picture below. Knowing that the earth's radius is 3,963 miles.
How many miles will a signal sent from Station 1 to the satellite and then to Station 2 have to travel?
When an integer is subtracted from 3 times the next consecutive integer, the difference is 23. Find the value of the lesser integer.
Answer:
10
Step-by-step explanation:
To find the value of the smaller integer, start by letting a variable be that integer. This helps us to refer to the integer with greater ease in our working.
Let the smaller integer be x.
Consecutive numbers refers to numbers coming after one another, such as 1, 2 and 3.
The next integer coming after the integer x would thus be (x +1). Three times the next consecutive integer would then be 3(x +1).
Subtract refers to a minus sign, thus the equation would be:
3(x +1) -x= 23
Expand:
3x +3 -x= 23
Simplify:
2x= 23 -3
2x= 20
Divide both sides by 2:
x= 20 ÷2
x= 10
Thus, the smaller integer is 10.
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*Note that when b is subtracted from a, the expression would be a -b.
Under certain conditions the pressure of a gas varies directly with the temperature. When the - pressure is 800 psi, the temperature is 400°. What is the temperature when the pressure is 450
The temperature when the pressure is 450 is 225°.
What is Direct Variation?In the case of an increase or decrease in both quantities by the same factor, two quantities are said to follow a direct variation. As a result, when one quantity rises, the other follows suit, and vice versa when one quantity falls. In other words, if the ratio of the first quantity to the second quantity is a constant term, the quantities are said to be directly proportional to one another. The term "coefficient or constant of proportionality" refers to this constant number.Given:
The pressure of a gas varies directly with the temperature.
So, P ∝ T
P = kT , here k is the constant of proportionality
Pressure(P) = 800psi
Temperature(T) = 400°
Putting the values to get the value of k,
P = kT
800 = 400k
k = 2
We need to find the temperature when the pressure is 450.
P = kT
450 = 2T
T = 450/2
T = 225°
Therefore, the required temperature is 225°.
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I have been struggling with this question for the past couple minutes I believe I have the formula correct, but it isn't working
Answer:
382.5 in^2
Explanation in attachment. Hope it helps! :)
If GI and JL are parallel lines and mZJKH = 70°, what is m<LKM
WILL GIVE BRAINLIEST
Answer:
70°
Step-by-step explanation:
Since m∠JKH and m∠LKM are verticle angles, they are equal to each other.
find the lcm of the numbers 3,6,16 using lists of multiples
Answer:
48
Step-by-step explanation:
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48
6 12 18 24 30 36 40 48
16 32 48
Write each number as a polynomial and then simplify the sum or difference
Answer:
[tex]90a+10b[/tex]
Step-by-step explanation:
[tex](100a+10b+c)-(10a+c) \\ \\ =100a+10b+c-10a-c \\ \\ =90a+10b[/tex]
An investor has $75,000 to invest in a CD and a mutual fund. The CD yields 6% and the mutual fund yields 7%.
The mutual fund requires a minimum investment of $10,000, and the investor requires that at least twice as much
should be invested in CDs as in the mutual fund. How much should be invested in CDs and how much in the
mutual fund to maximize the return? What is the maximum return?
A line has a slope of 1/3 and includes the points (6,1) and (9,j). What is the value of j?
WE WILL USE THE FORMULA OF CALCULATING GRADIENT
[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{j - 1}{9 - 6} \\ \frac{1}{3} = \frac{j - 1}{3} [/tex]
I WILL USE CROSS MULTIPLICATION
[tex]3(j - 1) = 3 \\ \frac{3(j - 1)}{3} = \frac{3}{3} \\ j - 1 = 1 \\ j = 1 + 1 \\ j = 2[/tex]
ATTACHED IS THE SOLUTION
BE ALERT I INSERTED THE KNOWN VALUES IN THE FORMULA OF FINDING THE GRADIENT.