The algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three" is [tex]\frac{-8}{n+3}[/tex] or [tex]-8 \div n+3[/tex]
Solution:Given statement is "the quotient of negative eight and the sum of a number and three"
To write the algebraic expression, follow these steps:
Let "n" be the number
The expression "negative eight" is equivalent to -8
Now look at the statement "the sum of a number and three"
"The sum of a number and three" is equivalent to n + 3
Now put all the statements together:
Quotient means you are dividing. So use division
"The quotient of negative eight and the sum of a number and three" = [tex]\frac{-8}{n+3}[/tex] or [tex]-8 \div n+3[/tex]
Use the following function rule to find f(4).
f(x) =
7
x
+ 5
HERE IS THE ANSWER 85
Answer:
33
Step-by-step explanation:
substitute 4 in the place of x.
multiply 4 by 7 then add 5 and your answer is 33.
joey earns $16 per hour as a telemarketer. he also earns a monthly bonus of $400 . joey earned $2000 last month. how many hours did he work
Answer:
100 hours
Step-by-step explanation:
Monthly salary = monthly bonus + total wage based on hours worked
Monthly salary = monthly bonus + (dollars per hour x number of hours worked)
Given, monthly salary = $2000
MOnthly bonus = $400
dollars per hour = $16/hr
let h = number of hours worked
hence, equation becomes
2000 = 400 + (16 x h)
2000 = 400 + 16h (subtract 400 from each side and rearrange)
16h = 2000 - 400
16h = 1600 (divide both sides by 16)
h = 1600 / 16 = 100 hours
What do all simple machines have in common?
A
They have a mechanical advantage.
B
They have few or no moving parts.
C
They can be used to do work.
D
All of the above
Answer:
D: All of the above.
Step-by-step explanation:
A. All simple machines are useful in some way, weather that be making it easier to lift heavy objects, activating other machines, or something else.
B. Any simple machine must be, well, simple. i. e. have few moving parts.
Take the lever, for example. It has only one moving part, yet it is still very useful.
C. They can be used to do work. Simple machines can be put together to make something that can do work.
Imagine a windmill that generates power, which then is taken by a motor attached to an Archimedes screw. All of these machines are simple, yet they are still used to do work.
solve with the quadratic formula
4×^2×+1=0
Answer:
Either x = + i/2 or x = i/2 is the solution for the given quadratic equation.
Step-by-step explanation:
Here, the given quadratic equation is:[tex]4x^2 + 1 = 0[/tex]
Now, comparing the given equation with standard Quadratic Form, [tex]ax^2 + bx + c = 0[/tex]
we get,a = 4, b =0 and c = 1
Now, the Quadratic Formula is given as:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
So, here the solution for the given expression is:
[tex]x = \frac{0 \pm \sqrt{(0)^2 - 4(4)(1)} }{2(4)} = x = \frac{0 \pm \sqrt{-16} }{8}\\\implies x = \frac{0 \pm4i}{8}\\\implies x = \frac{0 + 4i}{8} = \frac{i}{2} \\or, x = \frac{0 - 4i}{8} = \frac{-i}{2}[/tex]
Hence, either x = + i/2 or x = i/2 is the solution for the givenquadratic equation.
perform the indicated operation square root of 8 + square root of 50
Answer:
√8 + √50
= 2√2 + 5√2
=√2(2+5)
= 7√2
Hope this helps!
The probability that an event will
occur is 0.25.
Answer:
PLEASE PROVIDE MORE INFORMATION
Step-by-step explanation:
Evaluate the expression when m=6 and n= 7
8n+m
Answer:
62
Step-by-step explanation:
8 x n + m = ?
8 x 7 + 6
8 x 7 = 56
56 + 6 = 62
Answer: 62
Step-by-step explanation:
solution here m=6,n=7,and 8n+m=? now 8n+m =8×7+6 =56+6 =62
Which of these scatter plots has a trend line that would lie closest to y=x?
A. Scatter plot A
B. Scatter plot B
C. Scatter plot C
D. Scatter plot D
Correct Answer: A. Scatter plot A
Explanation: The line y=x slopes upward from the lower left corner of the graph to the upper right corner, at a 45-degree angle. The scatter plot whose points most closely match that trend is scatter plot A.
Answer:
A. Scatter plot A.Step-by-step explanation:
We need to find the scatter plot that is closest to y = x.
First of all, you must know the behaviour of y = x. That equation represents a straight line that passes through the origin of the coordinate system.
So, the right scatter plot must have the majority of points on this line that passes through the origin.
Notice that the Scatter plot A has this beahivour, if you draw a straight line through the origin and the points, you'll observe that the line best fits.
On the other hand, the other scatter plots are not following this linear behaviour.
Therefore, the right answer is A.
What is the genotype of the offspring missing on the first row of the Punnett square?
A. IBIB
B. IAIB
C. IBiO
D. none of the above
Answer:
Option B
Step-by-step explanation:
On the first row of the Punnett square, the offspring inherits IA from one parent and IB from another parent hence the resulting genotype is IAIB.
Decide whether the two equations are equivalent.
2a + 6 = 12
a+3 = 6
Answer:
Yes
Step-by-step explanation:
2a+6=12
2a=12-6
2a=6
a=6/2
a=3
--------------
a+3=6
a=6-3
a=3
----------
Yes, the two equations are equivalent.
If 1/2 is subtracted from four times the reciprocal of a number, the result is 0. Find the number.
Answer:
The Number is 8.
Step-by-step explanation:
Let the number be x.
Given:
1/2 is subtracted from four times the reciprocal of a number, the result is 0.
Hence the equation will become like;
[tex]4\times \frac{1}{x} - \frac{1}{2}=0[/tex]
Now Solving the equation we get.
[tex]\frac{4}{x} -\frac{1}{2}=0\\\\\frac{4}{x} = \frac{1}{2}\\\\x= 4\times 2\\x=8[/tex]
Now the we can see the number is 8, when 1/2 is subtracted from 4 times the reciprocal of number means 4/8 which becomes 1/2 and hence when 1/2 is subtracted from 1/2 it equals to 0.
Hence the number is 8.
Divide ..............
The quotient is: 4a-5
The remainder is: 0
Step-by-step explanation:
We need to divide -40a^6+50a^5 by -10a^5
The division is shown in figure attached.
The quotient is: 4a-5
The remainder is: 0
Keywords: Division of polynomials
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If a person weighs 240 pounds on Earth, what would be the difference in weight of the same person on Mars and on the Moon (based on the table and graph)?
The person weighs 56 pounds more on Mars than on the Moon.
The person weighs 56 pounds more on the Moon than on Mars.
The person weighs 560 pounds more on Mars than on the Moon.
The person weighs 560 pounds more on the Moon than on Mars.
Answer:
The answer is A.
Step-by-step explanation:
Just took the test. You are welcome.
Could someone please answer question b) ii) ?
The question is on the attached image.
b) ii) The value of y when x is 2.5 is -1.5
How to find the value of y
b) ii) The value of y when x is 2.5 is read from the graph to be approximately -1.8
An mage is attached to show how to read the value.
This can be solved by substitution
For x = 2.5
y = (2.5)² - (2.5) - 3 = 1.75
You roll a 6-sided die.
What is P(prime)?
Write your answer as a percentage.
Submit
You roll a 6-sided die. The probability of getting prime is 50%.
Solution:
Given, that we have rolled a 6 – sided die.
We have to find the P(prime) as percentage.
Now, It means that we have to find the probability of getting a prime number on the face.
On rolling a six sided die, the total possible outcomes are 1, 2, 3, 4, 5, 6
Number of possible outcomes = 6
We have to get a prime number on rolling a die
The prime numbers in possible outcomes are 2, 3, 5
So number of favorable outcomes = 3
[tex]\text {Probability of an event as percentage }=\frac{\text { favourable number of outcomes }}{\text { total number of outcomes }} \times 100[/tex]
[tex]\text {Probability of getting prime number on face of die }=\frac{3}{6} \times 100[/tex]
[tex]\begin{array}{l}{\text { P(prime) }=\frac{1}{2} \times 100} \\\\ {\text { P(prime) }=50 \%}\end{array}[/tex]
Hence, probability of getting prime is 50%.
Help please, I don’t understand it.
Answer:
[tex]K=-2J+28[/tex]
Step-by-step explanation:
For the given trend line, we need to find the y-intercept and slope of the line for determining its equation.
Equation of a line is of the form [tex]y=mx+b[/tex]
Where, 'm' is the slope and 'b' is the y-intercept.
Here, the variables are 'J' and 'K'.
The y-intercept is the point where the 'J' value is 0. From the graph, when 'J' is 0, then the 'K' value is 28. Therefore, the y-intercept is 28.
Slope is given as the ratio of change in 'K' and change in 'J'
The overall change in 'K' is 0 - 28 = -28.
The overall change in 'J' is 14 - 0 = 14
Therefore, the slope is given as:
[tex]m=\frac{\Delta K}{\Delta J}=\frac{-28}{14}=-2[/tex]
Therefore, the equation of trend line is given as:
[tex]K=-2J+28[/tex]
-3,6,-9,12,-15 which of the following represents the general term for the sequence give?
(-1)^n3^n
(-1)^n3n
(-1)^n+1(3)
The general term for the sequence [tex]a_{n}=(-1)^{n} 3 n[/tex]
Solution:Given sequence is -3, 6, -9, 12, -15
We have to find the general term of sequence
The terms in the sequence are found out by using the recursive definition:
[tex]a_{n}=(-1)^{n} 3 n[/tex]
Let us use this definition to find out the terms and check if it matches our given sequence
[tex]\begin{array}{l}{\text { For } n=1:-(-1)^{n} 3 n=(-1)^{1} \times 3 \times 1=-3} \\\\ {\text { For } n=2:-(-1)^{n} 3 n=(-1)^{2} \times 3 \times 2=1 \times 6=6} \\\\ {\text { For } n=3:-(-1)^{n} 3 n=(-1)^{3} \times 3 \times 3=-1 \times 9=-9} \\\\ {\text { For } n=4:-(-1)^{n} 3 n=(-1)^{4} \times 3 \times 4=1 \times 12=12} \\\\ {\text { For } n=5:-(-1)^{n} 3 n=(-1)^{5} \times 3 \times 5=-1 \times 15=-15}\end{array}[/tex]
Thus the general term is given by [tex]a_{n}=(-1)^{n} 3 n[/tex]
simplify the square root of -121?
Answer:
11i
Step-by-step explanation:
first you have to get a postive root.
[tex]\sqrt{-121} \\ \sqrt{-1} \sqrt{121} \\[/tex]
then you solve the square roots from there, keeping in mind the imaginary number answer to the square root of -1, i.
[tex]\sqrt{-1} = i\\ \sqrt{121} =11\\ 11i[/tex]
What is the y-intercept of the line that is
parallel to the line 2x + 10y = 7 and contains
the point (4, 9)?
Answer:
Equation: 2x + 10y = 98
y-intercept: (0, 9.8)
Step-by-step explanation:
The easiest possible way to solve thios problem follows:
Keep the form of the given line 2x + 10y = 7, replacing the '7' with the constant 'c:'
2x + 10y = c
Now take the coordinates of the given point (4, 9) and substitute them into the above equation, to find c:
2(4) + 10(9) = c
Then 8 + 90 = c, and c = 98
Then the desired equation is 2x + 10y = 98
To find the y-intercept, let x = 0 and solve for y. We get
10y = 98, so that y = 9.8. The y-intercept is thus (0, 9.8).
The y-intercept of the line parallel to 2x + 10y = 7 and containing the point (4, 9) is 8.6.
Explanation:The y-intercept of a parallel line can be found using the equation y = mx + b, where m is the slope and b is the y-intercept. Since the given line 2x + 10y = 7 is in the form Ax + By = C, we need to rearrange it to the slope-intercept form. Therefore, the equation becomes: 10y = -2x + 7 → y = (-2/10)x + 7/10. The slope of the given line is -2/10, which means any line parallel to it will also have a slope of -2/10. Now we can use the point-slope form to find the equation of the parallel line that passes through the point (4, 9):
y - y1 = m(x - x1) → y - 9 = (-2/10)(x - 4)
Expanding and simplifying the equation, we get:
y - 9 = (-2/10)x + 8/10 → y = (-2/10)x + 8/10 + 9 → y = (-2/10)x + 86/10
Therefore, the equation of the parallel line that contains the point (4, 9) is y = (-2/10)x + 86/10. The y-intercept of this line is 86/10 or 8.6.
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Which pair of triangles below shows the AAS Postulate. Explain
Answer:
We can conclude that Δ XYZ ≅ Δ RST by AAS postulate
Step-by-step explanation:
Δ XYZ and Δ RST are congruents by AAS postulate because:
1. Their non-included sides YZ and ST are equal (10 units = 10 units).
2. Their angles ∠Y and ∠S are equal.
3. Their angles ∠X and ∠R are equal.
4.Their non-included sides XZ and RT are equal.
Now, we can conclude that Δ XYZ ≅ Δ RST by AAS postulate.
5. 4x2 - 31x + 21
Factoring
Answer:
x=7 and x=(3/4)
Step-by-step explanation:
the williams have a farm that is in a rectangular shape. the length of the farm is hundred yards twice the width. the whole perimeter of the farm is 830 yards
Answer:
The length of the farm is 310 yards and the width is 105 yards
Step-by-step explanation:
The correct question is
The Williams have a farm that is in a rectangular shape. The length of the farm is one hundred yards more than twice the width. The whole perimeter of the farm is 830 yards
Find the dimensions of the farm
Let
x ----> the length of the rectangular farm
y ----> the width of the rectangular farm
we know that
The perimeter of the farm (rectangle) is equal to
[tex]P=2(x+y)[/tex]
we have
[tex]P=830/ yd[/tex]
so
[tex]830=2(x+y)[/tex]
simplify
[tex]415=(x+y)[/tex] -----> equation A
[tex]x=2y+100[/tex] ----> equation B
substitute equation B in equation A
[tex]415=(2y+100+y)[/tex]
solve for y
[tex]415=(3y+100)[/tex]
[tex]3y=415-100[/tex]
[tex]3y=315[/tex]
[tex]y=105\ yd[/tex]
Find the value of x
[tex]x=2y+100[/tex]
[tex]x=2(105)+100=310\ yd[/tex]
therefore
The length of the farm is 310 yards and the width is 105 yards
If gas prices increase 11% from $3.50 over the next month, what will the new price of gas be at the end of the month?
pls help :(
Multiply the current price by 1 + percentage of increase.
3.50 x 1.11 = 3.89
The new price will be $3.89
Which expression is equivalent to 3/4(4h-6)
Answer:
3h-9/2
Step-by-step explanation:
3/4(4h-6)=3h-18/4
simplify
3h-9/2
Answer:
3(3h-3/2) in its simplified form.
Step-by-step explanation:
Given the equation 3/4(4h-6),
First we will open the bracket up by multiplying through by 3/4 to have;
3h - 9/2
Since 3 is common at both sides of the resulting equation, we will factor it out to have;
3(h-3/2).
Since we cannot simplify further, then the expression 3/4(4h-6) is also equivalent to 3(h-3/2).
find all the solutions in there interval (0,2pi) for cos5x=-1/2
Answer:
[tex]\frac{2\pi}{15},\frac{4\pi}{15},\frac{8\pi}{15},\frac{2\pi}{3},\frac{14\pi}{15}, \frac{16\pi}{15}, \frac{4\pi}{3},\frac{22\pi}{15}, \frac{26\pi}{15}, \frac{28\pi}{15}[/tex]
Step-by-step explanation:
Solving trigonometric equations.
We are given a condition and we must find all angles who meet it in the provided interval. Our equation is
[tex]cos5x=-\frac{1}{2}[/tex]
Solving for 5x:
[tex]5x=\frac{2\pi}{3}+2n\pi[/tex]
[tex]5x=\frac{4\pi}{3}+2n\pi[/tex]
The values for x will be
[tex]x=\frac{\frac{2\pi}{3}+2n\pi}{5}[/tex]
[tex]x=\frac{\frac{4\pi}{3}+2n\pi}{5}[/tex]
To find all the solutions, we'll give n values of 0, 1, 2,... until x stops belonging to the interval [tex](0,2\pi)[/tex]
For n=0
[tex]x=\frac{\frac{2\pi}{3}}{5}=\frac{2\pi}{15}[/tex]
[tex]x=\frac{\frac{4\pi}{3}}{5}=\frac{4\pi}{15}[/tex]
For n=1
[tex]x=\frac{\frac{2\pi}{3}+2\pi}{5}=\frac{8\pi}{15}[/tex]
[tex]x=\frac{\frac{4\pi}{3}+2\pi}{5}=\frac{2\pi}{3}[/tex]
For n=2
[tex]x=\frac{\frac{2\pi}{3}+4\pi}{5}=\frac{14\pi}{15}[/tex]
[tex]x=\frac{\frac{4\pi}{3}+4\pi}{5}=\frac{16\pi}{15}[/tex]
For n=3
[tex]x=\frac{\frac{2\pi}{3}+6\pi}{5}=\frac{4\pi}{3}[/tex]
[tex]x=\frac{\frac{4\pi}{3}+6\pi}{5}=\frac{22\pi}{15}[/tex]
For n=4
[tex]x=\frac{\frac{2\pi}{3}+8\pi}{5}=\frac{26\pi}{15}[/tex]
[tex]x=\frac{\frac{4\pi}{3}+8\pi}{5}=\frac{28\pi}{15}[/tex]
For n=5 we would find values such as
[tex]x=\frac{\frac{2\pi}{3}+10\pi}{5}=\frac{32\pi}{15}[/tex]
[tex]x=\frac{\frac{4\pi}{3}+10\pi}{5}=\frac{34\pi}{15}[/tex]
which don't lie in the interval [tex](0,2\pi)[/tex]
The whole set of results is
[tex]\frac{2\pi}{15},\frac{4\pi}{15},\frac{8\pi}{15},\frac{2\pi}{3},\frac{14\pi}{15}, \frac{16\pi}{15}, \frac{4\pi}{3},\frac{22\pi}{15}, \frac{26\pi}{15}, \frac{28\pi}{15}[/tex]
Tim is laying ceramic tile on a kitchen floor. Each tile costs $3.19. How much do 100 tiles cost?
describe a situation that can be modeled by the integer -15 explain what zero represents in the situation
Answer:
Step-by-step explanation:
The current weather in a strange place is known to be 0 degrees, after a couple of hours, the weather has dropped 15 degrees, making the day much more colder than usual. What's the degree after the weather has dropped?
Solution:
0-15=-15
The integer -15 can be used to describe a situation of temperature falling below freezing point or owing someone money. In these situations, zero represents the freezing point or balanced position (no debt) respectively.
Explanation:A situation that can be modeled by the integer -15 could be the temperature outside on a very cold day in winter. If we are expressing the temperature in degrees Fahrenheit, for instance, a temperature of -15 could represent a day that is 15 degrees below the freezing point, which is 32 degrees Fahrenheit. In this situation, the integer zero represents the freezing point. So, if the temperature is -15, it means the temperature is 15 degrees below the freezing point.
Another example could be a debt. If you owe someone $15, then your balance can be represented by -15. In this case, zero represents the point where you do not owe any money, it is the neutrally balanced point of your financial situation.
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Find the exact circumference of a circle with the given radius.
32 cm
C=
7.51 cm
71 cm
6.251 cm
The circumference of a circle whose radius is given would be =200.96cm.
How to calculate the circumference of a given circle?
To calculate the circumference of a given circle whose radius is given, the following steps should be taken as follows:
The formula for circumference = 2πr
where;
radius = 32cm
Circumference = 2× 3.14× 32
= 200.96cm.
Need help with number 1 and explain
Answer:
0
Step-by-step explanation:
If the answer is between 0 to 0.49, the best estimate is 0.
If the answer is between 0.5-1.49, the best estimate is 1.
If the answer is 1.5 or greater, the best estimate is 2.
Without giving the fractions 1/10 and 1/12 a common denominator, we know the answer is between 2/12 and 2/10.
2/12 is less than 2/10. 2/10 is 0.2, which is less than 0.5.
Since the final answer is less than 0.5, the best estimate is 0.
I need help with this homogeneous equation
[tex]\frac{dy}{dx} = \frac{x^{2}+y^{2} }{2xy}[/tex]
Answer:
[tex]ln [1 - (\frac{y}{x} )^{2} ] + ln x + c = 0[/tex]. This is the solution.
Step-by-step explanation:
The homogeneous differential equation is given by
[tex]\frac{dy}{dx} = \frac{x^{2} + y^{2} }{2xy}[/tex]
⇒ [tex]\frac{dy}{dx} = \frac{1 + (\frac{y}{x} )^{2} }{2(\frac{y}{x} )}[/tex] ........ (1)
Now to solve this differential equation we assume that y = vx where v is another variable.
So, differentiating with respect to x we get [tex]\frac{dy}{dx} = v + x \frac{dv}{dx}[/tex]
Therefore, the above equation (1) becomes
[tex]v + x \frac{dv}{dx} = \frac{1 + v^{2} }{2v}[/tex] {Since [tex]v = \frac{y}{x}[/tex]}
⇒ [tex]x\frac{dv}{dx} = \frac{1 + v^{2} - 2v^{2} }{2v}[/tex]
⇒ [tex]x\frac{dv}{dx} = \frac{1 - v^{2}}{2v}[/tex]
⇒ [tex]\frac{2v}{1 - v^{2} } dv = \frac{dx}{x}[/tex] {By separation of variables}
Now, integrating both sides we get,
[tex]\int {\frac{2v}{ 1- v^{2}}} \, dv = \int {\frac{dx}{x} } \, dx[/tex]
⇒ [tex]- \int {\frac{d(1 - v^{2} )}{1 - v^{2}}} = \int {\frac{dx}{x} }[/tex]
⇒ [tex]- ln (1 - v^{2}) = ln x + c[/tex] {Where c is the integration constant}
⇒ [tex]ln [1 - (\frac{y}{x} )^{2} ] + ln x + c = 0[/tex] (Answer)