Answer:
• the equation kind is incorrect
• the equation is incorrect
• the equation should be: y = 15/x
Step-by-step explanation:
We observe that the data tells us the time is inversely proportional to the number of workers, and that the product of time and workers is 15 worker·hours. The form for inverse proportionality is ...
y = k/x
or
xy = k
Our observation tells us k = 15 (worker·hours), so our model equation is ...
y = 15/x . . . . . where x is the number of workers, and y is the hours to paint the room
What is the value of the discriminant in 3x^2 - 4x + 2 = 0?
Answer:
-8Step-by-step explanation:
[tex]\text{The formula of a discriminant of}\ ax^2+bx+c=0:\\\\b^2-4ac\\\\================================\\\\\text{We have the equation:}\\\\3x^2-4x+2=0\to a=3,\ b=-4,\ c=2\\\\\text{Substitute:}\\\\b^2-4ac=(-4)^2-4(3)(2)=16-24=-8[/tex]
I need help understanding linear inequalities. I'm trying to solve the following problem:
[tex]\frac{-x}{2}[/tex] < 1
How do I get rid of the 2 on the left side so it's just the x? I know what I do to one side I have to do to the other, and I've broken the problem down to this so far. Any help would be appreciated. Thanks!
All you have to do is treat the inequality like an equation and multiply both sides by 2.
[tex]-x<2 \\ \\ x>-2[/tex]
Answer: x> -2
Step-by-step explanation:
step 1 :take 2 to the other side ,and 1 will multiply by 2 which will give you 2
step 2 : take the negative or -1 to the other side ( you will divide 2 by -1 ) which will result to a -2
step 3: most important thing to remember once you multiply or divide by a negative number you will have to change the inequality sign ( in this case the smaller than sign changes to bigger than because you divided by -1 in step 3 )
hope this helped
y intercept,slope,and linear equation=
ANSWER
Y-intercept: 3000
Slope:-275
Linear equation:y=-275x+3000
EXPLANATION
The straight line touches the y-axis at
(0,3000).
The y-intercept is b=3000
The line also passes through (2,2450).
The slope is calculated using the formula,
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
[tex] = \frac{3000 - 2450}{0 - 2} [/tex]
[tex] = \frac{550}{ - 2} = - 275[/tex]
The slope is -275.
The linear equation is given by:
[tex]y = mx + b[/tex]
[tex]y = - 275x + 3000[/tex]
Hey help me on this??
Answer:
C
Step-by-step explanation:
Use such properties of logarithms:
[tex]\log_w\dfrac{a}{b}=\log_wa-\log_wb,\\ \\\log_wa^b=b\log_wa[/tex]
Thus,
[tex]\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\text{use the first property}=\\ \\=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\\ \\=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=\text{use the second property}=\\ \\=4\log(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).[/tex]
Answer:
The answer is C
Step-by-step explanation:
Use such properties of logarithms:
\log_w\dfrac{a}{b}=\log_wa-\log_wb,\\ \\\log_wa^b=b\log_wa
Thus,
\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\text{use the first property}=\\ \\=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\\ \\=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=\text{use the second property}=\\ \\=4\log(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).
Show the Standard form of this problem
the answer is C. move the decimal place to the left 4 times since it is positive to the 4th power
The wholesale cost of a sofa is $520. Based on selling price, the original markup was 69%. Find the final sale price after the following series of price changes occurred: a markdown of 13%, a markup of 30%, and a second markdown of 36%. Round each intermediate selling price to the nearest cent.
Answer:
$1214.19
Step-by-step explanation:
Let c and p represent the cost of the sofa and the original selling price, respectively. The original markup was 0.69·p, so we have ...
c + 0.69p = p . . . . . based on selling price, the original markup was 69%
c = p(1 -0.69) = 0.31p . . . . subtract the markup
p = c/0.31 . . . . . . . . . . . . . divide by the coefficient of c
So, the original selling price was ...
520/0.31 ≈ 1677.42
The first markdown decreased the selling price to ...
1677.42 - 0.13·1677.42 = 0.87·1677.42 ≈ 1459.36
The markup increased the selling price to ...
1459.36 +0.30·1459.36 ≈ 1897.17
And the final markdown decreased the selling price to ...
1897.17 -0.36·1897.17 ≈ 1214.19
The final sale price was $1214.19.
A tree 7ft y’all grows an average 6 in each year which equation models the trees height h after x years
Answer:
h = 7 + 6x
Step-by-step explanation:
Since we are trying to find the height of the tree, we put h on the left side of the equation. Since the tree is 7ft tall at the moment, we write 7ft on the right side of the equation. Knowing that the tree grows 6 inches each year (x) we write 6x on the right side of the equation.
Answer:
H=7+6x
Hope this helps
write the equation of the line
Answer:
y = 1/2x -8
Step-by-step explanation:
The two marked points are 1 unit apart vertically and 2 units apart horizontally. The vertical rise is positive for a positive horizontal run, so the slope is ...
rise/run = 1/2
The y-intercept is the leftmost marked point, at y=-8. Then the slope-intercept form of the equation of the line is ...
y = slope·x + y-intercept
y = 1/2x -8
You decide to put $2,000 in a savings account to save for a $3,000 downpayment on a new car. If the account has an interest rate of 4% per year and is compounded monthly, how long does it take until you have $3,000 without depositing any additional funds? 121.862 years 12.1862 years 10.155 years 1.0155 years
Answer:
10.153 years
Step-by-step explanation:
The future value of such an investment is given by ...
FV = P·(1 +r/12)^(12t)
where P is the principal invested, FV is the future value of it, r is the annual interest rate, and t is the number of years.
Dividing by P and taking the log, we have ...
FV/P = (1 +r/12)^(12t)
log(FV/P) = 12t·log(1 +r/12)
Dividing by the coefficient of t gives ...
t = log(FV/P)/log(1 +r/12)/12 = log(3000/2000)/log(1 +.003333...)/12 ≈ 121.842/12
t ≈ 10.153 . . . years
You buy a quart of ice cream that comes in a cylindrical tub. A quart has a volume of about 58 cubic inches. The tub has a height of 5 inches. What is the radius of the ice-cream tub? Use 3.14 for pi. Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
Givens
V = 58 in^3
h = 5 inches
pi = 3.14
Formula
V = pi * r^2 * h
Solution
58 = 3.14 * r^2 * 5
58 = 15.7 * r^2
58/15.7 = r^2
3.6942 = r^2
sqrt(r^2) = sqrt(3.6942)
r = 1.922 which when rounded is
r = 1.92
Answer: r=1.92
given what we know about the equation i can determine what steps are needed to solve this :)
volume
1) V = 58 in^3
we know that h=5inches
2) h = 5 inches
heres what pi equals
3) pi = 3.14
then we use pi in the equation
4)= pi * r^2 * h
heres the solution steps
1)58 = 3.14 * r^2 * 5
2)58 = 15.7 * r^2
3)58/15.7 = r^2
4)3.6942 = r^2
5)sqrt(r^2) = sqrt(3.6942)
6)r = 1.922 then we round and get r = 1.92
so final solution is r = 1.92
×║hope this helps║×
Given: m arc KP=2m arc IP
, m arc IVK=120°
Find: m∠KJL.
Answer:
40
Step-by-step explanation:
The measure of the angle KJL is 40°.
What is a circle?Circle definition states a shape that consists of points, in a two-dimensional plane, equidistant from a given point. A circle is a closed curve that has no corners or vertices.
Given is a circle O where m arc IVK = 120° and m arc KP = 2 × m arc IP,
We need to find the measure of the angle KJL,
So,
According to the question,
m arc IVK + m arc KPI = 360° [whole circumference of a circle is 360°]
m arc IVK + m arc KP + m arc IP = 360°
120° + m arc IP + 2 × m arc IP = 360°
3 m arc IP = 240°
m arc IP = 80°
Therefore,
m arc KP = 160°
Now, according to the property of a circle,
m ∠KJL = 1/2 × [m arc KP - m arc IP]
m ∠KJL = 1/2 × [160° - 80°]
m ∠KJL = 80°/2
m ∠KJL = 40°
Hence the measure of the angle KJL is 40°.
Learn more about circle click
https://brainly.com/question/29142813
#SPJ2
Please help on this question
Answer:
26 terms
Step-by-step explanation:
The n-th term of this sequence with a common difference of 5 and a first term of -2 is ...
an = -2 +5(n -1)
The sum of the first n terms is ...
(a1 +an)/2·n = (-2 -2 +5(n -1))/2 ·n = 1573
n(5n -9) = 3146
5n^2 -9n -3146 = 0 . . . . . quadratic in standard form
Using the quadratic formula, we can find the positive solution for n to be ...
n = (9+√((-9)^2-4(5)(-3146)))/(2·5) = (9+√63001)/10 = 260/10 = 26
26 terms must be added to give the desired sum.
_____
Relevant formulas are ...
Sn = n(2a1 +d(n-1))/2 . . . . sum of n terms of arithmetic sequence with first term a1 and common difference d
x = (-b±√(b^2 -4ac))/(2a) . . . . . solutions to ax^2 +bx +c = 0
PLEASE! Someone help me answer this and explain it
Answer:
12.5
Step-by-step explanation:i did that problem before
A bookcase has a mass of 30 kilograms. A book in the bookcase has a mass of 400 grams. How many books of the same mass would it take to equal the mass of the bookcase? A. 75 books B. 120 books C. 750 books D. 1,200 books
Answer: OPTION A
Step-by-step explanation:
You can convert 30 kilograms to grams ([tex]1\ kilogram= 1,000\ grams[/tex]), then:
[tex](30\ kilograms)(\frac{1,000\ grams}{1\ kilogram})=30,000\ grams[/tex]
Then, if a book in the bookcase has a mass of 400 grams and you need to find the number of books of the same mass that would take to equal the mass of the bookcase, you can divide the weight of the bookcase (in grams) by the weigth of one of these books.
Therefore:
[tex]books=\frac{30,000\ grams}{400\ grams}\\\\books=75[/tex]
What is the product of 5/6 and 2/3?
Answer:
The product of [tex]\frac{5}{6}[/tex] and [tex]\frac{2}{3}[/tex] is [tex]\frac{5}{9}[/tex] .
Step-by-step explanation:
Multiply both numerators and denominators.
[tex]\frac{5*2}{6*3}[/tex]
[tex]\frac{10}{18}[/tex]
Simplify this by dividing both the numerator and denominator by 2.
[tex]\frac{10/2}{18/2}[/tex]
[tex]\frac{5}{9}[/tex]
[tex]\text{Hey there!}[/tex]
[tex]\text{The word product means multiply}[/tex]
[tex]\dfrac{5}{6}\times\dfrac{2}{3}=\ ?\\\\\\\dfrac{5(2)}{6(3)}=\dfrac{5\times2}{6\times3}\\\\\bf{5\times2=10}\\\\\bf{6\times3=18}\\\\\\=\dfrac{10}{18}\\\\\\\text{Both numbers foes into two so we can DIIVIDE it by two}\\\\\\\dfrac{10\div2}{18\div2}=?[/tex]
[tex]10\div2=5\\\\\18\div2= 9\\\\\\\boxed{\boxed{\bf{Answer:\dfrac{5}{9}}}}\checkmark[/tex]
[tex]\text{Good luck on your asignment and enjoy your day!}\\\\\\\frak{LoveYourselfFirst:)}[/tex]
If possible, could someone assist me by showing me how to get the plausible answer as I was absent while my professer went over this topic.
Answer:
[tex]7.5m^2[/tex]
Step-by-step explanation:
Divide the composite shape into two shapes, a rectangle and a triangle.
We can see that the rectangle has dimensions of 3 x 2.
We can use the area formula.
[tex]A=b*h[/tex]
[tex]A=3*2[/tex]
[tex]A=6[/tex]
We can also see that the triangle has a height of 3 and a base of 1 (3 - 2).
We can use the area formula.
[tex]A=\frac{1}{2}(b*h)[/tex]
[tex]A=\frac{1}{2}(3)[/tex]
[tex]A=1.5[/tex]
Now we can add these areas together.
[tex]1.5 +6=7.5[/tex]
why does the function k(f(x)) provide a better model for the scatter plot when 4
Answer:
It reduces the distance from the plotted points to the function curve.
Step-by-step explanation:
The goodness of fit of a model is measured by the "residuals", the differences between the given points and the modeled points. The smaller the residuals, the better the model. Any change to the model that will put it closer to the plotted points makes it a better model. The change proposed in your problem statement does that.
a=8, b=5, C=90 degree; Find c, A, and B
This is for the law of sine and cosine
Answer:
• c = √89 ≈ 9.434
• A = arcsin(8/√89) ≈ 57.995°
• B = arcsin(5/√89) ≈ 32.005°
Step-by-step explanation:
By the law of cosines, ...
c² = a² + b² -2ab·cos(C)
Since c=90°, cos(C) = 0 and this reduces to the Pythagorean theorem for this right triangle.
c = √(8² +5²) = √89 ≈ 9.434
Then by the law of sines (or the definition of the sine of an angle), ...
sin(A) = a/c·sin(C) = a/c = 8/√89
A = arcsin(8/√89) ≈ 57.995°
sin(B) = b/c·sin(C) = b/c = 5/√89
B = arcsin(5/√89) ≈ 32.005°
Please help me!!!!!!!
Answer:
B(5,2)
Explanation:
AC=8 units
AB must equal 2 units.
If line AC is y=x-3, and x values are -1<x<7 in AC, then B is located in x= 5. Plug x in equation.
y=5-3
y=2
B(5,2)
Find the value of b in the graph of y=3x+b if it is known that the graph goes through the point:
O(3,8)
Answer:
b= -1
Step-by-step explanation:
y=3x+b
8=3(3)+b
8=9+b
b= -1
Which expression can you substitute in the indicated equation to solve the system below?
x + y = 6
12x + y = 5
1. 6 - y for x in 12x + y = 5
2. 5 + 12x for y in x + y = 6
3. 6 + y for x in 12x + y = 5
4. 5 - x for y in x + y = 6
Final answer:
To solve the system of equations x + y = 6 and 12x + y = 5, substitute 6 - y for x in 12x + y = 5 and solve for y.
Explanation:
To solve the given system of equations x + y = 6 and 12x + y = 5, we need to substitute the value of x or y into the second equation. In this case, substituting 6 - y for x in 12x + y = 5 will allow us to solve for y.
Let's substitute 6 - y for x:
12(6 - y) + y = 5
After simplifying, we get:
72 - 12y + y = 5
Combining like terms:
-11y = -67
Dividing both sides by -11, we find that y = 67/11 or approximately 6.09.
So, option 1: 6 - y for x in 12x + y = 5 is the correct expression to substitute.
A bag contains cars numbered from 1 to 14. Find the Probability of:
a) selecting a prime number or multiple of 4
b) selecting a multiple of 2 or 3
c) selecting 3 or 4
d) selecting 8 or a number less than 8
A)
Prime numbers and numbers with a multiple of four that are between 1 and 14 include: 1, 2, 3, 4, 5, 7, 8, 12, 13.
There are 9 numbers listed.
9/14 = ~0.64285... or roghly 65.3%
B) Numbers between 1 and 14 with the multiples of 2 or 3 include: 2, 4, 6, 8, 9, 10, 12, 14.
There are 8 numbers listed.
8/14 = ~0.5714... or, about 57.14%
C) 3 and 4 is a list of two numbers.
2/14 = 1/7 = ~0.1429, or about 14.9%
D) There is a total of numbers equal to or less than 8 in a list of 1 and 14.
8/14 = ~0.5714... or, about 57.14%
PLZ HELP I BEG YOU 20 POINTS!!!!
Answer:
[tex]b=\frac{g}{x} + \frac{5}{x^{3} } +\frac{1}{x^{2} }[/tex]
Step-by-step explanation:
[tex]10=\frac{5}{-2}-b(-2)^{2} +1\\\\\\9=\frac{5}{-2} -b(4)\\\\-18=5-b(4)\\\\-23=-b(4)\\\\\frac{-23}{4} =-b\\\\\frac{23}{4}=b\\\\\\b=\frac{23}{4}[/tex]
For which values of P and Q does the following equation have infinitely many solutions ?
Px+57=-75x+Q
Answer:
(P, Q) = (-75, 57)
Step-by-step explanation:
The equation will have infinitely many solutions when it is a tautology.
Subtract the right side from the equation:
Px +57 -(-75x +Q) = 0
x(P+75) +(57 -Q) = 0
This will be a tautology (0=0) when ...
P+75 = 0
P = -75
and
57-Q = 0
57 = Q
_____
These values in the original equation make it ...
-75x +57 = -75x +57 . . . . . a tautology, always true
How many 4-digit multiples of 2 are there?
there are 4,500 of 4 digit multiples of 2
Answer:
4500
Step-by-step explanation:
Find m∠1 if m∠2=73°, m∠3=107°, m∠4=92°. Justify your response!
Answer:
m∠1 = 92°
Step-by-step explanation:
∠2 corresponds to the supplement of ∠3 if (and only if) lines a and b are parallel. We find that
m∠2 + m∠3 = 73° +107° = 180°
so, the angles are supplementary and lines a and b are parallel.
Angles 4 and 1 are corresponding angles where the line d crosses the parallel lines a and b, so are congruent.
m∠1 = m∠4 = 92°
need help :) i’m bad at math lol
Answer:
i think it is the last one
Step-by-step explanation:
-2/25^3x^3
Enter the missing numbers in the boxes to complete the table of equivalent ratios please help me
Answer:
3 : 36 10: 120 6:72
Step-by-step explanation:
60 divided by 5 is 12
3 x 12 = 36
10 x 12 = 120
72/12= 6
3-36
5-60
6-72
10-120
One month equals 12$ saved
Use the ratio table to solve the percent problem what percent is 8 out of 40
Answer:
20%
Step-by-step explanation:
So, 40 is the dependent and 8 is the independent
40% divided by 8% equals 5%
100% divided by 20% equals 5%
What is the simplified form of 4z^2-16z+15/ 2z^2-11z+15
[tex]\frac{4z^2-16z+15}{2z^2-11z+15}[/tex] Factor the numerator and the denominator
[ax² + bx + c]
4z² - 16z + 15 Since a > 1, multiply a and c together, then find the factors of (a·c), that adds or subtracts to = b.
(a·c) --> (4 · 15) = 60
Factors of 60:
1 · 60, 2 · 30, 3 · 30, 4 · 15, 5 · 12, 6 · 10
[The only factor is 6 and 10, (-6) + (-10) = -16] So you substitute -6z - 10z for -16z
4z² - 6z - 10z + 15 Factor out 2z from 4z² - 6z, and factor out -5 from -10z + 15
2z(2z - 3) - 5(2z - 3) Factor out (2z - 3) and your left with:
(2z - 3)(2z - 5)
Do the same for the denominator, and you should get (z - 3)(2z - 5)
Now you have:
[tex]\frac{(2z - 3)(2z-5)}{(z-3)(2z - 5)}[/tex] You can cancel out (2z - 5)
[tex]\frac{2z - 3}{z-3}[/tex]
ANSWER
[tex]\frac{(2z-3)}{(z-3)} [/tex]
EXPLANATION
The given expression is:
[tex] \frac{4z^2-16z+15}{2z^2-11z+15} [/tex]
Let us split the middle terms to get,
[tex]\frac{4z^2-6z - 10z+15}{2z^2-6z - 5z+15} [/tex]
Factor by grouping:
[tex]\frac{2z(2z-3) - 5(2z - 3)}{2z(z-3) - 5(z - 3)} [/tex]
Factor further:
[tex]\frac{(2z - 5)(2z-3)}{(2z - 5)(z-3)} [/tex]
We cancel the common factors,
[tex]\frac{(2z-3)}{(z-3)} [/tex]
where
[tex]z \ne \frac{5}{2} \: or \: z \ne3[/tex]