Mahmoud earns $450 per week plus a 20% commission as a car salesman. He wants his
hourly salary to be at least $35.
The inequality that relates the number of hours to the weekly sales is:
[tex]450 + 0.20x \ge 35y[/tex]
The complete question implies that we define an inequality that represents the relationship between the number of hours worked in a week and the weekly sales
We make use of the following representation:
[tex]x \to[/tex] weekly sales from cars.
[tex]y \to[/tex] hours worked in a week
His weekly salary is then calculated as:
Salary (S) = Earnings per week + Commission * Sales from car
So, we have:
[tex]S = 450 + 20\% * x[/tex]
Express percentage as decimal
[tex]S = 450 + 0.20* x[/tex]
[tex]S = 450 + 0.20x[/tex]
Assume he works for y hours in a week.
His hourly rate is:
[tex]Hourly = \frac{S}{y}[/tex] --- i.e. weekly salary divided by number of hours
[tex]Hourly = \frac{450 + 0.20x}{y}[/tex]
For this rate to be at least [tex]\$35[/tex], the following condition must be true
[tex]Hourly \ge 35[/tex] --- i.e. is hourly rate must be greater than or equal 35
So, we have:
[tex]\frac{450 + 0.20x}{y} \ge 35[/tex]
Multiply both sides by y
[tex]450 + 0.20x \ge 35y[/tex]
Learn more about inequality:
https://brainly.com/question/20383699
X^4+x^3-6x^2-14x-12=0 Make a list of possible rational roots. Test the possible roots until you find one that produces a remainder of 0 Write the resulting cubic function. Use synthetic division to find a second root that will reduce the cubic expression to a quadratic expression
Step-by-step explanation:
The Rational Roots Test states that for a polynomial with integer coefficients, the factors of the constant / the factors of the leading coefficient are the possible rational roots.
Here, the constant (the value without an x attached to it) is -12 and the leading coefficient (the value that the x to the highest degree is multiplied by) is 1 as x⁴ is multiplied by 1. The factors of -12 are
±(1, 2, 3, 4, 6, 12), so the possible rational roots are ±(1, 2, 3, 4, 6, 12)/1 (as 1 is the only factor of 1).
Trying out a few roots until we get one that works using synthetic division, we can try
x+1 (the root is x=-1)
-1 | 1 1 -6 -14 -12
| -1 0 6 8
__________________________
1 0 -6 -8 -4
the remainder is -4, so this does not work
x+2 (the root is x=-2)
-2 | 1 1 -6 -14 -12
| -2 2 8 12
__________________________
1 -1 -4 -6 0
Therefore, x=-2 is a root and x+2 is a factor of the polynomial. The quotient of the polynomial and x+2 is
-6 + (-4)x + (-1)* x² + 1 * x³ = x³-x²-4x-6
Using the rational roots theorem, the possible roots of x³-x²-4x-6 are
±(1,2,3,6)
Starting with
x-1 (root is x=1), we have
1 | 1 -1 -4 -6
| 1 0 -4
_____________________
1 0 -4 -10
there is a remainder, so this is not a root
next, x-2 (root is x=2)
2 | 1 -1 -4 -6
| 2 2 -4
_____________________
1 1 -2 -10
there is a remainder, so this is not a root
next, x-3 (root is x=3)
3| 1 -1 -4 -6
| 3 6 6
_____________________
1 2 2 0
x-3 is a factor and 3 is a root. the quotient of (x³-x²-4x-6)/(x-3) is x²+2x+2
The exchange rate between dollars ($) and pounds (£) is $1 = £0.65 . The exchange rate between euros (€) and pounds is €1 = £0.74 . Khan changes €520 into pounds. He spends £260 and then changes the rest into dollars. Work out how many dollars he receives
Answer:
€520=£442.83
=£442.83-£260
=£182.83 into dollars=$251.52
Therefore he receives $251.52
Someone help asappppp
Answer:
all have "bases" less than one which is a decay...
only "C" is greater than 1 (1.01)
"C" is the answer
Step-by-step explanation:
Write an equation that represents the statement "the
product of a number, x, and the number 7 is 42."
Answer:
7x = 42
Step-by-step explanation:
"Product" refers to multiplication and "is" refers to equal to.
Hi! I'm happy to help!
This equation will be written like this
x×7=42
To make this easier to solve, we can use the inverse operation, division.
42÷7=x
42 divided by 7 is 6, so the answer is 6.
I hope this was helpful, keep learning! :D
What percent of 500 is 125
Answer:
25%
Step-by-step explanation:
125 of 500 can be written as: 125 /500
To find a percentage, we need to find an equivalent fraction with the denominator 100. Multiply both numerator & denominator by 100.
125 /500 × 100 /100
= ( 125 × 100/ 500 ) × 1 /100 = 25 /100
Answer:
25%
Step-by-step explanation:
Of means multiply and is means equals
P *500 = 125
Divide each side by 500
P = 125/500
P = .25
Change to percent form
P = 25%
Find the measure of the indicated angle.
Answer:
i think it the measured of the indicated angle is 55
will give brainlest pls help me with all three questions
Answer:
Hello,
Step-by-step explanation:
3)
[tex]x^2-4x+3=0\\x^2-3x-x+3=0\\x(x-3)-(x-3)=0\\(x-3)(x-1)=0\\\\x-intercepts\ are\ x=3\ or\ x=1[/tex]
4)
[tex]-x^2-8x+12=0\\x^2+8x-12=0\\(x^2+2*4x+16)-16-12=0\\\\(x+4)^2-28=0\\\\\\(x+4-2\sqrt{7} )((x+4+2\sqrt{7} )=0\\\\x-intercepts\ are \ x=-4+2\sqrt{7}\ and\ x=-4-2\sqrt{7}\\\\[/tex]
5)
[tex]f(x)=-3(x-7)(x+4)\\=-3(x^2-3x-28)\\\\=-3(x^2-2*\dfrac{3}{2} *x+\dfrac{9}{4} )+\dfrac{27}{4} +84\\\\=-3(x-\dfrac{3}{2})^2+\dfrac{363}{4} \\\\\\Vertex\ is\ (\dfrac{3}{2},\dfrac{363}{4})[/tex]
Kenya solved the equation below. Negative 6 (x minus 2) + 3 x = negative 3 (x + 3) + 21 What is the solution to Kenya's equation? –4 12 no solution infinitely many solutions
Answer: No solution
Step-by-step explanation:
-6(x - 2) + 3x = -3(x + 3) + 21
-6x + 12 + 3x = -3x - 9 + 21
Collect like terms
-6x + 3x + 3x = -9 + 21 - 12
-6x + 6x = - 9 + 9
0 = 0
In this scenario, it can be deduced that there is no solution to Kenya's equation.
Answer:
infinitely many solutions
Step-by-step explanation:
i got it right
3x + ky = 8
X – 2ky = 5
are simultaneous equations where k is a constant.
b) Given that y = 1/2 determine the value of k.
Answer:
(a): x is 3 and ky is -1
(b): k is -2
Step-by-step explanation:
Let: 3x + ky = 8 be equation (a)
x - 2 ky = 5 be equation (b)
Then multiply equation (a) by 2:
→ 6x + 2ky = 16, let it be equation (c)
Then equation (c) + equation (b):
[tex] { \sf{(6 + 1)x + (2 - 2)ky = (16 + 5)}} \\ { \sf{7x = 21}} \\ { \sf{x = 3}}[/tex]
Then ky :
[tex]{ \sf{2ky = 3 - 5}} \\ { \sf{ky = - 1}}[/tex]
[tex]{ \bf{y = \frac{1}{2} }} \\ { \sf{ky = - 1}} \\ { \sf{k = - 2}}[/tex]
Simultaneous equations are used to represent a system of related equations.
The value of k when [tex]y = \frac 12[/tex] is -2
Given that:
[tex]3x + ky = 8[/tex]
[tex]x - 2ky = 5[/tex]
[tex]y = \frac 12[/tex]
Substitute [tex]y = \frac 12[/tex] in both equations
[tex]3x + ky = 8[/tex]
[tex]3x + k \times \frac 12 = 8[/tex]
[tex]3x + \frac k2 = 8[/tex]
[tex]x - 2ky = 5[/tex]
[tex]x - 2k \times \frac 12 = 5[/tex]
[tex]x - k = 5[/tex]
Make x the subject in [tex]x - k = 5[/tex]
[tex]x = 5 + k[/tex]
Substitute [tex]x = 5 + k[/tex] in [tex]3x + \frac k2 = 8[/tex]
[tex]3(5 + k) + \frac k2 = 8[/tex]
Open bracket
[tex]15 + 3k + \frac k2 = 8[/tex]
Multiply through by 2
[tex]30 + 6k + k = 16[/tex]
[tex]30 + 7k = 16[/tex]
Collect like terms
[tex]7k = 16 - 30[/tex]
[tex]7k = - 14[/tex]
Divide both sides by 7
[tex]k = -2[/tex]
Hence, the value of constant k is -2.
Read more about simultaneous equations at:
https://brainly.com/question/16763389
If a sine curve has a vertical shift down 19 units with an amplitude of 21, what will the minimum and maximum values be? (i.e. how high and low will the graph go?)
Min Value:
Max Value:
Given:
Amplitude = 21
Vertical shift = 19 units down
To find:
The maximum and the minimum value.
Solution:
The general form of sine function is:
[tex]y=A\sin (Bx+C)+D[/tex]
Where, |A| is amplitude, [tex]\dfrac{2\pi}{B}[/tex] is period, [tex]-\dfrac{C}{B}[/tex] is phase shift and D is the vertical shift.
Here,
[tex]Maximum=D+A[/tex]
[tex]Minimum=D-A[/tex]
We have,
Amplitude: [tex]A = 21[/tex]
Vertical shift: [tex]D=-19[/tex]
Negative sign means shifts downwards.
Now,
[tex]Maximum=D+A[/tex]
[tex]Maximum=-19+21[/tex]
[tex]Maximum=2[/tex]
And,
[tex]Minimum=D-A[/tex]
[tex]Minimum=-19-21[/tex]
[tex]Minimum=-40[/tex]
Therefore, the minimum value is -40 and the maximum value is 2.
Instructions: Given the following coordinates complete the glide reflection
transformation.
A(-9,-2)
B(-9,-5)
C(-5,-4)
Transformation: Reflection over the y-axis and a translation of shifting up 5 units
Answer:
A(9,3)
B(9,0)
C(5,1)
Step-by-step explanation:
A company's stock price flucated over a period of four days. The table shows the change in stock price per day. The net change in the company's stock price over the four days
Answer:
The net change is -.30
Step-by-step explanation:
increase means add
decrease means subtract
+3.50
-3.70
+3.30
-3.40
-------------
-.30
The net change is -.30
Find the length of the third side. If necessary, write it in simplest radical form.
Answer:
a = sqrt(7)
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
where a and b are the legs and c is the hypotenuse
a^2 +3^2 = 4^2
a^2 +9 = 16
a^2 = 16-9
a^2 = 7
Taking the square root
a = sqrt(7)
The volume of a prism with side lengths measured in millimeters is 20. How could this measurement be written? Check all that apply.
20 millimeters
20 mm3
20 mm2
20 square millimeters
20 cubic millimeters
Answer:
20 mm^3, 20 cubic millimeters
Step-by-step explanation:
The volume of a prism is length times width times height.
Length, width, and height can have units of mm.
mm * mm * mm = mm^3
The units of a volume must be cubic units.
Answer: 20 mm^3, 20 cubic millimeters
Utilize graphing to find the solution to
the following system of equations.
4x + 3y = 25 AND y = -5x + 1
([?], [])
Answer:
you guess any value of x and then you substitute any three values for example for the first equation you can guess the value of x to be 1 or 2 or 3
Y = 2x - 4
(0, 4)
(3, -1)
(-1, -5)
(-4, 9)
Answer:
Y = 2x - 4
(2,-4)
gradient= 2
y-intersept = -4
Help please !!!!!!!!!
Answer: (a): Good course, (b): Bad course
Step-by-step explanation:
Firstly, because the standard deviation of the good course results is lower, there is less variation so he performs more consistently there.
Secondly, the trick with the second question is that while the mean of the bad course is slightly less, the standard deviation is quite a lot higher than that of the good course, so it's more likely that the highest single test score belongs to the bad course.
AB←→||CD←→. Find the measure of ∠BFG.
Answer:
Value of ∠ BFG = 135°
Step-by-step explanation:
Given:
AB || CD
∠ AFG = (3x + 15)°
∠ FGD = (5x - 5)°
Find:
∠ BFG
Computation:
We know that;
∠ AFG = ∠ FGD
3x + 15 = 5x - 5
3x - 5x = - 5 - 15
- 2x = - 20
2x = 20
x = 10
Value of ∠ AFG = 3x + 15
Value of ∠ AFG = 3(10) + 15
Value of ∠ AFG = 45°
∠ BFG = 180° - Value of ∠ AFG
∠ BFG = 180° - 45°
∠ BFG = 135°
Value of ∠ BFG = 135°
Question 8 If f (2) = (1 + 3) and g (2) VO+ 7, find g (f (x)). 9(f()) = 1 + 10 O g(f ()) = VI + 3 +7 Og(f (x)) = v= + 10 Og(f (2)) = 2? + 10
Answer:
x+10
Step-by-step explanation:
f(x) = (x+3)^2 and g(x) = sqrt(x)+7
g(f(x)) =
Replace f(x) in for x in the function g(x)
= sqrt((x+3)^2)+7
= x+3 +7
= x+10
How many solutions does this equation have x^4 - 6x^2 -7 = 0
Answer:
2 solutions
Step-by-step explanation:
x^4-6x^2-7=0
Replace x^2 by y
(x^2)^2-6x^2-7=0
y^2-6y-7=0
D=b^2-4ac= (-6)^2-4*1*(-7)= 36+28=64
sqrtD=8
y1=(-b-sqrtD)/2a=-2/2=-1
y2= (-b+sqrtD)/2a=14/2=7
x^2=-1(n0 roots) x^2=7 x=sqrt7 or x=-sqrt7
2 roots
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Answer:
The distribution is positively skewed.
Step-by-step explanation:
It's not symmetric because the distribution in the chart isn't equally shown or marked. It's not negative skewed either because for it to be negative the graph would have to go down in a negative direction, usually the left, but in the picture you posted the graph is going down in the right direction. Lastly, positively skewed graphs or charts look like the one you posted. They go down in the right direction, hence why they're called "positively" skewed. The right tail of the distribution is longer in positively skewed graphs or charts.
Daphne borrows $2500 from a financial institution that charges 6% annual interest, compounded monthly, for 2 years. The amount that Daphne will need to pay back at the end of the term is
A hot air balloon is released into the air. During its straight ascent, the angle of elevation was 15° and, 3 minutes later, the angle of elevation increased 20°. How fast is the balloon traveling, in km/h, if the angle measurements were taken 300m away from the launch site?
Answer:
The speed of the balloon is 0.16 m/s.
Step-by-step explanation:
CD = 300 m
Let AD = x
AB = y
time, t = 3 min
Triangle, ADC
[tex]tan 15 = \frac{AD}{BC}\\\\0.27 \times 300 = x \\\\x = 80.4 m[/tex]
Triangle, BCD
[tex]tan 20 = \frac{BD}{BC}\\\\0.36 \times 300 = x + y \\\\x + y = 109.2 m[/tex]
So, y = 109.2 - 80.4 = 28.8 m
Speed = 28.8/180 = 0.16 m/s
SOMEONE HELP ME PLEASE
Answer:
so thats 2/6 or 1/3
Step-by-step explanation:
A die has 6 sides your odds of getting 2 or lesser are 1/3 or 33%
Ао
D
B
120°
Angle A =
degrees.
Answer:
A = 120
Step-by-step explanation:
Angle A is a vertical angle to 120 and vertical angles are equal
A = 120
[tex]\Large\rm\underbrace{{\green{ \: Angle \: A \: = \: 120 \degree}}}[/tex]
Because vertically opposite angles are always equal.
what is the answer to
(35+5)[16+(12÷ 4)]
Hi there!
»»————- ★ ————-««
I believe your answer is:
760
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the answer...}}\\\\(35+5)[16+(12\div 4)]\\------------------\\\text{Follow \textbf{PEMDAS}}\\\\\rightarrow 35+ 5 = 40\\\\40[16+(12\div 4)]\\\\\rightarrow 12\div4 = 3\\\\\rightarrow 16 + 3 = 19\\\\40(19)\\\\\rightarrow 40 * 19\\\\\boxed{760}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
What is the equation of the line that passes through (-12,6) and (-6,1)?
Identify the perimeter and area of an equilateral triangle with height 12 cm. Give your answer in simplest radical form.
Answer:
perimeter is 36 cm
Step-by-step explanation:
After getting RM24 from his mother, Samuel had 3 times as much as he had previously. How much did he have previously?
Answer:
Samuel had RM8 previously
Step-by-step explanation:
24÷3=8
