9. The annual interest rate is 21%. The balance after the grace period was $700. No
payments were received. What is the interest for the month?
Answer:
Interest for the month = $12.25
Step-by-step explanation:
Given:
Amount in bank = $700
Rate of interest per month = 21% / 12 = 0.0175
Find:
Interest for the month
Computation:
Interest for the month = Amount in bank × Rate of interest per month
Interest for the month = $700 × 0.0175
Interest for the month = $12.25
solving these quadratics for x using complete the square 3x^2-4x-1=0
Answer:
in picture
Step-by-step explanation:
Jenna was asked to find a fraction equivalent to 4/6 with a numerator of 14.Her answer is 14/16. What error did jenna make in writing equivalent fractions
Answer: Jenna did not multiply how much 4 goes into 14 which is 3.5 she should have multiplied 4*3.5=14 and 6*3.5=21
Step-by-step explanation:
so the answer should have been 4/6 is equivalent to 14/21
Hopes This Helpsplease help// geometry question.... geometry question pt.2
Answer:
a) E
b) line segment AB
Step-by-step explanation:
a) E
b) line segment AB (It's AB with the line over it - no arrowheads)
A shopper’s discount club charges a monthly fee of $15 and sells gasoline for $2.05 per gallon. The gas station across the street sells gasoline for $2.35 per gallon and charges no fee. Write and equation to model how many gallons of gasoline would you have to buy in one month to spend the same amount at either store
Answer:
15 + 2.05 x = 2.35 x
Step-by-step explanation:
Let x be the number of gallons you would have to buy for the two places to be the same.
At the club, there is a monthly fee of $15 that is charged once in a month. They also charge $2.05 per gallon, which is charged every gallon of gas you buy.
We can write an expression: 15 + 2.05 x
At the gas station, they charge $2.35 per gallon with no other fees.
We can also write an expression: 2.35 x
For the prices to be the same, we have 15 + 2.05 x = 2.35 x
If we were to solve, then we have:
(2.35 - 2.05) x = 15
x = 15 / 0.3 = 50 gallons
PLS SOLVE THIS , IM UNABLE TO GET IT
Step-by-step explanation:
Remember:
X = 2.5
Y = 1.5
Z = 1
The chart:
X Y Z
I 10000 7000 8000
II 6000 10000 5000
X
The first column represents X. Since X's value is 2.5, we multiply both those numbers by 2.5.
[tex]10,000*2.5=25,000[/tex]
[tex]6000*2.5=15,000[/tex]
These are the values of X.
Y
The second column represents Y. Since Y's value is 1.5, we multiply both of the values by 1.5.
[tex]7,000*1.5=10,500[/tex]
[tex]10,000*1.5 = 15,000[/tex]
These are the values of Y.
Z
The last column represents Z. Since Z's value is 1, we do not need to multiply the numbers, since they are already multiplied by 1.
[tex]8,000[/tex]
[tex]5,000[/tex]
These are the values of Z.
ADDING
Now that we have are 6 numbers solved, all we have to do is add them all together.
[tex](25+15+10.5+15+8+5)\\25,000+15,000+10,500+15,000+8,000+5,000=78,500[/tex]
Our final answer: $78,500 is the total. (first option)
A community sports league is raising money by making custom shirts to sell at league games. They plan to sell the shirts for $13. Each shirt costs $6 to make. They spent $55 for advertising. Use n to represent the number of shirts they sell. Multiply this by the money they make for each shirt, then subtract the advertising cost. Which expression represents the money that the league raises?
O A. 55 – (13 – 6) n
O B. (13-6) n - 55
O C. 13n - 6 - 55
O D. 13 – 6n – 55
Answer:
B. (13-6) n - 55
Step-by-step explanation:
The number of shirts to be sold is n
The cost to purchase one shirt is $13
The cost of making each shirt is $6
Let's assume the shirt is one
Profit for a Shirt = (13-6)
But then there are no number of shirts
Profit= (13-6)n
But then also, an advert was run for the total shirts combined
Profit= (13-6)n -55
Answer:
b. (13-6)n-55
ap3x
Find all solutions of the equation in the interval (0,2π)
cot theta +root 3 = 0
Answer:
θ = 5π/6 rad and 11π/6 rad
Step-by-step explanation:
Given the expression cotθ+√3=0
Subtract √3 from both sides
cotθ+√3-√3=0-√3
cotθ = -√3
Since cotθ = 1/tanθ
1/tanθ = -√3
Reciprocate both sides:
tanθ = -1/√3
θ = tan^-1(-1/√3)
θ = -30°
Since the angle is negative, and tanθ is negative in the second and fourth quadrant.
In the second quadrant;
θ = 180-30
θ = 150°
Since 180° = πrad
150° = 150π/180
150° = 5π/6 rad
In the fourth quadrant;
θ = 360-30
θ = 330°
Since 180° = πrad
330° = 330π/180
330° = 11π/6 rad
Hence the solutions are 5π/6 rad and 11π/6 rad.
Lets See how fast can you Answer an High school Math Problem? 1. What is the degree of 7x + 1? 2. What is the solution to the system x + y = 5 and 3x - y = 3? 3. What is (x^4)/(x^0)? I'll check over your answer! You MUST answer all the question and get all the answers right to get Brainliest! Also I need to see how you got that answer!
Answer:
1) 1
2) (2,3)
3) x⁴
Step-by-step explanation:
1)
We have the expression:
[tex]7x+1[/tex]
The degree of an equation is the largest exponent of the equation.
We can rewrite our expression as:
[tex]=7x^1+1x^0[/tex]
1 is the largest exponent.
Thus, our degree is 1.
2)
We have the system of equations:
[tex]x+y=5\\3x-y=3[/tex]
To solve, we can use substitution.
From the first equation, subtract x from both sides:
[tex]y=5-x[/tex]
Substitute this into the second equation:
[tex]3x-(5-x)=3[/tex]
Simplify:
[tex]3x-5+x=3[/tex]
Add 5 to both sides:
[tex]3x+x=8[/tex]
Combine like terms:
[tex]4x=8[/tex]
Divide both sides by 4:
[tex]x=2[/tex]
So, x is 2.
Substitute this back into the first equation:
[tex]x+y=5[/tex]
Substitute x for 2:
[tex]2+y=5[/tex]
Subtract 2 from both sides:
[tex]y=3[/tex]
Our solution is (2,3)
3)
We have the expression:
[tex]\frac{x^4}{x^0}[/tex]
Anything to the zeroth power (except for 0) is 1. Assuming x is not 0:
[tex]=x^4/1\\=x^4[/tex]
And that's the simplest it can get.
Answer:
[tex]\Huge \boxed{\mathrm{1. \ 1}} \\ \\ \\ \Huge \boxed{\mathrm{2. \ (2,3)}} \\\\\\ \Huge \boxed{{3. \ x^4 }}[/tex]
Step-by-step explanation:
The degree is the largest exponent on the variable.
[tex]7x^1 + 1x^0[/tex]
The largest exponent on the variable is 1.
The degree is 1.
System of equations:
[tex]x+y=5 \\ \\ 3x-y=3[/tex]
Solving y for the first equation.
Subtracting x from both sides.
[tex]y=5-x[/tex]
Substitution method.
[tex]3x-(5-x)=3[/tex]
Distribute negative sign.
[tex]3x-5+x=3[/tex]
Combining like terms.
[tex]4x-5=3[/tex]
Adding 5 to both sides.
[tex]4x=8[/tex]
Dividing both sides by 4.
[tex]x=2[/tex]
Substitution method.
[tex]y=5-2 \\ \\ \\ y=3[/tex]
[tex]\displaystyle \frac{x^4 }{x^0 }[/tex]
Subtract exponents with same bases when dividing.
[tex]x^{4-0}[/tex]
[tex]x^4[/tex]
Give two other names for WQ
Answer:
Two other names for WQ are QW and line g.
Step-by-step explanation:
A line can have as many points as possible. The two other names for WQ are QW and line g
From the given plane, we can observe the following:
Points W and Q are on the same lineLine g has points Q and W on it.This means that, we can rename WQ as
QW i.e. this is done by writing Q before W.Line g i.e. by giving WQ the name of the line, on which both points are.Hence, the two other names for WQ are QW and line g
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The temperature at 6:00am was -4 degrees The temperature increased 20 degrees by noon what was the temperature at noon
Answer:
16 degrees
Step-by-step explanation:
Add 20 to -4
-4 + 20
= 16
So, the temperature at noon was 16 degrees
Answer:
16 degrees
Step-by-step explanation:
The question states that it increased +20 degrees by noon from 6:00 am. So,
-4 + 20 = 16
The temp would be 16 degrees at noon.
A bicycle has a listed price of $749.95 before tax. If the sales tax rate is 6.5% , find the total cost of the bicycle with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
749.95+ 44.997 *or 45.00 giving 794.95
Please help Im stuck in this homework assignment.
Answer:
(0,3)
Step-by-step explanation:
You need to pick a point, P, that will give you a distance from A to P that is twice as long as from P to B, or ration 2:1
Point A is (-2,-7), point B is (1,8), and I picked (0.3) because it looked like it could be, but now we need to test it.
Distance formula is:
[tex]d=\sqrt{(x_{2}-x_{1})^{2} + {(y_{2}-y_{1})^{2} } \\[/tex]
So AP would be
[tex]AP=\sqrt{(0--2)^{2} + {(3--7)^{2} } \\[/tex]
[tex]AP=\sqrt{(2)^{2} + {(10)^{2} } \\[/tex]
Do the same with PB, and you will find it's 5.1, giving an approximate ratio of 2:1.
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 5 + 54x − 2x3, [0, 4]
Answer:
The absolute maximum and minimum of [tex]f(x) = 5 + 54\cdot x -2\cdot x^{3}[/tex] on [tex][0,4][/tex] are 113 and 5.
Step-by-step explanation:
Let be [tex]f(x) = 5 + 54\cdot x -2\cdot x^{3}[/tex], the first and second derivatives of the function are, respectively:
[tex]f'=54-6\cdot x^{2}[/tex]
[tex]f''=-12\cdot x[/tex]
Now, let equalize the first derivative to zero and solve the resulting expression:
[tex]54-6\cdot x^{2} = 0[/tex]
[tex]x^{2} = 9[/tex]
[tex]x =\pm 3[/tex]
According to the given interval, only [tex]x=3[/tex] is a valid outcome. Lastly, this is evaluated in the second derivative expression:
[tex]f''=-12\cdot(3)[/tex]
[tex]f'' = -36[/tex]
[tex]x = 3[/tex] leads to an absolute maximum.
[tex]f(3) = 5 + 54\cdot (3) -2\cdot (3)^{3}[/tex]
[tex]f(3) = 113[/tex]
The absolute minimum is determined by evaluating at each extreme of the interval:
[tex]x = 0[/tex]
[tex]f(0) = 5 + 54\cdot (0) -2\cdot (0)^{3}[/tex]
[tex]f(0) = 5[/tex]
[tex]x = 4[/tex]
[tex]f(4) = 5 + 54\cdot (4) -2\cdot (4)^{3}[/tex]
[tex]f(4) = 93[/tex]
The absolute maximum and minimum of [tex]f(x) = 5 + 54\cdot x -2\cdot x^{3}[/tex] on [tex][0,4][/tex] are 113 and 5.
Which shapes can the composite figure be
decomposed into? Check all that apply.
circle
rectangle
triangle
trapezoid
Square
Answer:
B C D
Step-by-step explanation:
i did the assignment
Answer:
rectangle, triangle,trapezoid
Step-by-step explanation:
Find the equation of a sphere if one of its diameters has endpoints: (-9, -12, -6) and (11, 8, 14).
= 0
Answer:
Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is [tex](x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30[/tex].
Step-by-step explanation:
There are two kew parameters for a sphere: Center ([tex]h[/tex], [tex]k[/tex], [tex]s[/tex]) and Radius ([tex]r[/tex]). The radius is the midpoint of the line segment between endpoints. That is:
[tex]C(x,y,z) = \left(\frac{-9+11}{2},\frac{-12+8}{2},\frac{-6+14}{2} \right)[/tex]
[tex]C(x,y,z) = (1,-2,4)[/tex]
The radius can be found by halving the length of diameter, which can be determined by knowning location of endpoints and using Pythagorean Theorem:
[tex]r = \frac{1}{2}\cdot \sqrt{(-9-11)^{2}+(-12-8)^{2}+(-6-14)^{2}}[/tex]
[tex]r = 10\sqrt{3}[/tex]
The general formula of a sphere centered at (h, k, s) and with a radius r is:
[tex](x-h)^{2}+(y-k)^{2}+(z-s)^{2} = r^{2}[/tex]
Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is [tex](x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30[/tex].
Evaluate f(-2) for f(x)= 8x^2-7x+3
Answer: 49
Step-by-step explanation:
We know, x = -2
Substituting value of x in [tex]8x^{2} -7x+3[/tex],
[tex]8(-2)^{2} - 7(-2) + 3\\=8(4) -7(-2) + 3\\=32+14+3\\=49[/tex]
Answer:
f(-2)=8*(-2)^2-7*(-2)+3=8*4+14+3=32+17=49
Step-by-step explanation:
(HELP URGENT RESPOND QUICKLY) What is the correct classification of 32?
Answer: Option 1. irrational number, nonrepeating decimal
Step-by-step explanation:
the simplified version of √32 is 4√2
√2 is not a rational number since it can't be written in the form of fraction, so √32 is also irrational.
√2 is equal to 1.414213562... this is nonrepeating, which means, √32 is nonrepeating.
Hope this helps!! :)
Please let me know if you have any question or need further explanation
Ronald and Tim both did their laundry today. Ronald does laundry every 6 66 days and Tim does laundry every 9 99 days.
Answer:
Find a number that can be divided by both 6 and 9, which is 18. That means they will do laundry on the same day every 18 days.
Answer: 18 Days
Step-by-step explanation:
Let's look at their indivigual schedules for hte nex little While
<-0------6------12---->
t=Tim does laundry every 9 days
<-0---------9---------->
They haven't done laundry on the same day again yet, so let's keep going!
When we keep goin, we see thar the multiple first meet at 18
Ronal
<-0----6----18----27---->
Tim
<-0----9----18----27--->
Mathematically, we say that 18 is the least common multiple of 6 and 9. in math notation this looks like:
lcm (6, 9) = 18
Which comparison is false? a) 4 liters < 1 gal b) 1ft < 1 meter c) 25 grams < 1 oz d) 10 km < 9 miles
Answer:
a. is false
Step-by-step explanation:
4 liters= 1.057 gal
1.057 is greater than 1
Hope this helps :)
Determine whether the following functions are even, odd, or neither.
f(x) = x2 + 4x - 7:
f(x) = 4.x2 +1:
f(x) = 5x5 – 42:
3. A car is traveling at a speed of 60 miles per hour. What's the dependent variable in this situation?
A. The speed at which the car travels
B. The age of the car
C. The number of hours the car has traveled
D. The distance the car has traveled
Answer:
The answer is A) the speed at which the car has traveled
Step-by-step explanation:
Simplify the expression to a polynomial in standard form: (4x+5) (x^2-3x-2) PLEASE HLEP
Answer:
[tex]4x^3-7x^2-23x-10[/tex]
Step-by-step explanation:
So we have the expression:
[tex](4x+5)(x^2-3x-2)[/tex]
Distribute. Multiply (4x+5) to each term:
[tex](x^2)(4x+5)+(-3x)(4x+5)+(-2)(4x+5)[/tex]
Distribute:
[tex]=(4x^3+5x^2)+(-12x^2-15x)+(-8x-10)[/tex]
Combine like terms:
[tex]=(4x^3)+(5x^2-12x^2)+(-15x-8x)+(-10)[/tex]
Add and simplify:
[tex]=4x^3-7x^2-23x-10[/tex]
And this is in descending order, so it's in standard form.
−6w + 9wy + 6 + 2wy − 4y
Answer:
-6w + 11wy + 6 - 4y
Step-by-step explanation:
Step 1: Write out expression
-6w + 9wy + 6 + 2wy - 4y
Step 2: Combine like terms
-6w + 11wy + 6 - 4y
Answer:
11wy-6w-4y+6
Step-by-step explanation:
−6w + 9wy + 6 + 2wy − 4y
Combine like terms
−6w + 6 + 2wy+ 9wy − 4y
11wy-6w-4y+6
Why can't you use the product of powers rule to simplify
this expression? Explain.
3^4.2^8
Answer:
Because the base of this expression is not same.
Multiply: (x+3y)(x-2y)? Show steps please
Answer:
x² + xy - 6y²
Step-by-step explanation:
FOIL
(x+3y)(x-2y)
F= x²
O= -2xy
I= 3xy
L= -6y²
Add these together = x² + xy - 6y²
Step-by-step explanation:
Hey, there!
Let me simply clear you.
While multiplying algebraic expression, you must be very careful about sign and brackets.
Here,
[tex](x + 3y)(x - 2y)[/tex]
Let's multiply (x-2y) by (x+3y)
[tex] = x(x - 2y) + 3y(x - 2y)[/tex]
[tex] = ({x}^{2} - 2xy) + (3xy - 6 {y}^{2}) [/tex]
Open brackets.
[tex] = {x}^{2} - 2xy + 3xy - 6 {y}^{2} [/tex]
Simplify the like terms.
[tex] = {x}^{2} + xy - 6 {y}^{2} [/tex]
Therefore, the answer is x^2 + xy- 6y^2.
Hope it helps.....
square root of 1.9321
Answer:
square root of 1.9321 = 1.39
Step-by-step explanation:
(AM GIVING BRAINLIEST) Find all complex numbers z such that z^4 = -4 Note: All solutions should be expressed in the form a+bi, where a and b are real numbers. plz explain
Answer:
z = {1 +i, 1 -i, -1 +i, -1 -i}
Step-by-step explanation:
Using Euler's formula, you can write this as ...
z^4 = 4e^(i(π+2kπ))
Then the 4th root is ...
z = 4^(1/4)e^(i(π/4 +kπ/2)) = √2(cos(π/4+kπ/2) +i·sin(π/4+kπ/2))
for integers k in the range 0 to 3.
z = √2(±1/√2 ±i·1/√2) . . . signs are independent
z = ±1 ±i . . . . . . signs are independent; hence 4 solutions
z = {1 +i, 1 -i, -1 +i, -1 -i}
_____
Comment on roots of complex numbers
In the complex domain, each number has a number of roots equal to the index of the root. That is, there are four 4th roots. They all have the same magnitude, but their angles are separated by 360°/(root index) = 90°. Here, the principal fourth root of 4∠180° is 4^(1/4)∠(180°/4) = √2∠45° = 1+i.
Adding 90° is equivalent to multiplying by i, so the other 3 roots are √2∠135° = -1+i, √2∠225° = -1 -i, and √2∠315° = 1 -i.
z = {1 +i, 1 -i, -1 +i, -1 -i}
4(x - 5) = 4 (4 + x)
Answer:
x=0
Step-by-step explanation:
4(x-5) = 4(4+x)
4x-20 = 16+4x
4x-4x = 16+20
0x=36
x = 36/0
x = 0
hope it might help
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The three sides of a triangle are 4cm, 6cm and 8cm.
(a) find the cosine of the largest angle
(b) show that the area of the triangle is 3√15cm²
(c) find the length of the shortest altitude of the triangle
Answer:
In bold below.
Step-by-step explanation:
(a) The largest angle is opposite the largest side.
So by the Cosine Rule:
8^2 = 4^2 + 6^2 - 2*4*6 cos x
cos x = (8^2 - 4^2 - 6^2) / (-2*4* 6)
= -0.25.
x = 104.48 degrees.
(b) Area of the triangle = 1/2 * 4 * 6 sin 104.48
= 11.62
= 3 √15.
(c) The shortest altitude will have the longest sides as the base.
Area = 1/2 * altitude * base
3√15 = 1/2 * 8 * a
a = 3√15 / 4 cm
= 0.75√15 cm.
The cosine of the largest angle is 104.48 degrees
The area of the triangle is 3√15cm² is 3 √15
The length of the shortest altitude of the triangle is 0.75√15 cm.
A triangle can be defined as a figure that has three lines. It can be of various dimensions it can a scale as Pythagoras or an isosceles triangle. They all have different properties.
(a)
With the help of the Cosine Rule:
[tex]8^2[/tex] = [tex]4^2 + 6^2 - 2 \times 4\times6 cos x[/tex]
cos x = [tex](8^2 - 4^2 - 6^2) / (-2 \times 4 \times 6)[/tex])
= -0.25.
x = 104.48 degrees.
(b)
Area of the triangle
=[tex]1/2 \times 4 \times 6 sin 104.48[/tex]
= 11.62
= 3 √15.
(c)
Area =[tex]1/2 \times altitude \times base[/tex]
3√15 = 1/2 * 8 * a
a = 3√15 / 4 cm
= 0.75√15 cm.
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