The simplified form of polynomials are:
1. (a² - 3a)² = 3a²
2. (1/2x³ + 6x)² = -12x²
Given,
We have to expand the given polynomials and simplify them.
1. The polynomial: (a² - 3a)²
Here,
The polynomial is in the form of (a - b)²
So,
(a - b)² = a² - 2ab + b²
Then,
(a² - 3a)² = (a²)² - (2 × a² × 3a) + (3a)²
(a² - 3a)² = a⁴ - 6a³ + 9a²
(a² - 3a)² = a²(a² - 6a + 9)
Here,
(a² - 6a + 9) is in quadratic form. Solve using quadratic formula.
a = 1, b = -6 and c = 9
[tex]\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}[/tex] = [tex]\frac{6(+-)\sqrt{(-6)^{2}-4(1)(9) } }{2(1)}[/tex] = [tex]\frac{6(+-)\sqrt{36 - 36} }{2}[/tex] = [tex]\frac{6(+-)\sqrt{0} }{2}[/tex] = (6±0) / 2
= 6/2 = 3
Then,
(a² - 3a)² = a²(a² - 6a + 9)
Here,
(a² - 6a + 9) = 3
So,
(a² - 3a)² = 3a²
2. The polynomial: (1/2x³ + 6x)²
Here, the polynomial is in the form (a + b)²
(a + b)² = a² + 2ab + b²
Here,
(1/2x³ + 6x)² = (1/2x³)² + (2 × 1/2x³ × 6x) + (6x)²
(1/2x³ + 6x)² = 1/4x⁶ + 6x⁴ + 36x²
(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)
a = 1/4, b = 6 and c = 36
Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}[/tex]
= [tex]\frac{-6(+-)\sqrt{(-6)^{2} -4(1/4)(36)} }{2(1/4)}[/tex] = [tex]\frac{-6(+-)\sqrt{36-36} }{1/2}[/tex] = (-6±0) / (1/2) = -6 × 2 = -12
Therefore,
(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)
Here,
(1/4x⁴ + 6x² + 36) = -12
Then,
(1/2x³ + 6x)² = -12x²
That is,
The simplified form of polynomials are:
1. (a² - 3a)² = 3a²
2. (1/2x³ + 6x)² = -12x²
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The midpoint of UV is (5,−11). The coordinates of one endpoint are U(3,5). Find the coordinates of endpoint V.
Using the mid point, the coordinates of the end point V is (7, -27)
How to find the coordinate using the mid point?A midpoint is a point lying between two points and is in the middle of the line joining the two points.
In other words, the midpoint of a line segment is a point that lies halfway between 2 points.
Therefore, the coordinates of the endpoint V can be found as follows:
using the mid point,
(xₙ, yₙ) = (x₁ + x₂ / 2, y₁ + y₂ / 2)
Therefore,
(5, -11) = (3 + x₂ / 2, 5 + y₂ / 2)
Hence,
5 = 3 + x₂ / 2
cross multiply
10 = 3 + x₂
10 - 3 = x₂
x₂ = 7
Hence,
- 11 = 5 + y₂ / 2
-22 = 5 + y₂
-22 - 5 = y₂
y₂ = - 27
Therefore, the coordinates of V is (7, -27)
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-The polynomial function p(x) = x² + 4x³ - 7x² - 22x + 24 has known factors of (x + 4) and (x - 1).
a. Rewrite p(x) as the product of linear factors.
b. Draw a rough sketch of the graph of the function.
Answer:
p(x) = (x +4)(x +3)(x -1)(x -2)see the first attachment for a graphStep-by-step explanation:
Given p(x) = x⁴ + 4x³ - 7x² - 22x + 24 with known factors (x +4) and (x -1), you want the function written as a product of linear factors, and a sketch of the graph.
A graphing calculator can help with both parts of this. It can show you the remaining zeros are -3 and 2, so the remaining linear factors are (x +3) and (x -2). At the same time, it produces a graph of the function. This is shown in the first attachment.
a. RewriteSynthetic division is a convenient way to find the remaining factors of the polynomial. Dividing by (x+4) gives ...
p(x) = (x +4)(x^3 -7x +6) . . . . . . shown in the second attachment
And dividing the cubic by (x -1) gives ...
p(x) = (x +4)(x -1)(x^2 +x -6) . . . . . . shown in the second attachment
The quadratic will have linear terms with constants that sum to 1 and have a product of -6. These constants are 3 and -2.
The rewrite of p(x) is ...
p(x) = (x +4)(x +3)(x -1)(x -2)
b. Graph
The 4th degree polynomial has a positive leading coefficient, so is above the x-axis at both the left and right ends of the graph. The graph crosses the x-axis at x = -4, -3, 1, and 2.
We note these roots are symmetrical about x=-1, so there will be a maximum at that point. That maximum is p(-1) = (-1 +4)(-1 +3)(-1 -1)(-1 -2) = 3·2·(-2)(-3) = 36. The minimum values will be found approximately halfway between -4 and -3, and again between -1 and -2. Those minima will be approximately p(-3.5) = (-.5)(.5)(-4.5)(-5.5) ≈ -6.2
The y-intercept is +24, the constant in the polynomial.
With the zero crossings, line of symmetry, local maximum, approximate local minima, and the y-intercept, we can make a passable sketch of the graph.
A graph is seen in the first attachment.
AB = 2x-2, BC = 3 and AC = 3x-5 find x
we can made a visula representation of the problem so:
So we can made an equation like:
[tex]\begin{gathered} AB+BC=AC \\ 2x-2+3=3x-5 \end{gathered}[/tex]and we can solve for x so:
[tex]\begin{gathered} 2x+1=3x-5 \\ 5+1=3x-2x \\ 6=x \end{gathered}[/tex]Answer: X=6
Step-by-step explanation: you can set AB plus BC to AC because they both are equal to the full line so..
2X-2+3=3X-5
First off add like terms so..
-2+3= 1 and then add 5 to the negative 5 and 1 which now leaves you with
2X+6=3X
Now you see more like terms ( 2X,3X)
Now subtract 2X from 3x which will leave you with
6=1X
Now to separate X and get you answer you see it’s 1X and 1X = X prior to defined answer, therefore you will be with X=6. Have a great day
how many lines of symmetry does the word checkbook have?
Answer:
none (as shown) or
one if all uppercase letters
Step-by-step explanation:
A line of symmetry is a line you could place on a shape (usually a square, rectangle, triangle, etc, but here the "shape" is the word checkbook) which, if you folded the shape on the line, the two halves of the shape would exactly match each other.
"checkbook" does NOT have any lines of symmetry. BUT,
CHECKBOOK
does have a line of symmetry, horizontally, right thru the middle.
-20 less than or equal to 4x
We will have the following:
[tex]-20\le4x[/tex]When we solve for x we will have
[tex]-\frac{20}{4}\le x\Rightarrow-5\le x[/tex]So, x is equal or grater than -5.
Your weekly base salary is $150. You earn $20 for each cell phone that
you sell.
a. What is the minimum amount you can earn in a week?
b. Write and solve an inequality that represents the number of cell phones
you must sell to make at least $630 a week.
c. Write and solve an inequality that represents the number of cell phones
you must sell to make at least $750 a week.
d. The company policy is that as a part-time employee, the maximum
you can earn each week is $950. Write and solve an inequality that
represents the number of cell phones you can sell each week.
The minimum that could be earned is $150. The required inequalities are solved below:
What is an inequality?
An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line. There are multiple notations used to denote various types of inequalities: The symbol a b indicates that an is smaller than b. The symbol a > b indicates that an is more than b. In either scenario, a and b are not equal. These are characterized as stringent inequalities because an is either strictly less than or strictly bigger than b. Equivalence is not allowed.
(a) The minimum that could be earned is $150.
(b) The required inequality is given as 150+20x≥630
or, 20x≥630-150
or, x≥480/20
or, x≥24
(c) The required inequality is given as 150+20x≥750
or, 20x≥750-150
or, x≥600/20
or, x≥30
(d) The required inequality is given as 150+20x≤950
or, 20x≤950-150
or, x≤800/20
or, x≤40
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3. 40 ounces of granola costs $6.52
a. How much does granola cost per ounce? (Give your answer to the nearest cent.) pleasee help
Answer: $0.2
Step-by-step explanation:
To find the answer you divide 6.52 by 40 which will get 0.163. To check the answer and make sure its correct you can multiply 0.163 by 40 to get 6.52 making the answer correct so 0.2 is the answer to the nearest cent. Hope this helps :)
Here is the answer again
A new pet store is offering 12% off for their grand opening! A parakeet originally costs $17. What is the sale price after the discount?
Let:
Oc = original cost = $17
Sp = Sale price
D = Discount percent = 12% = 12/100 = 0.12
The sale price will be:
[tex]\begin{gathered} Sp=Oc-0.12\cdot Oc \\ Sp=17-0.12\cdot17 \\ Sp=17-2.04 \\ Sp=14.96 \end{gathered}[/tex]The sale price is $14.96
What is the perimeter of this rectangle?
The perimeter of the rectangle is 6.89
Perimeter of the rectangle:
The perimeter (P) of a rectangle is the total length of all the sides of the rectangle.
The formula for the perimeter of the rectangle is
P = 2(l + w)
The letter ‘P’ denotes the perimeter of a rectangle. Let l denote the length and w denote the width of the rectangle.
Given,
Here we have the graph with the following points:
(-3/2, -1 7/9), (7/2, -1 7/9), (7/2, 3 2/9), and (-3/2 3 2/9)
Now we need to find the perimeter of the rectangle.
To calculate the perimeter, first we have to find the length and width of the rectangle.
To calculate the length, we have to use the values of x axis,
That is,
=> -3/2 + 7/2
=> (-3+7)/2
=> 4/2
=> 2
Therefore, the length of the rectangle is 2.
Now, we have to find the width of the rectangle using the y axis coordinates,
=> -1 7/9 + 3 2/9
Convert the mixed fraction into normal form, then we get,
=> -16/9 + 29/9
=> (-16 + 29)/9
=> 13/9
Therefore, the width of the rectangle is 13/9
Now, we have to use this to calculate the perimeter of the triangle,
P = 2 (2 + 13/9)
P = 2 ((18+13)/9)
P = 2 (31/9)
P = 62/9
P = 6.89
Therefore, the perimeter of the rectangle is 6.89.
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if the work required to stretch a spring 3 ft beyond its natural length is 15 ft-lb, how much work (in ft-lb) is needed to stretch it 18 in. beyond its natural length? give your answer in decimal form.
The amount of work needed to stretch the spring 18 in. from its natural position is 3.75 ft-lb.
According to the Hooke's Law, the work done on the spring is:
W = 1/2. k . x²
Where:
k = spring constant
x = displacement.
Notice that the work done is directly proportional to x².
Hence,
W₁ : W₂ = x₁² : x₂²
Parameters given:
W₁ = 15 ft-lb
x₁ = 3 ft
x₂ = 18 in. = 1.5 ft
Plug the above parameters into the ratio equation:
15 : W₂ = 3² : (1.5)²
W₂ = (1.5)² . 15 / 3² = 15/4 = 3.75 ft-lb
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7. The vertices of a triangle are P(-7,-4), Q(-7, -8), and R(3, -3). Name the vertices of the
image reflected across the line y=x.
OP(4, 7), Q8, 7), R'(3,-3)
OP(4,-7), Q8, -7), R'(3, 3)
OP(-4,-7), Q(-8,-7), R'(-3, 3)
OP(-4, 7), Q(-8, 7), R'(-3,-3)
(1 point)
A place where two or more curves, lines, or edges converge is known as a vertex in geometry (plural: vertices or vertexes), and it is frequently identified by letters like,,,. As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.
The solutions are:
P' = (-4,-7)
Q ' = (-8,-7) (-8,-7)
R ' = (-3,3) (-3,3)
All you have to do is flip the provided points P, Q, and R's x and y coordinates.
The common principle is (x,y) —-> (y,x)
Thus, when we reflect across the line y = x, something like P = (-7,-4) becomes P'= (-4,-7). The similar approach is taken with the other points.
How do you locate a triangle's vertices?
Finding the triangle's vertices on the line y = x as an image
The steps below are used to locate a triangle's vertices using its midpoints:
Identify the midpoints' x and y values;
Calculate the midpoint using the following equations: A = (x 1+ x 3 - x 2, y 1 + y 3-y 2); B = (x 1+x 2-x 3, y 1+y 2-y3); C = (x 2+x 3-x 1, y 2 + y 3 -y 1);.
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bricklayer brenda would take nine hours to build a chimney alone, and bricklayer brandon would take 1010 hours to build it alone. when they work together, they talk a lot, and their combined output decreases by 1010 bricks per hour. working together, they build the chimney in 55 hours. how many bricks are in the chimney?
When seen as a function, a relationship exists between a set of inputs and outputs.
The number of bricks in the chimney exists 900.
What is meant by functions?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Simply described, a function is an input-output connection where each input is coupled to exactly one output range, codomain, and domain are included in each function. A function exists generally denoted by f(x) where x exists the input.
Let x be the number of bricks in the chimney. The work done exists the rate multiplied by the time.
Using w = rt, we get
[tex]$x=\left(\frac{x}{9}+\frac{x}{10}-10\right) \cdot 5[/tex]
Expanding the above equation, we get
[tex]$\left(\frac{x}{9}+\frac{x}{10}-10\right) \cdot 5: \quad \frac{19 x}{18}-50$[/tex]
x = (19x / 18) - 50
Multiply both sides by 18
[tex]$x \cdot 18=\frac{19 x}{18} \cdot 18-50 \cdot 18[/tex]
Simplifying the above equation,
x × 18 = 19x - 900
Subtract 19x from both sides
x × 18 - 19x = 19x - 900 - 19x
Simplifying the above equation, we get
-x = -900
Divide both sides by -1
[tex]$\frac{-x}{-1}=\frac{-900}{-1}[/tex]
x = 900
Therefore, the value of x exists 900.
The complete question is:
Bricklayer Brenda would take nine hours to build a chimney alone, and bricklayer Brandon would take hours to build it alone. When they work together, they talk a lot, and their combined output decreases by bricks per hour. Working together, they build the chimney in hours. How many bricks are in the chimney?
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Consider the following.
sin(x) + sin(3x) = 4 sin(x) cos2(x)
Prove the identity.
Proved the identity sin(x) + sin(3x) = 4sin(x) cos²(x)
Given,
sin(x) + sin(3x) = 4 sin(x) cos²(x)
We have to prove the above given identity:
So,
sin(x) + sin(3x)
sin(x) + sin(2x + x)
By using the identity sin (A + B) we get,
sin(x) + sin (2x) cos(x) + cos (2x) sin(x)
Now use the identities:
sin 2x and cos 2x
We get,
sin(x) + 2sin(x) cos(x) cos(x) + (2cos²(x) - 1) sin(x)
Then,
sin(x) + 2sin(x) cos²(x) + 2sin(x) cos²(x) - sin(x)
We get,
4 sin(x) cos²(x)
Hence proved the identity sin(x) + sin(3x) = 4sin(x) cos²(x)
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if a 95% confidence interval for the mean head circumference for adults, based on the results of measuring head circumference for 30 adults, is (21.42, 23.18) inches, what is the margin of error? inches.
The margin of error is 0.88.
What is a margin of error?
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings.
Here, we have
Lower confidence interval = 21.42
Upper confidence interval = 23.18
Now,
Sample mean(x) = (Lower confidence interval + Upper confidence interval)/2
x = (21.42 + 23.18)/2
x = 44.6/2
Sample mean (x) = 22.3
Now, we find the margin of error,
margin of error = Upper confidence interval - x
= 23.18 - 22.3
= 0.88
Hence, the margin of error is 0.88.
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The margin of error is 0.88.
What is a margin of error?In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings.Here, we have
Lower confidence interval = 21.42Upper confidence interval = 23.18Now, calculate:
Sample mean(x) = (Lower confidence interval + Upper confidence interval)/2
x = (21.42 + 23.18)/2x = 44.6/2Sample mean (x) = 22.3Now, we find the margin of error:
margin of error = Upper confidence interval - x
= 23.18 - 22.3= 0.88Hence, the margin of error is 0.88.
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refrigerant r-410a is a mixture of refrigerants r-32 and r-125. it takes 60 pounds of r-32 and 40 pounds of r-125 to make 100 pounds of r-410a. find the ratio of r-32 to r-125. fill in the blanks with the correct answer.
The ratio of r-32 to r-125 is 3:2
A ratio in math displays how many times one number is contained in another. Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B). When both sides of a ratio are whole numbers and cannot be divided by a whole number, the ratio is in its simplest form.
Given,
Refrigerant r-32 and r-125 are the two main constituents of refrigerant r-410.
60 pounds of r-32 and 40 pounds of r-125 make up to 100 pounds of r-410.
The ratio of r-32 to r-125 = 60/40 =3/2.
Hence, the required ratio of r-32 to r-125 is 3:2
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suppose that 30% of the 10,000 signatures on a certain recall petition are invalid. would the number of invalid signatures in a sample of 3000 of these signatures have (approximately) a binomial distribution? explain. g
Approximately, all of the signatures in the sample of 3000 signatures are invalid . We get this outcome by using binomial distribution .
This problem it is said that 30% of 10000 signatures on certain recall petition are invalid . So, here is the two outcomes possible one is the signatures are invalid and other signature are valid .
Probability of Success (signature are valid ) = p = favourable outcomes / total outcomes
Favourable outcomes for Success = 70% of 10,000= 7000
Total number of possible outcomes = 10,000
P = 7000/10,000 = 7/10
Probability of failure (signature are invalid ) = q= 1- p = 1- 7/10 = 3/10
We have to find out probability of getting invalid signature from a sample of 3000 signatures..
Using the binomial distribution,
P(X = x ) = ⁿ C ₓ pˣ (1- p)⁽ⁿ⁻ˣ⁾
n = 3000 , x= 0 for none of signatures from 3000 are invalid.
P(X=0) = ³⁰⁰⁰C ₀ (3/10)⁰ ( 7/10) ³⁰⁰⁰
= 1 . 1 . (7/10)³⁰⁰⁰ = (7/10)³⁰⁰⁰ = 0
Probability of getting invalid signature out of sample 3000 is
1 – ( 7/1000)³⁰⁰⁰ = 1
This implies that all the signatures in sample of 3000 are invalid.
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Question 19:
1 2 2 4 8 32 ?
Answer:
256
Step-by-step explanation:
1,2,2,4,8,32
1*2=2
2*2=4
4*2=8
8*4=32
632*8=256
5. For which values of x and y is line p parallel to line q? (1 point)
R
(26y)⁰
Ox= 5, y = 3
Ox= 1, y = 5
Ox=3, y=5
Ox=3, y=6
(16x + 2)°
(45x-51
Answer:
x = 3 and y = 5
Step-by-step explanation:
1st: The sum of the same side interior angles equal 180°. Use this to solve for x.
45x - 5 + 16x + 2 = 180
61x - 3 = 180
61x - 3 + 3 = 180 + 3
61x/61 = 183/61
x = 3
2nd: find the measure of angle 16x + 2
16x + 2
16(3) + 2
48 + 2
50°
3rd: the sum of the 50° angle and the angle 26y° is 180 since they make a straight angle. Make an equation and solve for y.
50 + 26y = 180
50 - 50 + 26y = 180 - 50
26y = 130
26y/26 =130/26
y = 5
Jasmine, multiply your age by 3 and add 6. Thenmultiply this sum by 2. James, multiply your age by 2and add 4. Then multiply this sum by 3. I predict youwill both get the same number!») B. Choose 4 whole numbers for the twins' age and test eachexpression. Make a table to show the numbers you tried and theresults.
Same age
See explanation below
Explanation:Let the age of Jasmine = y
Multiplying Jasmine age by 3 and adding 6:
= (y × 3) + 6
= 3y + 6
Multiplyng the sum by 2:
2 × the sum = 2 × (3y + 6)
= 6y + 12
Let James age = z
Multiplying the age by 2 and adding 4:
James age × 2 = z × 2 = 2z
adding 4 = 2z + 4
Multiplying the sum y 3:
3 × the sum = 3 × (2z + 4)
= 6z + 12
Now since they are twins, they ae most likely same age
This means:
6y + 12 = 6z + 12
subtracting 12 from both sides:
6y = 6z
dividing both sides by 6:
y = z
Hence, Jasmine age is the same as James age
B) The expression for Jasmine = 2(3y + 6) = 6y + 12
The expression for James = 3(2z + 4) = 6z + 12
let the twin's age = 2, 3, 4, 5
when twin's age = 2
6y + 12 = 6(2) + 12 = 12 + 12 = 24
6z + 12 = 6(2) + 12 = 12 + 12 = 24
when twin's age = 3
6y + 12 = 6(3) + 12 = 18 + 12 = 30
6z + 12 = 6(3) + 12 = 18 + 12 = 30
when twin's age = 4
6y + 12 = 6(4) + 12 = 24 + 12 = 36
6z + 12 = 6(4) + 12 = 24 + 12 = 36
when twin's age = 5
6y + 12 = 6(5) + 12 = 30 + 12 = 42
6z + 12 = 6(5) + 12 = 30 + 12 = 42
Plotting the table:
Just answer what the ss says
The scatterplot of the data is attached accordingly. The Linear Regression equation for Y is ŷ = 0.82X + 2.31. Note that there is a positive correlation. This is because the y variable tends to increase as the x variable increases.
What is linear regression?Linear regression is a statistical method for modeling the connection between a scalar output and one or more explanatory factors. When there is only one independent factor, simple linear regression is employed; when there are more than one, multiple linear regression is utilized.
Note that the regression equation is usually given as:
ŷ = bX + a; where
y = dependent variable
b = Slope/coefficient
X = Independent Variable
a = Constant/ Intercept.
Notice that the regression line splits evenly between the data points exhibiting a linear relationship that is positively correlated.
From the graphing calculation, we have:
The sum of X = 21
The sum of Y = 33.39
Mean X = 3
Mean Y = 4.77
Sum of squares (SSₓ) = 28
Sum of products (SP) = 22.96
Recall that the regression equation is given as:
ŷ = bX + a;
Where;
b = SP/SSₓ and
a = [tex]M_{y}[/tex] -[tex]bM_{x}[/tex]
Hence,
b = 22.96/28
= 0.82
a = [tex]M_{y}[/tex] - bMₓ = 4.77 - (0.82*3) = 2.31
hence,
ŷ = 0.82X + 2.31.
Lets find Y if x = 10
y = 0.82 (10) + 2.31 [plugging in the value]
= 8.2 +2.31
= 10.51
Let's find X where Y = 10
10 = 0.82X + 2.31. [Plugging in the value]
collect like terms over the equation sign
10-2.31 = 0.82X
⇒ 7.69 = 0.82X [Divide both sides by 0.82
7.69/0.82 = X
X = 9.37804878049
X [tex]\approx[/tex] 9.38
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A bicyele store costs $2400 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicyeIs $120How many bicycles must the store sell each month 1o break even?Write a system of equations to represent the situation, then solve*Show both the equations and the solution
Answer:
The system of equations is:
• C(x)=2400+60x
,• R(x)=120x
The number of bicycles to break even = 40
Explanation:
Let the number of bikes sold = x
• The operating cost of the store per month = $2400
,• Cost Price Per bike = $60
Thus, the total monthly cost for the store:
[tex]C(x)=2400+60x[/tex]Next, the average selling price of each bicycle is $120, therefore, the monthly revenue of the store:
[tex]R(x)=120x[/tex]The store breaks even when the cost equals its revenue.
[tex]\begin{gathered} R(x)=C(x) \\ 120x=2400+60x \end{gathered}[/tex]We then solve for x:
[tex]\begin{gathered} \text{ Subtract 60x from both sides of the equation} \\ 120x-60x=60x-60x+2400 \\ 60x=2400 \\ \text{ Divide both sides of the equation by 60} \\ \frac{60x}{60}=\frac{2400}{60} \\ x=40 \end{gathered}[/tex]The store must sell 40 bicycles in order to break even.
PLEASE HELP ASAPPPPP!!!!!!!!!!!!!
The quadratic function f(x) has roots of −2 and 6, and it passes through the point (1, 15). What is the vertex form of the equation of f(x)?
f(x) = (x − 2)2 + 16
f(x) = (x + 2)2 + 16
f(x) = −(x − 2)2 + 16
f(x) = −(x + 2)2 + 16
Answer:
f(x) = −(x − 2)^2 + 16
Step-by-step explanation:
See attached graph.
Based on the given proof that the triangles are congruent
Answer:
They are congruent by SAS:
Side: AB = CB
Angle: ∠ABD = ∠CBD
Side: BD = BD
Explanation:
Two triangles are congruent if they have the same interior angles and the same length of their corresponding sides.
If two of the angles are equal, we can say that all the interior angles are equal.
So, based on the given information we get:
1. AC ⊥ BD means that AC is perpendicular to BD, therefore,
∠ADB = ∠CDB = 90°
2. It is given that ∠A = ∠C
3. Since both of their interior angles are equal, we can say that all the interior angles are equal and:
∠ABD = ∠CBD
4. The triangle ABC is isosceles because two of their interior angles are equal, therefore AB = CB
5. BD = BD because it is the same segment.
6. By SAS (Side-angle-Side) we can say that ΔABD = ΔCBD
Because the side AB is equal to side CB, the angle ABD is equal to angle CBD, and the side BD is equal to itself.
Cindy struck out 7, 14, 6, 4, 5, and 6 batters in softball games this season. In discussingher stats with a newspaper reporter, Cindy's coach mentions that the average number ofCindy's strikeouts is 7. Is the coach's statement misleading? Explain why or why not.O No; the mean of her strikeouts is 7.O None of the other answers are correctO Yes, she struck out 7 batters only one time.O No; she typically strikes out 7 batters in a game.O Yes; the median of her strikeouts is 7.
Given that the batters were 7, 14,6,4,5 and 6 then to find the average, you add the batters and divide by their number
[tex]\text{sum}=7+14+6+4+5+6=42[/tex][tex]\text{Average}=\frac{42}{6}=7[/tex]Here you notice that the average is 7, so the coach's statement is true.
Your answer is , No;the mean of her strikeouts is 7
Which of the following are solutions to the equation below?Check all that apply.x-5x+ 1 = 0A. x =5+29B. x = 5 - 292.C. x= 5+ V212D. x= -1 - 212E. x = =*+,x21F. x =5 - 2152
It is calculated using the quadratic formula
[tex]x\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In the equation
[tex]x^2-5x+1=0[/tex]a = 1, b = -5 and c = 1
Substitute the given to the quadratic formula
[tex]\begin{gathered} x\text{ = }\frac{5+\sqrt[]{21}}{2} \\ x\text{ = }\frac{5-\sqrt[]{21}}{2} \end{gathered}[/tex]Finding the final amount in a word problem on compound interest
Remember that the formula to calculate the total amount in an account with compoud interest is:
[tex]P(1+r)^n[/tex]Where:
• P, is the principal (amount incially invested)
,• r ,is the rate of interest
,• n, is the times that the interest is compounded
Using this and the data given we'll get:
[tex]2000(1+\frac{4.8}{100})^9=3049.87[/tex]Thereby, we can conclude that the accounts balance after 9 years is $3,049.87
Which of the following is a disadvantage of using a check casher, compared to a bank?
Responses
You wait longer to get your money at a check casher than at a bank
You wait longer to get your money at a check casher than at a bank
You pay a higher fee to cash checks at a check casher than at a bank
You pay a higher fee to cash checks at a check casher than at a bank
You can only cash checks worth more than $500 at a check casher
You can only cash checks worth more than $500 at a check casher
You can cash fewer checks at a check casher than at a bank
The main disadvantage of using a check cashier is that, 'You pay a higher fee to cash checks at a check casher than at a bank'
Check casher;
A check casher is someone who works in the check-cashing industry, with the exception of someone who doesn't cash checks for others on any one day that total more than $1,000 in cash, money, or other assets.
Disadvantage of Check cashers;
Fees for cash checking services can be as low as $1 or as much as 2% of the check amount depending on where you are. These costs reduce one's capacity to make ends meet or have extra money available. Always be aware of the prices and fees before using a check cashing service.
That is,
The main disadvantage of using a check cashier is that, 'You pay a higher fee to cash checks at a check casher than at a bank'
Learn more about check casher here;
https://brainly.com/question/16520246
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2g + (g + 5) >= 6g - 10 whats the solution set?
Answer: g ≤ 5
Step-by-step explanation: 2g + (g + 5) >= 6g - 10 ⇒ g ≤ 5
PLEASE HELP ME ASAP!!!
Answer:
1256
Step-by-step explanation:
A=3.14*20^2
=400*3.14
=1256
(6) If the store likes to keep 30 tiles in stock at all times how many bundles do they need to order now, after selling the 150 tiles to the customer? Think about how many you had left over from the customer when ordered 150 tiles.
function:
number of tiles: 12b+38
Where;
b=number of bundles
150+30 = 12b+38
Solve for b:
150+30 = 12b+38
180 = 12b+38
180-38 =12b
142 =12b
142/12 =b
11.8 =b
12 bundles