please help please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please
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part 1 of the question is asking us to evaluate expressions to the power of 2. To do that let's remember the following:
[tex]a^2=a\times a[/tex]Ther is, when a number is elevated to second power it means we have to multiply that number by itself. For example:
[tex]\begin{gathered} 1^2=1\times1=1 \\ 2^2=2\times2=4 \\ 3^2=3\times3=9 \end{gathered}[/tex]In the second part of this question, we are asked to evaluate the square root of a number. Let's remember that the square root is the inverse operation of elevating a number to the second power. That is if we have:
[tex]\sqrt[]{a}=b[/tex]it means:
[tex]b^2=b\times b=a[/tex]For example:
[tex]\begin{gathered} \sqrt[]{1}=1 \\ \sqrt[]{4}=2 \\ \sqrt[]{9}=3 \end{gathered}[/tex]The third part of the questions asks us to solve for "x" the following equation:
[tex]x^2=9[/tex]To do that we take square root on both sides:
[tex]\sqrt[]{x^2}=\sqrt[]{9}[/tex]Since the square root of a number to the second power is the same number and the square root of 9 is 3, we get:
[tex]x=3[/tex]Related Questions
A small square has an area of 40 inches squared. A large square has sides that are 8 times longer than the small square. What is the area of the large square?
Answers
Solution
Given that
Area f small square = 40 inches squared.
[tex]\begin{gathered} a=40 \\ \\ \text{ since a}=l^2 \\ \\ \Rightarrow40=l^2 \\ \\ \Rightarrow l=\sqrt{40} \end{gathered}[/tex]Let the side of the large square be L
Since the large square has sides that are 8 times longer than the small square
=> L = 8l
[tex]\begin{gathered} \Rightarrow L=8l \\ \\ \Rightarrow L=8(\sqrt{40}) \end{gathered}[/tex]Hence, the area of Large square is;
[tex]A=L^2=(8\sqrt{40})^2=64\times40=256[/tex]Hence, the area of the large square is: 256 inches squared.
A public storage company charges new customers an initial fee of $35.00. Each month of storage costs $18.75. The company uses the formula T = 35.00 + 18.75m to calculate the total charges, where T is the total charges, and m is the number of months of storage. How many months of storage would cost a new customer $260.00?
Answers
Answer:
12 months
Explanation:
Given the function that models the total chacrge of a company as T = 35.00 + 18.75m where;
T is the total charges,
m is the number of months of storage
Given
T = $260.00
we are to find the value of m
Substitute
260 = 35 + 18.75m
18.75m = 260 - 35
18.75m = 225
m = 225/18.75
m = 12
Hence it will take 12 months to cost a new custimer $260.00
P(x) = -0.3x² + 75x - 2000, where x represents the selling price.
1. At what price should the stands be sold to earn the maximum profit?
2. According to the function given, what is the maximum profit that the company can make?
3. What are the break-even points (the selling prices for which the profit is 0)? Give the answer to the nearest cent.
Answers
Answer:
Below in bold.
Step-by-step explanation:
P(x) = -0.3x² + 75x - 2000
Convert this to vertex form:
p(x) = -0.3(x^2 - 250)^2 - 2000
= -0.3[(x - 125)^2 - 125^2] - 2000
= -0.3[(x - 125)^2 - 15625] - 2000
= -0.3(x - 125)^2 + 4687.5 - 2000
= -0.3(x - 125)^2 + 2687.5
2687.5 is the maximum value of the profit.
1. This corresponds to a selling price of $125 for the stands.
2. Maximum profit is $2687.5.
3. At the breaking points P(x) = 0:
-0.3(x - 125)^2 + 2687.5 = 0
(x - 125)^2 = 2687.5 / -0.3 = 8958.33
x - 125 = +/- sqrt( 8958.33)
x = 125 +/- sqrt( 8958.33)
x = 30.352, 219.648,
So, the breaking even points are $30.35 and $219.65 to nearest cent.
Prealgebra- Write an equation of the line that passes through the points(Question in photo) (Can only attach one photo at time, so for graphing part of question, i will send the photo)
Answers
Given:
Point 1 → (-5, 0.6)
Point 2 → (5, -2.4)
Find: the equation of the line and its graph
Solution:
To help us determine the equation of the line passing through the given points, let's use the Two-Point Form formula.
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Let's plug into the formula above the coordinates of the two points.
[tex]y-0.6=\frac{-2.4-0.6}{5-(-5)}(x-(-5))[/tex]Then, solve.
[tex]y-0.6=\frac{-3}{10}(x+5)[/tex]Multiply -3/10 by the terms inside the parenthesis.
[tex]y-0.6=-\frac{3}{10}x-1.5[/tex]Add 0.6 on both sides of the equation.
[tex]y-0.6+0.6=-\frac{3}{10}x-1.5+0.6[/tex][tex]\begin{gathered} y=-\frac{3}{10}x-0.9 \\ or \\ y=-0.3x-0.9 \end{gathered}[/tex]Hence, the equation of the line passing through the given points in slope-intercept form is y = -0.3x - 0.9.
In the equation, the slope is -3/10 while the y-intercept is -0.9.
Since the slope is negative, the line must be leaning to the left. Since the y-intercept is -0.9, the line must cross the y-axis or the vertical line at -0.9. Hence, the graph of the equation is:
7+3(p-1)=64 how to solve
Answers
Answer:
p = 20
Step-by-step explanation:
7 + 3(p - 1) = 64 ( subtract 7 from both sides )
3(p - 1) = 57 ( divide both sides by 3 )
p - 1 = 19 ( add 1 to both sides )
p = 20
during an election, a group of 4 council members must be selected from a group of 18 people running for these positions. how many such selections are possible?
Answers
The possible number of ways of selection by using combination formula is 3060.
What is combination?
A grouping of items where the order in which they were chosen is irrelevant is known as combination.
Given that the number of people in the group is 18. Only 4 people will be member of the council.
The formula of combination is [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex] , where r number of objects are selected from n objects.
In the given question the value of n is 18 and the value of r is 2.
Substitute the value of n and r in [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex].
[tex]^{18}C_{4}=\frac{18!}{4!(18-4)!}[/tex]
Solve the above expression:
18^C_4 = 18x17x16x15x14/4x14
18^C_4 = 18x17x16x15/4x3x2x1
3060 18^C_4 = 3060
The number of ways such selection is 3060.
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The cost of entering a carnival and riding rides is given by the linear equation, c(r) = 1.25r + 6.00, where c(r) is the total cost of attending the carnival and r is the number of rides. the slope of the linear equation represents the response area .
Answers
Answer: Cost per rides
Step-by-step explanation:
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!
What is the standard form of the equation of a quadratic function with roots of 2 and −5 that passes through (1, −3)?
y = −0.5x2 + 1.5x − 5
y = −0.5x2 + 1.5x + 5
y = 0.5x2 + 1.5x − 5
y = 0.5x2 + 1.5x + 5
Answers
Answer:
y = 0.5x^2 + 1.5x − 5
Step-by-step explanation:
See attached graph
Please help ASAP starting to fall behind! This equation really confuses me and if someone could help that would be amazing!
Given the function:
f(x) = x² - 4x - 2
Find the following values.
a) f(2)
f(2)=
b) f(4)
f(4)=
c) f(-3)
f(-3)=
Answers
f(4) = 4^2 - 4*4 - 2 = 16 - 16 - 2 = -2
f(-3) = (-3)^2 - 4*-3 - 2 = 9 + 12 - 2 = 19
Dog food comes in two different sized bags. The 40 lb bag sells for $24 while the 10 lb
bag sells for $7. Which is cheaper and by how much? (compare unit rates)
Answers
Answer:
The 40 lb bag is cheaper by $4
Step-by-step explanation:
10 x 4 = 40
7 x 4 = 28
If you bought the 10 lb bag 4 times, you'd spend more money than just buying the 40 lb bag once.
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An elevator in a skyscraper rises 240 feet in 15 minute. What is the
elevator’s rate in feet per minute?
Answers
Answer:
Step-by-step explanation:
answer is 16
the vertex of the function shown below is located at?
Answers
Given the graph of the parabola
AS shown in the figure
The coordinate of the vertex is the point (2.5, 2.25)
so, the answer will be:
the vertex of the function shown below is located at (2.5, 2.25)
how many 1/5 inch pieces can be cut from a piece of ribbon 7/20 of an inch long.
Answers
1) Gathering the data
1/5 inch
7/20 inches long
2) Let's them divide, 7/20 by 1/5 inches
When divide fractions, we multiply the reciprocal of the second fraction
and if possible we can simplify
3. Jackson's soccer coach filled the teams' water container with 40 quarts of
water. Since 32 ounces equal 1 quart, how many times can a soccer player fill a
16-ounce water bottle before using all the water?
Answers
40 times 32 = 1280
40 quarts = 1280 ounces of water
1280 ounces of water divided by 16 ounce water bottle = 80 refills
find angle x giving your answer to one decimal place
Answers
⇒I will use the trig ratios to find the value x.
[tex]\frac{sin(x)}{11cm}=\frac{sin( 38)}{8} \\[/tex]
⇒Moving on solving I will use the cross multiplication
[tex]8sin(x)=11sin(38)\\sin(x)=\frac{11sin(38)}{8} \\x=sin^{-1} (\frac{11sin(38)}{8} )\\x=57,8[/tex]
∴ x=57,8°
Goodluck!!
How can you show two figures are congruent?
O Use the Third Angles Theorem.
O Use rigid transformations.
O Confirm they have the same symmetries.
Answers
If at least two sides and one angle of two triangles are similar, then the triangles are congruent.
What in mathematics is the congruent?
It is claimed that two figures are "congruent" if they can be positioned exactly over one another. Both the shape and size of the bread slices are same if you lay one slice on top of the other. Congruent refers to having precisely the same form and size.Use the Third Angles Theorem for two figures are congruent.
When two of a triangle's angles match up with two of another triangle's angles, the third angle must likewise match up.
If at least two sides and one angle of two triangles are similar, then the triangles are congruent.
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Given f(x) = -x - 2, find f(-6).
Answers
Answer:
f( -6) = 4
Step-by-step explanation:
f(x) = -x -2 You will replace x with -6
f(-6) - -(-6) -2
f(-6) = 6 - 2
f(-6) = 4
How is 6 divided by (-3) equals -2
Answers
Since a positive number divide or multiplies a negative number
Then the answer will be a negative number
So:
6 / -3 = -2
6 is a positive number and it's being divide by -3 which is a negative number
So the answer is -2
HELP ME PLEASE ASAP!!!
2. Use the space provide to respond to each statement concerning the given graph of a radical function.
a.) State the domain of the function.
b.) State the range of the function.
c.) Identify the end behavior of the function.
d.) Identify the y – intercept. Write as an ordered pair.
e.) Explain how you know this function is increasing?
Answers
Part a
The domain is the set of x-values, which is [tex](-\infty, \infty)[/tex].
Part b
The range is the set of y-values, which is [tex](-\infty, \infty)[/tex].
Part c
As [tex]x \to \infty[/tex], [tex]y \to \infty[/tex], and as [tex]x \to -\infty[/tex], [tex]y \to -\infty[/tex].
Part d
The y-intercept is when x=0, which is [tex](0, 1)[/tex].
Part e
The function is increasing when y increases as x increases, which is true for this function.
For the polynomial function f(x)=x^3 - 2x^2 - 5x + 6, we have f(0)=6, f(2) = -4, f(-2) = 0, f(3) = 0 , f(-1) = 8 , f(1) =0. Rewrite f(x) as a product of linear factors.
Answers
The given polynomial function f(x)=x^3 - 2x^2 - 5x + 6 as a product of linear factors as (x+2).(x-3).(x-1)
In the above question, a polynomial function is given
f(x)=x^3 - 2x^2 - 5x + 6
However, we know that, zero of a polynomial means all the x-values that bring a polynomial, p(x), to zero are referred to as its zeros, which means putting any value of x in the function we should get value of f(x) as zero
And, in the question, it is given as
f(0)=6, f(2) = -4, f(-2) = 0, f(3) = 0 , f(-1) = 8 , f(1) =0
We can clearly see that, f(-2) = 0, f(3) = 0, f(1) =0
=> (x+2), (x-3), (x-1) are the linear factors of the given polynomial
Hence, we can write the given polynomial function f(x)=x^3 - 2x^2 - 5x + 6 as a product of linear factors as (x+2).(x-3).(x-1)
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Point T is located at (2, 5). Point A is located at (-3, 1.5). Point A is the midpoint of segment TB.
Point B is the midpoint of segment TY. What are the coordinates of point Y?
Answers
Using the midpoint, the coordinates of point Y in the line segment TY is (-18, -9).
How to use midpoint to find coordinates?Point T is located at (2, 5). Point A is located at (-3, 1.5). Point A is the midpoint of segment TB.
Therefore, the mid point formula can be represented as follows:
(xₙ, yₙ) = (x₁ + x₂ / 2, y₁ + y₂ / 2)
Hence, let's find the coordinates of point B.
(-3, 1.5) = (2 + x₂ / 2 , 5 + y₂ / 2)
2 + x₂ / 2 = - 3
cross multiply
2 + x₂ = -6
x₂ = -6 -2
x₂ = - 8
1.5 = 5 + y₂ / 2
3 = 5 + y₂
y₂ = 3 - 5
y₂ = -2
Therefore, the coordinates of B is (-8, -2)
Hence, let's find the coordinate of point Y. The coordinates of point B is the mid point of segment TY.
(-8, -2) = (2 + x₂ / 2 , 5 + y₂ / 2)
(-8, -2) = (2 + x₂ / 2 , 5 + y₂ / 2)
2 + x₂ / 2 = - 8
-16 = 2 + x₂
x₂ = -18
-2 = 5 + y₂ / 2
-4 = 5 + y₂
-4 - 5 = y₂
y₂ = -9
Therefore, the coordinates of y is (-18, -9)
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PLEASE HELP ASAP GIVING 20
Answers
Answer:
I agree with your answer.
Step-by-step explanation:
What is (3 x 10^7) (3 x 10^8)?
Answers
[tex] = 3 \times 3 \times {10}^{7} \times 10^{8} \\ = 9 \times {10}^{7 + 8} \\ = 9 \times {10}^{15} \\ [/tex]
NOTE YOU CAN WRITE IT IN FULL BUT I CHOSE NOT TO BECAUSE IT'S LARGE .
GOODLUCK
HELPPppppp PLS AOUHF
Answers
As per the given three coordinate of the triangle, the area of the triangle is 9.5 square units.
Area of triangle:
In the triangle ABC as with vertices or coordinates are A(x1, y1), B(x2, y2), and C(x3, y3), has the area,
Area(ΔABC) = (1/2){x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)}
As the area is always positive.
Given,
Here we have the triangle VWX,
And their coordinates are V (-9,-7), W(-4,-5), and X(-6,-2).
Now we have to find the area of the triangle.
To find the area of the triangle, let us consider the coordinates (x1,y1) as v(-9,-7), (x2,y2) as W(-4,-5) and (x3,y3) as X(-6,-2).
Now, we have to apply the values on the formula, in order to get the area of the triangle,
=> A = 1/2 |(-9 [-5-(-2)] + (-4)[-2 - (-7)] + (-6)[-7 - (-5)]|
When we expand the terms, then we get,
=> A = 1/2 |(-9)[-3] + (-4)[5] + (-6)[-2]|
Further simplify the expression will gives you the following,
=> A = 1/2 |27 - 20 + 12|
=> A = 1/2 |19|
Therefore, the area of the triangle is 9.5 square units.
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Use the order of operations to find the value of the expression.12÷2*3-(7-5)O A.0O B.6O C.16O D.19
Answers
Given:
given expression is
[tex]12\div2\ast3-(7-5)[/tex]Find:
The main objective is to evaluate the expression.
Explanation:
we will use BoDMAS formula for evaluating the expression.
[tex]\begin{gathered} 12\div2\ast3-(7-5)=12\div2\ast3-2 \\ =6\ast3-2 \\ =18-2 \\ =16 \end{gathered}[/tex]Conclusion:
Therefore, correct option is C.16
the length and width of a rectangle are consecutive integers. the area of the rectangle is 210 square meters. find the length and width of the rectangle
Answers
The length and the width of the rectangle are 14 and 15 meters, respectively
How to determine the dimension of the rectangle?From the question, the statement is given as
Length and width are consecutive integers
Where
Area = 210 square feet
Represent the dimensions with x and y
Where Length = x and Width = y
And also, we have
y = x + 1
The area of a rectangle is
Area = Length x width
Mathematically, this can be represented as
Area = x * y
So, we have
x * y = 210
Substitute y = x + 1 in x * y = 210
x * (x + 1) = 210
Express 210 as 14 * 15
x * (x + 1) = 14 * 15
This means that
x = 14
Substitute x = 14 in y = x + 1
y = 14 + 1
Evaluate
y = 15
So, we have
x = 14 and y = 15
Hence, the length and the width are 14 and 15 meters
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10m +6 < 76 or -6 - 10m s≤ -86
Answers
Answer:
m < 7 or m ≥ 8Step-by-step explanation:
Given system10m + 6 < 76 or- 6 - 10m ≤ - 86Solve each inequality:
10m + 6 < 7610m < 76 - 610m < 70m < 7or
- 6 - 10m ≤ - 86- 10m ≤ - 86 + 6- 10m ≤ - 80m ≥ 8The answer is: m < 7 or m ≥ 8
8/13 x 3 =
SHOW YOUR WORKl
Answers
13 x 3 = 39
Answer: 24/39
8/13 x 3/1 = 24/13
24 - 13 =11
So, simplified answer is 1 11/13 or 24/13
Hope this helps!
3.21. a causal lti system has the following system function:(2(a) what is the roc for h(z)? (b) determine if the system is stable or not. (e) determine the difference equation that is satisfied by the input x[n) and the output yin. (d) use a partial fraction expansion to determine the impulse response h[n].
Answers
The ROC essentially specifies the parameters under which the system's impulse response, h(n), will converge.
What is meant by the roc for h(z)?When applying the z-transform on the sequence h, the ROC concept is applied to the function H(z) (n). The ROC essentially specifies the parameters under which the system's impulse response, h(n), will converge. Neither X(z), the input, nor Y(z), the output, are involved in the ROC.
The region (regions) where the z-transform converges is known as the region of convergence (ROC). We can uniquely determine the inverse z-transform thanks to ROC. Let's first think about some examples. The unit sample δ(n)has z-transform 1 , hence ROC exists all the z plane .
The Registrar of Companies assigns the company registration number, or CIN number as it is known in India (ROC). The Ministry of Corporate Affairs oversees the ROC, which is present in several Indian states. It is utilized to locate the essential information for every firm that is registered in India.
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Avery is in the business of manufacturing phones. She must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. The labor and materials cost $100 for each phone manufactured, and the total cost of producing 3 phones in a day would be $600. Write an equation for C, in terms of p, representing total cost, in dollars, of producing pp phones in a given day.
Answers
If Avery is in the business of manufacturing phones. The equation for C, in terms of p, representing total cost, in dollars, of producing pp phones in a given day is: 100p + 300.
Determining the equation for total costGiven data:
Labor and materials cost = $100
Numbers of phones = 3
Total cost = $600
Where,
P = Total cost
The equation for C in terms of p is:
100p + 300
Now let determine the total cost
Total cost = $600 + ( 3 × $100)
Total cost = $600 $300
Total cost =$600
Therefore 100p + 300 is the equation.
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