Using concept of Linear equations, we find $40 is the daily fee for renting a moving truck.
Linear equations are generally equations of the first order. The linear equations are defined for the lines in the coordinate system. When the equation having a homogeneous variable of degree 1 (i.e. only one variable), then it is called as a linear equation in one variable. A linear equation can have more than one variables. If the linear equation has two variables, then it is known as linear equations in two variables and so on. Some of the examples of linear equations which are listed here 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.
So, lets suppose daily fee for renting a movie a truck is $x
Then according to question,
Daily fee+ total distance travelled × charge per mile=total cost
=>x+48×0.50=64
On solving x, we get x=40
Hence, daily fee cost is $40 which is required for renting a moving truck.
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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.
462 people get on an empty train at a station. At the first stop, 234 more people get on the train, and 95 people get off. There are no more stops until the train reaches it final destination, where everybody gets off the train. How many people get off the train at the final destination?
Answer:
wow your so goood
Step-by-step explanation:
Select the correct answer.
Which of the following represents a function?
B. {(0,1), (3,2), (-8,3), (-7,2), (3,4)}
C. x -5 -1 9 8 -1
y 1 7 23 17 1
The relation which represents a function is the mapping diagram.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value).
In this scenario, the same x-value of the given ordered pairs (3, 2) and (3, 4) have the different output variable (y-value) and as such does not represent a function. Similarly, the table of values has the same x-value (-1) which outputs different numerical values.
Based on the ordered pairs and table shown above, we can reasonably and logically deduce that it is only the mapping diagram that represents a function.
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Zach submitted the work shown below when trying to simplify the expression 3 + 2(2x - 4) what mistake did he make and what is the correct simplified expression with correct steps
Answer:
The number “2” that is a outside the brackets multiplies both of the numbers inside the brackets.
Step-by-step explanation:
3+2(2x-4)
3+4x-8
4x-5
Select the correct answer. A circle with center O (0,0) has point B (4,5) on its circumference, which is joined by a line to O. What is the general form of the equation for the given circle centered at O(0, 0)? A. x2 + y2 + 41 = 0 B. x2 + y2 − 41 = 0 C. x2 + y2 + x + y − 41 = 0 D. x2 + y2 + x − y − 41 = 0
The general form of the equation: x2 + y2 − 41 = 0
The Correct option is (B).
Given,
A circle with center O (0,0) has point B (4,5) on its circumference
To find the what is the general form of the equation for the given circle centered at O(0, 0).
Now, According to the question:
How do you find the equation of a circle with center (0,0)?
x2 + y2 = r2 , and this is the equation of a circle of radius r whose center is the origin O(0, 0). The equation of a circle of radius r and center the origin is x2 + y2 = r2 .
The general form of the equation:
x2 + y2 − 41 = 0
Hence, The general form of the equation: x2 + y2 − 41 = 0
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after 4 years what is a total amount of a compound interest investment of $30,000 at 2% interest compounded monthly?round to the nearest cent
Compound interest formula:
A = P (1+r/n)^nt
Where:
A = total amount
P = principal investment
r= interest rate in decimal form = 2/100 = 0.02
t= years
n= number of compounding periods in a year= 12
Replacing:
A = 30,000 (1+0.02/12)^4x12
A = 30,000 (1.001666667)^48
A= 32,496.45
(No need to graph unless want to)Determine the period and asymptotes please grade 12 trig
SOLUTION:
The parent function is;
[tex]f(x)=sec(x)[/tex]The transformation applied is;
[tex]y=-2f(\frac{1}{4}x-\pi)+2[/tex]Graphing this, we have;
The period is the time to complete a cycle .
From the graph, the period is;
[tex]8\pi[/tex]The asymptotes are those lines for which sec x is undefined. those are lines where;
[tex][/tex]Hi,Hope you could help me with the attached question. Thanks!A random sample of 380 married couples found that 298 had two or more personality preferences in common. In another random sample of 574 married couples, it was found that only 36 had no preferences in common. Let p1 be the population proportion of all married couples who have two or more personality preferences in common. Let p2 be the population proportion of all married couples who have no personality preferences in common.
We were given that:
For P
For the figure below, give the following
Answer:
Step-by-step explanation:
B
Salesman A gets paid $300 a month plus $8 for every sale he makes. Salesman B gets paid $1500 a mont. Write and equation and solve to see how many salesman a must make in order to make the same amount of salesman b
The salesman A must make 150 order to make the same amount of salesman B .
In the question ,
it is given that ,
Salesman A gets paid $300 per month
for every sale salesman A get $8 .
let the number of sales made by salesman A be "x" .
So, amount made by salesman A = 300 + 8x
Salesman B earns per month = $1500 .
To make the amount earned by both the salesman same ,
300 + 8x = 1500
8x = 1500 - 300
8x = 1200
x = 1200/8
x = 150
Therefore , The salesman A must make 150 order to make the same amount of salesman B .
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help on both problems
Answer:
114 cm^2; x = 6: it is not possible because the lengths of the sides when solved are not the right size. x - 1 is bigger than 2x - 4 in the picture but in reality it is not. it doesnt make sense
Step-by-step explanation:
for the first one the area of a trapezoid is [tex]\frac{1}{2} h(b_{1} +b_{2})[/tex]
so
first find the height of the triangle
8^2 + h^2 = 10^2
64 + h^2 = 100
h^2 = 36
h = 6
so
the height is 6
now plug it in
[tex]\frac{1}{2} * 6 (25 + 13)[/tex]
[tex]\frac{1}{2} * 6(38)[/tex]
114 cm is the first answer
for the second one you can add all of them together and set them equal to 27
x - 1 + 2x - 4 + 3x - 4 = 27
6x - 9 = 27
6x = 36
x = 6
that is the second answer
it is not possible because the lengths of the sides when solved are not the right size. x - 1 is bigger than 2x - 4 in the picture but in reality it is not. it doesnt make sense
hellp please ?????????????
Answer:
see explanation
Step-by-step explanation:
since the dilatation is centred at the origin , then multiply each of the original coordinates by the scale factor of 2
Q (2, 2 ) → Q' (2(2), 2(2) ) → Q' (4, 4 )
P (0, 0 ) → P' (2(0), 2(0) ) → P' (0, 0 )
R (- 2, - 4 ) → R' (2(- 2), 2(- 4) ) → R' (- 4, - 8 )
S (4, - 2 ) → S' (2(4), 2(- 2) ) → S' (8, - 4 )
How many square mega meters are in 9,000,000 square kilometers?
Answer:
9 square megameters
Explanation:
Given:
[tex]\begin{gathered} 1.0\times10^6\text{ square kilometers}=1\text{ square megameter} \\ \implies1\text{ square kilometers}=\frac{1}{1.0\times10^6}\text{ square megameter} \end{gathered}[/tex]We want to find out how many square megameters are in 9,000,000 square kilometers.
Multiply both sides of the equation by 9,000,000.
[tex]\begin{gathered} 1\times9,000,000\text{ square km}=\frac{9,000,000}{1.0\times10^6}\text{ square megameter} \\ \implies9,000,000\text{ square km}=9\text{ square megameter} \end{gathered}[/tex]There are 9 square megameters in 9,000,000 square kilometers.
Monica deposits $200 into a savings account that pays a simple interest rate of 4.4%. Paul deposits $300 into a savings account that pays a simple interest rate of 3.3%. Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she correct? Justify your response.
Formula of simple interest rate:
[tex]S\mathrm{}I=\frac{P\times R\times T}{100}[/tex]Where,
[tex]\begin{gathered} P=\text{ Principal} \\ R=\text{ Rate} \\ T=\text{ Time} \end{gathered}[/tex]For Monica interest rate is:
[tex]\begin{gathered} S\mathrm{}I\mathrm{}=\frac{200\times4.4\times1}{100} \\ =8.8 \end{gathered}[/tex]For Paul interest rate is:
[tex]\begin{gathered} S\mathrm{}I\mathrm{}=\frac{300\times3.3\times1}{100} \\ =3\times3.3 \\ =9.9 \end{gathered}[/tex]No, Paul interest rate higher then Monic.
Hi I just need Part A. I’m in high school calculus 1 and this is a homework. thank you !
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define what happens when a function is shrunk vertically
When the factor is greater than 1, the condition that satisfies the function is to multiply by 1.4
When the graph is verticcally shrunk, this means that the function is multiplied by 1.4
Hence, the function becomes:
[tex]1.4\times f(x)=1.4\cdot f(x)[/tex]STEP 2: Define what happens when the graph is shifted left by 3 units.
If the function is shifted left by 3 units, this implies that we add 3 units to the x of the function.
This gives:
[tex]1.4.f(x+3)[/tex]the length of a rectangle is 5 meters less twice it’s width. if the perimeter of the rectangular is 38 meters, then what is the value of the length
The length has a value of 9 meters
How to determine the length of the rectangle?From the question, we have the following parameters that can be used in our computation:
Length = 5 meters less twice it’s width
This means that
Length = 2Width - 5
The perimeter is given as
Perimeter = 38 meters
The perimeter is calculated as
Perimeter = 2 x (Length + Width)
So, we have
2 x (2Width - 5 + Width) = 38
Divide by 2
2Width - 5 + Width = 19
This gives
3Width= 21
Divide
Width - 7
Recall that Length = 2Width - 5
So, we have
Length = 2 * 7 - 5
Evaluate
Length = 9
Hence, the length is 9 meters
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Sally can paint a room in 4 hours while it takes Steve 3 hours to paint the same room. How long would it take them to paint the room if they worked together?
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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Use the Exemption amounts in Figure 2.2 on page 132 to find the
(a) amount for exemptions and (b) annual state income taxes.
11. Jeff Falls, a heating system
salesman, is single with 3
dependents. He earns $57,900
annually, and his state's tax rate
is 3%.
13. Rick Delgado earns $43,500
annually as an automobile
mechanic. He is married but
has no dependents. The state
tax rate is 4.6%.
12. Sara Moon is a video editor
who earns $63,840 annually.
She is married, has 2 dependents,
and her state tax rate is 4%.
14. Julie Bookwalter is single,
claims 1 dependent, and
earns $32,300 annually. The
state tax rate is 2.5%.
11. The amount he pays in annual state income tax is $1,497.
13. The amount that will be paid for tax will be $2000.
14. The amount he pays in annual state income tax is $707.50.
How to estimate the annual state income tax?11. Given;
Annual earnings = $57,900
State tax rate = 3%
Amount earned in exemption = $8,000
Taxable Income = Annual Income - Exemptions
Igor's taxable income = $57,900 - $8,000 = $49,900
Taxable Income × Tax rate = Amount paid as tax
The amount he pays is therefore; $49,900 × 3% = $1,497
13. The amount that will be paid as tax will be:
= 4.6% × $43500
= $2000
Therefore, the amount is $2000.
12. a) We can see that the exemptions for a married person are $4000 and $2000 per dependent. Since there are 2 dependents, therefore:
Amount for exemptions = $4000 + (2 dependents × $2000 per dependent)
Amount for exemptions = $4000 + $4000 = $8000
Amount for exemptions = $8000
b) Taxable wages = Annual gross pay - Exemptions
Taxable wages = $63840 - $8000 = $55840
Annual state income taxes = Taxable wages × State tax rate
Annual state income taxes = $55840 × 4% = $2233.6
14. The amount he pays in annual state income tax is $707.50.
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Identify the range of the function.
A [-4,0]
B (-4,0)
C [-3,1]
D (-3,1)
Answer: [-4, 0] which is choice A
=====================================================
Reason:
lowest point is when y = -4
highest point is when y = 0
The range is any value of y between these values, including the endpoints themselves. We say the range is [tex]-4 \le y \le 0[/tex] which condenses to the interval notation [-4, 0]
Use square brackets to include the endpoints.
If there were open holes at the highest and lowest points, then we would use curved parenthesis instead.
Select the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other.
BRO HELP ITS DUE TMRW WILL GIVE BRAINLIEST AND POINTS
Considering the given figure, the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other is: In parallelogram EFGH show EK is congruent to KG and F.K is congruent to KH
How to determine the correct rephrase of the proof about parallelogram diagonalsThe diagonals refer to the lines running between the two opposite ends of the parallelogram
Bisecting means sharing into two equal parts
congruent means a copy that is equal in dimension hence can be used in place of the other image
The diagonals of a parallelogram bisect each other means that the diagonals cut each other to form two equal parts such that each part is congruent to each other.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answer:
Well your answer is down below
Step-by-step explanation:
First as a Inequality −3(2x−5)<5(2−x)
Step 1: Simplify both sides of the inequality.
−6x+15<−5x+10
Step 2: Add 5x to both sides.
−6x+15+5x<−5x+10+5x
−x+15<10
Step 3: Subtract 15 from both sides.
−x+15−15<10−15
−x<−5
Step 4: Divide both sides by -1.
−x−1<−5−1 x>5
So your answer is x>5
hope this helps
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I will give 100 points!!
New Orleans is 2 feet about sea level, salton city has an elevation that is lower then New Orleans. What is a possible elevation in feet of salton city.
(Please give explanation!!)
Answer:
Salton City could have an elevation less than -2 or greater than 2 (depends on what u meant.
Step-by-step explanation:
Usually when u talk abt elevation, when it is lower than sea level, you write it with a negative sign. If you meant that new Orleans is 2 feet below sea level, the Salton City elevation could be anything less than -2. If you meant 2 feet above sea level, the New Orleans elevation could be anything above 2.
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CAN U PLSSSSSS HELP ME WITH THIS PROBLEM????
5. How many ways are there to distribute 10 indistinguishable candies among 4 different
children? Children may end up with no candies.
5/7 of the teaching staff in a certain primary school are females, what fraction of the staff are males
Answer: 2/7
Step-by-step explanation:
Substract 7/7 AKA the whole, by 5/7 tp get 2/7
2/7 is the fraction of males.
change from radical form to exponential expression in fractional form. No need to evaluate just be put in simplest form
To convert from radical form to exponential in fractional form, we can follow:
[tex]\sqrt[m]{b^n}=b^{\frac{n}{m}}[/tex]Firstly, notice that 9 is the same as 3 squared:
[tex]\sqrt[4x+2]{9}=\sqrt[4x+2]{3^2}[/tex]Now, we can apply the change:
[tex]\sqrt[4x+2]{3^2}=3^{\frac{2}{4x+2}}[/tex]Also, notice that we can factor out the 2 on the denominator to cancel with the two on the numerator:
[tex]3^{\frac{2}{4x+2}}=3^{\frac{2}{2(2x+1)}}=3^{\frac{1}{2x+1}}[/tex]So, the expression in the simples form and fractional exponent is:
[tex]3^{\frac{1}{2x+1}}[/tex]214 ÷ 9 = ___.
Twenty-three and two-ninths
Twenty-three and five-ninths
Twenty-three and seven-ninths
24
Answer:
Twenty-three and seven-ninths
Step-by-step explanation:
Might not be correct I don't really remember how to do this
Is the following statements true or false?
Answer: False
Step-by-step explanation: The two lines do not overlap so they do not intercept.
A square has side length of 7.3 in. If the area is multiplied by 1/9, what happens to the perimeter. Please help!
Note that if the area of any figure is multiplied by a factor of a.
The perimeter will be multiplied by √a
From the problem, the are of the square is multiplied by 1/9, so we need to get the square root of that factor to get the factor for the perimeter.
[tex]\sqrt[]{\frac{1}{9}}=\frac{1}{3}[/tex]Therefore, the answer is C. multiplied by 1/3
Inequalities in Two Triangles.
[?] < x < [ ]
I will mark the answer as brainliest, thanks!
The inequality of the two triangle are 32° < x < 68° and the range of the value x is defined as x ≥ 4.
Inequality:
Inequality means the relationship between two values that are not equal is defined by inequalities which means they are not equal.
Given,
Here we have the two triangles with some angle values.
Now, we need to find the inequality of these triangle.
To find the inequality of the triangle first we have to write down the values provided, they are,
77, 11x - 33, 68°, 32°
Through this we have identified that, the value of x is lies in between 68° and 32°.
So, it ca be written as,
32° < x < 68°
The next this is to use the triangle inequality theorem, that is,
"The sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c."
Therefore, based on the given equation we have written it as,
11x - 33 ≥ 77
Subtract 33 on both sides then we get,
11x ≥ 44
Therefore, x ≥ 4.
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Given m || n, find the value of x and y.
119°
to
yº
E
x+119°=180°(Co-interior angles are supplementary m || n)
[tex]x = 180 - 119 \\ x = 61[/tex]
y=119°(alternate angles are equal m ||n)
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