Answer:
Jane's rate is 21.25 mph.
Jack's rate is 41.25mph
Explanation:
Let x represent Jane's speed.
Jack's speed will be x+20.
Their combined speed is;
[tex]x+x+20=2x+20[/tex]After 4 hours, their combined distance covered is 250 miles;
[tex]\begin{gathered} 4(2x+20)=250 \\ 8x+80=250 \end{gathered}[/tex]solving for x;
[tex]\begin{gathered} 8x=250-80 \\ 8x=170 \\ x=\frac{170}{8} \\ x=21.25\text{ mph} \end{gathered}[/tex]Jane's rate is 21.25 mph.
Since jack's rate is 20 mph faster than Jane's rate.
Jack's rate is;
[tex]\begin{gathered} 21.25+20 \\ =41.25\text{mph} \end{gathered}[/tex]Jack's rate is 41.25mph
I already have the first part what is the value of x?
ANSWER
A) 540º
B) x = 121º
EXPLANATION
PART A
The sum of the interior angles of a polygon is:
[tex](n-2)\cdot180[/tex]Where n is the number of sides of the polygon.
This polygon has 5 sides, so the sum of its interior angles must be:
[tex](5-2)\cdot180=3\cdot180=540º[/tex]PART B
Now that we know the sum of the interior angles we can find x:
[tex]x+87+92+135+105=540[/tex]Solving for x:
[tex]\begin{gathered} x+419=540 \\ x=540-419 \\ x=121º \end{gathered}[/tex]Accurately sketch or graph: f(x) = x^4/4 - 2x^3/3 -x^2/2 + 2xon the interval [ -2.5, 2.3] using the graph paper provided.
Graphing the function f(x) over the interval [-2.5, 2.3], we have the following
x-intercepts
Judging on the graph, the x-intercept of the function f(x) are the following
[tex]x=-1.619\text{ and }x=0[/tex]critical points
Finding the first derivative and setting it to zero and solve for x to get the critical points in the interval [-2.5,2.3] we have
[tex]\begin{gathered} f\mleft(x\mright)=\frac{x^4}{4}-\frac{2x^3}{3}-\frac{x^2}{2}+2x \\ f^{\prime}\left(x\right)=x^3-2x^2-x+2 \\ \\ x^3-2x^2-x+2=0 \\ \left(x−2\right)\left(x+1\right)\left(x−1\right)=0 \end{gathered}[/tex]Therefore, the critical points are x = 2, x = 1, x = -1.
relative minimums
Basing on the graph our relative minimum is at x = -1, and x = 2
asymptotes
Since the given function is a polynomial function, the function has no asymptotes
critical numbers
same as critical points with x = 2, x = 1, and x = -1.
relative maximum
observing the graph, the relative maximum of the function is at x = 1.
inflection points
get the second derivative of the function and set it to zero
[tex]\begin{gathered} f^{\prime}\left(x\right)=x^3-2x^2-x+2 \\ f^{\prime}^{\prime}\left(x\right)=3x^2-4x-1 \\ 3x^2-4x-1=0 \end{gathered}[/tex]Using the quadratic formula we have the values at
[tex]x=\frac{2}{3}\pm\sqrt{\frac{7}{3}}[/tex]end behavior
Since the function is a polynomial with a degree of 4, and a positive leading coefficient, the end behavior of the function is increasing in both approaching to -2.5, and 2.3.
PLEASE HELP FAST! The function f (t) = 450(0.945)t/30 šo represents the change in a quantity over t months. What does the constant 0.945 reveal about the rate of change of the quantity?
It shows that the the quantity is smaller than the time (In proportion).
A baseball diamond is square. The distance from home plate to first base is 90 feet. In feet, what is the distance from home plate to second base?
Options: 127, 81, 19, 13
The distance from home plate to second base is 90[tex]\sqrt{2}[/tex] ≈ 127.3 feet so option 1 is correct.
Given :
A baseball diamond is square.
The distance from home plate to first base is 90 feet which is nothing but side of square.
Let x be the distance from home plate to second plate.
we need to find home plate to second plate distance which is nothing but diagonal of square.
with 2 sides of length 90 feet and one diagonal forms a right angled triangle.
According to pythagorean theory:
[tex]90^{2}[/tex] + [tex]90^{2}[/tex] = [tex]X^{2}[/tex]
[tex]X^{2}[/tex] = 8100 + 8100
[tex]X^{2}[/tex] = 16200
[tex]X^{}[/tex] = 90*[tex]\sqrt{2}[/tex] ≈ 127.3 feet
Therefore the distance from home plate to second base is 90[tex]\sqrt{2}[/tex] ≈ 127.3 feet so option 1 is correct.
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solve the equation b. 3(x + 8) = 21
given that 3(x+8)=12
on multiplying 3 into(x+8) we get
3x+24=21
3x=21-24
x=-3/3
x=-1
According to the provided equation
3x + 24 = 21
3x = 21 - 24
3x = -3
x = -3/3
x = -1
Excuse the quality of my picture. I am trying to find which piecewise functions are represented by this graph.
Let's begin with the line that goes from minus infinity to zero
the equation of this line is
[tex]y=x+2[/tex]because of the filled circle we know that this interval touch the zero
[tex](-\infty,0\rbrack[/tex]in inequality, this will be
[tex]x\le0[/tex]then for the line that is between 0 and 2, we have a filled circle in the number two therefore we can touch this number
the interval will be
[tex](0,2\rbrack[/tex]in inequality notation
[tex]0 for the line that starts in 2 we have an emptythe interval
[tex](2,\infty)[/tex]in inequality notation
[tex]x>2[/tex]Therefore the piecewise function i
[tex]f(x)=f(x)=\begin{cases}x+2,ifx\le0 \\ \frac{x}{3}+1,if02\end{cases}[/tex]the correct option is the second one
Describe one possible way to estimate (without paper pencil and calculator) the value of 0.99804 x 32.785
One way of estimating this product is rounding each number to the nearest tenth first:
[tex]\begin{gathered} 0.99804=1.0\\ \\ 32.785=32.8 \end{gathered}[/tex]Then, the product of 32.8 and 1 is equal to 32.8, because every number multiplied by 1 is equal to itself.
Also, since the number 0.99804 is very close to 1, we can just keep the second value of the product, so the estimated result would be 32.785.
To install an outdoor swimming pool will cost you £800 in England. how much will it cost you to install a swimming pool of the same capacity in South African Rand?
Answer:
It would cost you approximately R15836.13
Which expression will produce an answer with the fewest significant figures?A. 15.4 - 8.1B. 4350 - 2210C. 18.8 - 6.5D. 54.5 * 30.7
we have following:
[tex]\begin{gathered} 15.4-8.1=7.3\cong7\rightarrow2sf \\ 4350-2210=2140\rightarrow3sf \\ 18.8-6.5=12.3\cong12\rightarrow3sf \\ 54.5\cdot30.7=1673.15\cong1670\rightarrow3sf \end{gathered}[/tex]therfore, the answer is the option A.
The length of each edge of a cube is x centimeters. If xis an integer, why is the volume of the cube not equal to 15 cmº? show work please i want to understand:)
Apparently, there is a typing mistake in the statement of the question:
The length of each edge of a cube is x centimeters. If xis an integer, why is the volume of the cube not equal to 15 cm squared? show work please i want to understand:)
The answer is:
Because the units of volume are cm^3, or m^3, not cm^2 nor m^2.
The measure of the volume is cm * cm * cm, meanwhile the area is cm * cm.
Student became unresponsive.
The graph of the function f(x) = –(x + 3)(x – 1) is shown below. On a coordinate plane, a parabola opens down. It goes through (negative 3, 0), has a vertex at (negative 1, 4), and goes through (1, 0).Which statement about the function is true?The function is positive for all real values of x wherex < –1.The function is negative for all real values of x wherex < –3 and where x > 1.The function is positive for all real values of x wherex > 0.The function is negative for all real values of x wherex < –3 or x > –1.
The graph of the function is shown below:
From it we notice that the function is positive in the interval (-3,1) and negative otherwise. With this in mind we conclude that the true statement is:
The function is negative for all real values of x where x < –3 and where x > 1.
What is the range of the given function?{(-2, 0), (-4, -3), (2, -9), (0, 5), (-5, 7)}{x|x=-5, -4, -2, 0, 2}{y | y=-9, -3, 0, 5, 7}{x|x=-9, -5, -4, -3, -2, 0, 2, 5, 7}{y|y=-9, -5, -4, -3, -2, 0, 2, 5, 7}
The range of a function is the set of all possible y-values the function takes.
We have the function:
[tex]\left\{\left(-2,0\right),(-4,-3),(2,-9),(0,5),(-5,7)\right\}[/tex]Then, the range is:
[tex]Ran={}\lbrace y|y=-9,-3,0,5,7\rbrace[/tex]Answer:B
Step-by-step explanation:
cuz it is
which could be a graph of y=ax^4 + bx^3 + cx^2 + dx + e where a,b,c,d and e are real numbers not equal to 0 and a<0?
y=ax^4 + bx^3 + cx^2 + dx + e
Since a< 0 we know that it has to go to - infinity for x going to - infinity and x going to + infinity. That rules out choices B and C.
The maximum number of turning points a polynomial can have is n-1 where n is the degree of the polynomial
(turning points is change of direction)
The graph D has 5 turning points and the degree of the polynomial is 4 so it is not possible
A is your solution.
find all the zerosf(x)=16x^5-72x^4+137x^3+43x^2-244x+120
For f(1), the given polynomial function f(x) = 16x⁵ - 72x⁴ + 137x³ + 43x² - 244x + 120 is zero.
Given,
The polynomial function;
f(x) = 16x⁵ - 72x⁴ + 137x³ + 43x² - 244x + 120
We have to all the zeros .
Here,
We can use Rational zero theorem;
That is,
f(x) = 16x⁵ - 72x⁴ + 137x³ + 43x² - 244x + 120
Find p/q
Where, p is 16x⁵ - 72x⁴ + 137x³ + 43x² - 244x + 120 and q is 16
So,
p/q = (±16, ±72, ±137, ±43, ±244, ±120) / ±16
= ±1, ±4.6875. ±8.5625, ±2.6875, ±15.25, ±7.5
Now,
f(1) = 1 × 1⁵ - 4.6875 × 1⁴ + 8.5625 × 1³ + 2.6875 × 1² - 15.25 × 1 + 7.5
f(1) = 1 - 4.6875 + 8.5625 + 2.6875 - 15.25 + 7.5
f(1) = 0
That is,
For f(1), the given polynomial function f(x) = 16x⁵ - 72x⁴ + 137x³ + 43x² - 244x + 120 is zero.
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Find the equation of the line through (7,2) which is parallel to the line y=-3x-2
The general slope-intercept form of the line: y = m * x + b
The parallel lines have the same slope
Given the equation of the line: y= -3x - 2
the slope of the given line = -3
The required line is parallel to the given line
So, the slope of the required line = m = -3
The equation of the line will be: y = -3x + b
The required line passes through the point (7, 2)
So, when x = 7, y = 2
We will find the value of b as follows:
[tex]\begin{gathered} 2=-3\cdot7+b \\ 2=-21+b \\ b=2+21=23 \end{gathered}[/tex]So, the answer will be the equation of the line is:
[tex]y=-3x+23[/tex]A textbook store sold a combined total of 260 chemistry and physics textbooks in a week. The number of chemistry books sold was three times the number of physics textbooks sold. How many textbooks of each type were sold?
Let:
x = Chemistry textbooks sold
y = Physics textbooks sold
The textbook store sold a combined total of 260, so:
[tex]x+y=260[/tex]The number of chemistry books sold was three times the number of physics textbooks sold, so:
[tex]x=3y[/tex]Let:
[tex]\begin{gathered} x+y=260_{\text{ }}(1) \\ x=3y_{\text{ }}(2) \end{gathered}[/tex]Replace (2) into (1):
[tex]\begin{gathered} 3y+y=260 \\ 4y=260 \\ y=\frac{260}{4} \\ y=65 \end{gathered}[/tex]Replace the value of y into (2):
[tex]\begin{gathered} x=3(65) \\ x=195 \end{gathered}[/tex]If 1/2 cup of water fills 2/3 of a plastic container, how many containers will 1 cup full?
1 cup will fills double than 1/2 cup, so:
[tex]\frac{2}{3}\cdot2=\frac{4}{3}[/tex]With 1 cup you will be able to fills 4/3, in other words 1 full container and 1/3 of another.
I don’t know how to solve for eI already solved everything else, I just need to know how to write an equation for f(x)=___ using my answers from questions c & d
e)
1) Since we know the slope, and the y-intercept from the previous items we can tell the function's rule is:
[tex]f(x)=\frac{1}{2}x+13[/tex]Note that the slope tells us how steep is the line, and the b-coefficient is 13.
2) And that is the answer.
Put the following equation of a line into slope-intercept form, simplifying allfractions.4x + 10y = –20
Given the equation of the line:
[tex]4x+10y=-20[/tex]The general slope - intercept form is :
[tex]y=m\cdot x+b[/tex]Where: m is the slope and b is y - intercept
So, we will transform the given equation to the slope - intercept form as following:
[tex]\begin{gathered} 4x+10y=-20 \\ \\ 10y=-4x-20 \end{gathered}[/tex]Divide both sides by ( 10):
[tex]\begin{gathered} \frac{10y}{10}=\frac{-4x-20}{10} \\ \\ y=-\frac{4}{10}x-\frac{20}{10} \\ \\ y=-\frac{2}{5}x-2 \end{gathered}[/tex]So, the slope - intercept form of the given equation is :
[tex]y=-\frac{2}{5}x-2[/tex]Question 1 (1 point) page 6 #1 Match each spinner with its likelihood to land on black. Column A Column B 1. impossible a 2. unlikely 3. equally likely 4. likely 5. certain b. - o Type here to search
Answer:
1.......c
2.....a
3.....b
4......e
5.....d
Because of the size of the black section,
rewrite the following as an exponential expression in simplest form
The given expression is,
[tex]^5\sqrt[]{\sqrt[]{x}}[/tex]It can be written in exponential terms as,
[tex]\begin{gathered} ^5\sqrt[]{x^{\frac{1}{2}}} \\ =(x^{\frac{1}{2}^{}})^{\frac{1}{5}} \\ =x^{\frac{1}{2}\ast\frac{1}{5}^{}}^{} \\ =x^{\frac{1}{10}} \end{gathered}[/tex]Therefore, the simplest exponential form of the given expression is,
[tex]x^{\frac{1}{10}}[/tex]Find the distance between the pair of points,(9, 3), (9,7)Set up the problem here:
We are given the following two points.
[tex]\mleft(9,3\mright)\: and\: (9,7)[/tex]Let us find the distance between these two points.
Recall that the distance formula is given by
[tex]undefined[/tex]Help me please ?
anyone ?
Mathematics .
The length of the midsegment of trapezoid ABCD is 6.23 units.
In this question, we have been given a trapezoid ABCD with vertices A(0,0), B(2, 5), C(3, 5) and D(8, 0)
We need to find the length of the midsegment of trapezoid.
We know that the length of the midsegment is one-half the sum of the lengths of the bases.
The length of base AB,
AB = √(2 - 0)² + (5 - 0)²
AB = √4 + 25
AB = √29
AB = 5.38
The length of base CD would be,
CD = √(8 - 3)² + (0 - 5)²
CD = √5² + (-5)²
CD = √25 + 25
CD = 5√2
So, the length of the midsegment would be,
l = 1/2[(5.38 + 5√2)]
l = 6.23
Therefore, the length of the midsegment of trapezoid ABCD is 6.23 units.
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A survey was conducted to find the possible relationship between age groups and the most favored of three book genres. The data is representedin the frequency table.MotivationalDo-It-YourselfTotalBiographies1101134026321-30 years31-40 years804421995· 10741-50 years9269268Total285153312750To the nearest tenth, what percentage of people were in the 41 – 50 age group and favored the Do-It-Yourself books?
The Solution.
The total number of people surveyed = 750.
The number of age group 41 - 50 that favored the Do-It-Yourself books = 69
The percentage of the people in age group 41 - 50, and favored the Do-It-Yourself books is calculated as below:
[tex]\frac{69}{750}\times100=9.2\approx9\text{ \%}[/tex]Hence, the correct answer is 9 percent.
In an inverse variation, y = 2 when x = 8. Write an inverse variation equation that showsthe relationship between x and y
The general equation for the inverse variation is,
[tex]\begin{gathered} y\propto\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}[/tex]Substitute the value of x and y in the equation to obtain the value of k.
[tex]\begin{gathered} 2=\frac{k}{8} \\ k=8\cdot2 \\ =16 \end{gathered}[/tex]Thus, relation between x and y is,
[tex]y=\frac{16}{x}[/tex]Simplify the expression. Express your answer as a power. 130^6/130^4
hi I need help with this question because my math teacher explains it very hardly for me to understand
The reflection image is as follows,
The remains of an ancient ball court include a rectangular playing alley with a perimeter of about 24m. The length of the alley is three times the width. Find the length and the width of the playing alley.The width is ? m and the length is ? m
ANSWER
Length of the playing alley = 9m
Width of the playing alley = 3m
STEP-BY-STEP EXPLANATION:
Given information
The perimeter of a rectangular playing alley = 24 m
The length of the alley is three times the width
Let l represents the length of the alley
Let w represents the width of the alley
Step 1: Write the formula for calculating the perimeter of a rectangle
[tex]\text{Perimeter of a rectangle = 2(l + w)}[/tex]Where l is the length and w is the width of the rectangle
Recall, length = 3 times the width of the alley
Mathematically,
[tex]\begin{gathered} l\text{ = 3 }\times\text{ w} \\ l\text{ = 3w} \end{gathered}[/tex]Step 2: Substitute the value of l = 3w into the above formula
[tex]\begin{gathered} P\text{ = 2(l + w)} \\ p\text{ = 24m} \\ l\text{ = 3w} \\ 24\text{ = 2(3w + w)} \end{gathered}[/tex]Step 3: Solve for w
[tex]\begin{gathered} 24\text{ = 2(4w)} \\ 24\text{ = 8w} \\ \text{Divide both sides by 8} \\ \frac{24}{8}\text{ = }\frac{8w}{8} \\ w\text{ = 3 m} \end{gathered}[/tex]From the calculations above, you will see that the width of the playing alley is 3m
Step 4: Solve for l
[tex]\begin{gathered} \text{Recall, l = 3w} \\ w\text{ = 3} \\ l\text{ = 3 }\times3 \\ l\text{ = 9m} \end{gathered}[/tex]Hence, the length of the playing alley is 9m
Solve each system by substitution.y = x + 5 4x + y = 201. Substitute the value of from the first equation into the second equation. 4x + = 20 2. Now solve for .3. Substitute the value of in one of the original equations. Solve for .4. Write your answer as an ordered pair .Solution: ( , )
1. Substitute the value of y from the first equation to the second equation
4x + x+5 = 20 (First fill in the blank)
2. Solve for x
4x + x + 5 = 20
5x + 5 = 20
5x = 20 - 5
5x = 15
5x/5 = 15/5
x = 3
3. Substitute x = 3 to the original equation
y = x+5
y = 3 + 5
y = 8
4. Therefore, the solution of the system of equation is (3,8) (second fill in the blank)
spent $95 buying 13 books to donate to the local elementary school. Activity books cost $5 each and story books cost $11 each, how many of each type of book did purchase?
Answer:
Number of Activity books = 8
Number of Storybooks = 5
Explanation:
Let x represent the number of activity books.
Let y represent the number of storybooks.
Let's go ahead and set up our equations as follows;
[tex]\begin{gathered} x+y=13\ldots\ldots\text{.}\mathrm{}\text{Equation 1} \\ 5x+11y=95\ldots\ldots\ldots\ldots\text{.Equation 2} \end{gathered}[/tex]From equation 1, we can see that x = 13 - y
Let's go ahead and substitute the value of x into equation 2 and solve for y;
[tex]\begin{gathered} 5(13-y)+11y=95 \\ 65-5y+11y=95 \\ 6y=30 \\ y=\frac{30}{6} \\ y=5 \end{gathered}[/tex]Since y = 5, let's substitute the value of y into equation 1 and solve for x;
[tex]\begin{gathered} x+5=13 \\ x=13-5 \\ x=8 \end{gathered}[/tex]