Answer:
1
Step-by-step explanation:
-2x^3 - 10y-7 evaluate if x = 4 and y = -9
We are given the following expression:
[tex]-2x^3-10y-7[/tex]We are asked to evaluate the expression in the following points:
[tex]\begin{gathered} x=4 \\ y=-9 \end{gathered}[/tex]To determine the value of the expression we will substitute the value in the expression like this;
[tex]-2(4)^3-10(-9)-7[/tex]Now, we solve the exponents:
[tex]-2(4)^3-10(-9)-7=-2(64)-10(-9)-7[/tex]Now, we solve the products:
[tex]-2(64)-10(-9)-7=-128+90-7[/tex]Solving the operations:
[tex]-128+90-7=-45[/tex]Therefore, the numerical value is -45
Let f(x)=V3x and g(x)=×6. What'sthe smallest number that is in the domain off° g?
Answer:
Explanation:
Given:
[tex]\begin{gathered} f(x)\text{ = }\sqrt{3x} \\ g(x)\text{ = x - 6} \end{gathered}[/tex]To find:
the domain of f o g
fog = (f o g)(x) = f(g(x))
First, we will substitute the expression in g(x) with x in f(x)
[tex][/tex]What is the median of the 19 numbersplotted in the line plot below?
Recall that the median of a set of numbers is the number in the middle of the set, after the numbers have been rearranged from lowest to highest.
From the plot, we get that the number, arranged from lowest to highest are:
[tex]40,40,40,40,40,41,41,41,42,42,43,43,43,43,44,44,44,45,45.[/tex]The number in the middle of the above set is:
[tex]42.[/tex]Therefore the median of the given numbers is:
[tex]42.[/tex]Answer: 42.
A) Graph the ellipse. Use graph paper or sketch neatly on regular paper. The ellipse must be hand drawn - no computer tools or graphing calculator. Give the center of the ellipse. Give the vertices of the ellipse. Give the endpoints of the minor axis. Give the foci.
The general equation of an ellipse is:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1.[/tex]Where:
• (h, k) are the coordinates of the centre,
,• a and b are the lengths of the legs.
The parts of the ellipse are:
In this case, we have the equation:
[tex]\frac{(x+1)^2}{5^2}+\frac{(y-4)^2}{4^2}=1.[/tex]So we have:
• (h, k) = (-1, 4),
,• a = 5,
,• b = 4.
A) The graph of the ellipse is:
B) The center of the ellipse is (h, k) = (-1, 4).
C) The vertices of the ellipse are:
• (h + a, k) = (-1 + 5, 4) = ,(4, 4),,
,• (h - a, k) = (-1 - 5, 4) =, (-6, 4),,
D) The endpoints of the minor axis are:
• (h, k + b) = (-1, 4 + 4 ) = ,(-1, 8),,
,• (h, k - b) = (-1, 4 - 4) = ,(-1, 0),.
E) To find the focuses, we compute c:
[tex]c=\sqrt[]{a^2-b^2}=\sqrt[]{5^2-4^2}=\sqrt[]{25-16}=\sqrt[]{9}=3.[/tex]The focuses of the ellipse are:
• (h + c, k) = (-1 + 3, 4) = ,(2, 4),,
,• (h - c, k) = (-1 - 3, 4) = ,(-4, 4),.
Answer
A)
B) (-1, 4)
C) (4, 4), (-6, 4)
D) (-1, 8), (-1, 0)
E) (2, 4), (-4, 4)
Giving a test to a group of students, the grades and gender are summarized belowIf one student is chosen at random,Find the probability that the student was male OR got a(n) "A". (Please enter a reduced fraction.)
To find the probability that the student was male or got an A, we have to find the probabilities that the student was male (event A), got an A (event B) and the intersection between these events (A∩B).
[tex]P(A)=\frac{48}{75}=\frac{16}{25}[/tex][tex]P(B)=\frac{26}{75}[/tex][tex]P(A\cap B)=\frac{12}{75}=\frac{4}{25}[/tex]Now, to find the asked probability, use the following formula:
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cup B)=\frac{48}{75}+\frac{26}{75}-\frac{12}{75} \\ P(A\cup B)=\frac{62}{75} \end{gathered}[/tex]The answer is 62/75.
Roxanne likes to fish. She estimates that 30% of the fish she catches are trout, 20% are bass, and 10% are perch. She designs a simulation.Let 0, 1, and 2 represent trout.Let 3 and 4 represent bass,Let 5 represent perch.Let 6, 7, 8, and 9 represent other fish.The table shows the simulation results. what is the estimated probability that at least one of the next four roxanne catches will be bass?
We have 20 equally probable events in the table. So, each box has probability equal to 1/20.
With this in mind, we must find the numbers 3 and 4 in each box. Then, we can see that there are 12 boxes containing these numbers. Therefore, the probability to catch a bass is
[tex]\begin{gathered} P(\text{bass)}=12\cdot(\frac{1}{20}) \\ P(\text{bass)}=\frac{12}{20} \\ P(\text{bass)}=\frac{3}{5} \end{gathered}[/tex]By converting these result in percentage, we have
[tex]\frac{3}{5}\cdot100=60[/tex]that is, 60% could be bass fish.
What is the image of (-6, -2) after a dilation by a scale factor of 4 centered at theorigin?
The image of (-6, -2) after dilation by a scale of 4 is (-24, -8)
Explanation:The image of (-6, -2) after dilation by a scale of 4 is
(-6*4, -2*4)
= (-24, -8)
Two shaded cubes are shown. 6 feet 4 feet 6 feet 4 feet 4 feet 6 feet Ben states that the combined volume of these two shaded cubes is equal to the volume of this cube. 10 feet Vo feet 10 feet Find the combined volume of the two shaded cubes, and use it to explain whether Ben is right or not. Ben is correct. Ben is not correct.
The volume of a cube is given by the formula:
[tex]V=s^3[/tex]Where
s is the side length of a cube
Combined Volume of two cubes
Now, let's find the combined volume of the cubes with side lengths shown:
[tex]\begin{gathered} V=4^3+6^3 \\ V=64+216 \\ V=280 \end{gathered}[/tex]Volume of larger cube
Plugging into the formula, we get:
[tex]\begin{gathered} V=s^3 \\ V=10^3 \\ V=1000 \end{gathered}[/tex]Thus, we clearly see that:
[tex]280\neq1000[/tex]Thus,
Ben isn't correct
A car that travels 35 mi in 40 min at a rate of…….miles per hour.
We want to determine the rate in miles per hour.
From the infomation given,
distance = 35 miles
time = 40 min
We would convert the time from minutes to hour. Recall,
60 minutes = 1 hour
40 minutes = x hour
By crossmultiplying,
60x = 40
x = 40/60 = 2/3 hour
This means that 40 minutes = 2/3 hour
Rate = distance/time
By substituting the values into the formula,
rate = 35/(2/3)
rate = 52.5
The 52.5 miles per hour
For the figure below, give the following. (a) one pair of vertical angles (b) one pair of angles that form a linear pair (c) one pair of angles that are congruent 1/2 1 3 4 5 / 6 7 78
Let's remember the following definitions:
1. Vertical angles are those angles that are opposite to each other and share the same vertex. Their measures are equal (They are congruent).
2. A Linear pair of angles are those adjacent angles formed when two lines intersect each other. They are Supplementary, which means that they add up to 180 degrees.
For this case you can see two lines "l" and "m" that are cut by the line "n".
a) Based on the definitions shown above, you can identify this pair of Vertical angles:
[tex]\angle1\text{ and }\angle4[/tex]Because the are opposite and share the same vertex.
b) You can also identify this pair of angles that form a Linear pair:
[tex]\angle2\text{ and }\angle4[/tex]c) Since you know that Vertical angles are congruent, you can determine that this pair of angles are Vertical angles and congruent:
[tex]\angle6\text{ and }\angle7[/tex]Therefore, the answers are:
a)
[tex]\angle1\text{ and }\angle4[/tex]b)
[tex]\angle2\text{ and }\angle4[/tex]c)
[tex]\angle6\text{ and }\angle7[/tex]Can you please help me
The formula to calculate the volume of a prism is given as
[tex]V=\text{Base Area }\times Height[/tex]The volume is given as 45 and the height is 9.
Hence, we can get the base area as
[tex]\begin{gathered} A=\frac{V}{h} \\ A=\frac{45}{9} \\ A=5 \end{gathered}[/tex]Therefore, the area of the base is 5 ft².
The correct option is OPTION B.
solve quadratic formulax^2-4x+3=0
The general formula for a equation of the form:
[tex]ax^2+bx+c=0[/tex]is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case we notice that a=1, b=-4 and c=3. Plugging this values in the general formula we get:
[tex]\begin{gathered} x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1)(3)}}{2(1)} \\ =\frac{4\pm\sqrt[]{16-12}}{2} \\ =\frac{4\pm\sqrt[]{4}}{2} \\ =\frac{4\pm2}{2} \end{gathered}[/tex]then:
[tex]x_1=\frac{4+2}{2}=\frac{6}{2}=3[/tex]and
[tex]x_2=\frac{4-2}{2}=\frac{2}{2}=1[/tex]Therefore, x=3 or x=1.
instructions for building a polynomial roller coaster in factored form
The polynomial that is used to represent the roller coaster in factored form is y = +a x (x- 500) (x- 1000)
The given conditions are.
The negative intercept at x = 500
the roller coaster passes through the x-axis at x=0 and at x=1000
The polynomial equation is of the form will be
y = a x (x- 500) (x- 1000)
The polynomial will have a root at x=0 , at x=500 and at x = 1000
Polynomials are used in many areas of mathematics and science. For instance, they are employed in calculus, but numerical analysis is used to approximate other functions instead.
Polynomial functions are used in a variety of situations, from basic physics and biology to economics and social science. From straightforward word problems to intricate scientific conundrums, polynomial equations are utilized to represent a wide range of topics.
Polynomials are used in higher mathematics to construct algebraic varieties and polynomial rings, two key concepts in algebra and algebraic geometry with the use of variables.
Therefore the polynomial that is used to represent the roller coaster in factored form is y = a x (x- 500) (x- 1000)
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Four times a number b is six times the sum of b and five
The number b is -15
Here, we want to write an equation and solve it
We go step by step
Four times a number b
= 4 * b = 4b
is six times the sum of b and 5
The sum of b and 5 is b+ 5
six times this is = 6(b + 5)
Now euating the two, we have;
4b = 6(b + 5)
4b = 6b + 30
collect like terms
6b - 4b = -30
2b = -30
b = -30/2
b = -15
Which expression has a quotient of 63? 1) 4650÷752) 2867÷473) 3276÷52
To find the term with quotient in 63 in from the given option divide each quotient with 63. If the quatiend is divisible that term contain the quotient 63.
The quotient in the first option is 4650. Divide the quotient with 63.
[tex]\frac{4650}{63}=72.38[/tex]The final answer contains decimal places. Thus, there first option does not contain 63 as quotient.
The quotient in the second term is 2867. Divide the quotient with 63.
[tex]\frac{2867}{63}=45.190[/tex]The final answer contains decimal places. Thus, there second option does not contain 63 as quotient.
The quotient in the second term is 3276. Divide the quotient with 63.
[tex]\frac{3276}{63}=52[/tex]The final answer does not contain any decimal places. Thus, the third option contains 63 as quotient.
Thus, the correct option is option 3) 3276÷52.
It walks for 37.5 meters at a speed of 3 meters per minute. For how many minutes does it walk?
Data
• distance: 37.5 meters
,• speed: 3 meters/minute
,• time: ? minutes
,•
From definition:
speed = distance/time
Replacing with data, and solving for time:
3 = 37.5/time
time = 37.5/3
time = 12.5 minutes
I will show you the pic
Part b
we have
2y=-x-8
Remember that
the equation in slope intercept form is
y=mx+b
so
Isolate the variable y
divide by 2 both sides
2y/2=-(x/2)-8/2
y=-(1/2)x-4Part c
we have
y-4=-3(x-3)
apply distributive property right side
y-4=-3x+9
Adds 4 both sides
y=-3x+9+4
y=-3x+13f(x) = 3x2 + 4x – 6g(x) = 6x3 – 522 – 2Find (f - g)(x).O A. (f - g)(x) = -6x3 + 8x2 + 4x – 4O B. (f - g)(x) = 623 – 2x² + 4x - 8O C. (f - g)(x) = 6x3 – 8x2 - 4x + 4O D. (f - g)(x) = -6x3 – 2x2 + 4x – 8SUBMIT
We are being asked to subtract one function from another function.
[tex](f-g)(x)=f(x)-g(x)[/tex][tex]\begin{gathered} (f-g)(x)=(3x^2+4x-6)-(6x^3-5x^2-2)=3x^2+4x-6-6x^3+5x^2+2 \\ (f-g)(x)=-6x^3+8x^2+4x-4 \end{gathered}[/tex]Answer: .
Michael monthly salary after tax is 2,675 if Michele pays for rent,food,and other Bill's totaling 2,140 then how much money is left
We are told that Michael has a total of $2675. If he spends $2140, then the total amount left is the difference between the total and the spent amount, that is:
[tex]2645-2140=505[/tex]Therefore, he has $505 left.
Slove for x Cosec(x-20°)=2/√3
The trignometric ratio is x Cosec(x-20°)=2/√3 is x = 80°.
What is trigonometry as it is a ratio?Trigonometric: A ratio is the sum of the values of all trigonometric functions whose values depend on the ratio of the sides of a right-angled triangle.The trigonometric ratio of a right-angled triangle is determined by the ratio of the triangle's sides to any acute angle.Metric and trigon are the respective Greek words for measurement and triangle.Right triangles have a 90° angle, and trigonometric ratios are specific measurements of these triangles.Now, calculate the trigonometric ratio as follows:
cosec(x-20) = 2/√3cosec ( x-20) = cosec ( 60 )x - 20 = 60x = 80°Therefore, the trignometric ratio is x Cosec(x-20°)=2/√3 is x = 80°.
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Question 18(1 point)Passes through the points, (0,6), (-8,6)What is the slope?
Given the coordinates of two points that passes through a line:
[tex]\text{ (0,6) and (-8,6)}[/tex]Let's name the points:
x1, y1 = -8,6
x2, y2 = 0,6
To be able to get the slope of the line (m), we will be using this formula:
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}[/tex]Let's plug in the coordinates to the formula to get the slope (m).
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]undefined[/tex]Find the next number in the series
4, 8, 12, 20,-
●
32
34
36
38
-
Answer:
4, 8, 12, 20, 24, 28, 32, 34, 36, 38, 42, 46, 50...
Step-by-step explanation:
If it's counting by four, then the replacing number(s) are 24 and 28.
The next term of the sequence will be 32
What is the formula to calculate the nth term of an Arithmetic Sequence ?
The formula to calculate the nth term of an Arithmetic Sequence is -
a(n) = a + (n - 1)d
[a] - first term of A.P.
[d] - Common difference of A.P.
[n] - position of term
We have the following series -
4, 8, 12, 20 ...
We can write the [n]th term of this series as -
a[n] = a[n - 1] + a[n - 2]
So, for n = 5, we can write -
a[5] = a[4] + a[3] = 20 + 12 = 32
Hence, the next term of the sequence will be 32.
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Using the given graph of the function f, find the following.(d) whether it is even, odd, or neither
The function is even function if graph of function is symmetric about y-axis, he function is odd function if graph of function is symmetric about origin.
From the graph of function it can be observed that (-2,0) and ()
And the surface area of each hemisphere below.7.8C
The surface area of the hemisphere is computed using the equation
[tex]SA=3\pi r^2[/tex]For the hemisphere with a radius of 14 yds, the surface area of the hemisphere is
[tex]SA=3\pi(14)^2=588\pi[/tex]For the hemisphere with a diameter of 12.2 yds, we need to find its radius first. The radius is just half of the diameter, hence, the radius of this hemisphere is 6.1 yds. Computing for its surface area, we have
[tex]SA=3\pi(6.1)^2=111.63\pi[/tex]Mason is standing on the seashore. He believes that if he makes a wish
and throws a seashell back into the ocean, his wish will come true. Mason is
standing at the origin of a coordinate plane and the shoreline is represented by the
graph of the line
y = 1.5x + 13. Each unit represents 1 meter. How far does Mason need to be able
to throw the seashell to throw one into the ocean? Round your answer to the
nearest centimeter.
To throw a seashell into the ocean, Mason needs to throw it above the line y = 1.5x + 13, which represents the shoreline.
This means that the seashell's height, y, must be greater than 1.5 times its horizontal distance, x, plus 13. We can use the Pythagorean theorem to find the distance, d, that Mason needs to throw the seashell, given by d = sqrt(x^2 + y^2).
We want to find the minimum value of d that satisfies y > 1.5x + 13. This occurs when y is equal to 1.5x + 13, since any larger value of y would require a larger value of d.
So we can substitute y = 1.5x + 13 into the equation for d and get:
d = sqrt(x^2 + (1.5x + 13)^2)
To find the minimum value of d, we can use calculus and find the derivative of d with respect to x, and set it equal to zero. Alternatively, we can use a graphing calculator or an online tool to plot the function d and find its minimum point. Either way, we get that the minimum value of d occurs when x is approximately -5.2 meters and y is approximately 5.2 meters. The corresponding value of d is approximately 14.7 meters.
Therefore, Mason needs to be able to throw the seashell at least 14.7 meters, or 1470 centimeters, to throw it into the ocean.
Which two expressions are equivalent?A. A(0.52)-21B. A(1.04)-C. A(0.96)D. A(0.96 0.08
Equivalent expressions are expressions that have the values when we put the same values for the variables.
From the given expressions, let's find the equivalent expressions.
From the given expressions, let's substitute 1 for t and evaluate.
The expressions with the same result will be equivalent expressions.
[tex]\begin{gathered} A(0.52)^{-2t} \\ \\ A(0.52)^{-2(1)} \\ \\ A(0.52)^{-2} \\ \\ A(\frac{1}{0.52^2}) \\ \\ A(\frac{1}{0.274}) \\ \\ =3.698A \end{gathered}[/tex][tex]\begin{gathered} A(1.04)^{-t}_{} \\ \\ A(1.04)^{-1} \\ \\ A(\frac{1}{1.04}) \\ \\ A(0.96) \\ \\ =0.96A \end{gathered}[/tex][tex]\begin{gathered} A(0.96)^t \\ \\ A(0.96)^1 \\ \\ A(0.96) \\ \\ =0.96A \end{gathered}[/tex][tex]\begin{gathered} A(0.96)^{0.08t}^{} \\ \\ A(0.96)^{0.08(1)} \\ \\ A(0.96)^{0.08} \\ \\ A(0.998) \\ \\ =0.998A \end{gathered}[/tex]The expressions with the same result are the expressions in options B and C:
[tex]\begin{gathered} B.A(1.04)^{-t} \\ \\ C.A(1.96)^t \end{gathered}[/tex]Therefore, the two expressions that are equivalent are:
[tex]\begin{gathered} B.A(1.04)^{-t} \\ \\ C.A(1.96)^t \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} \text{ B. A(1.04})^{-t} \\ \\ \text{ C. A(1.96)}^t \end{gathered}[/tex]solve the following inequality for z. write your answer in the simplest form.10z-3(z - 8)<-6z+ 9 - 1
Let's start!
As a first step you have to simplify both sides of the inequality:
7z+24<-6z+8
Then, add 6z to both sides:
7z+24+6z<-6z+8+6z
13z+24<8
Now, we are going to subtract 24 from the both sides of the inequality:
13z+24-24<8-24
13z<-16
As a final step, you have to divide both sides by 13.
13z/13<-16/13
z<-16/13
POSSIBLE Match the function rule to the table of values. f(x)=2 х f (x) = (3) f(x) = 32 2 f () = ( 1 ) 28
First, we must evaluate each function at the given values of x.
When x=-2, we have
[tex]\begin{gathered} f(x)=2^x\Rightarrow f(-2)=2^{-2}=\frac{1}{2^2}=\frac{1}{4}=0.25 \\ \end{gathered}[/tex][tex]f(x)=(\frac{1}{3})^x\Rightarrow f(-2)=(\frac{1}{3})^{-2}=\frac{1}{3^{-2}}=3^2=9[/tex][tex]f(x)=3^x\Rightarrow f(-2)=3^{-2}=\frac{1}{3^2}=\frac{1}{9}=0.11[/tex][tex]f(x)=(\frac{1}{2})^x\Rightarrow f(-2)=(\frac{1}{2})^{-2}=\frac{1}{2^{-2}}=2^2=4[/tex]Now, we must compare these result with the tables. Then the solutions are:
Kim owes her friend $235 and plans to pay $5 per week. Select the equation of the function that shows
Answer:
The function is: y = 235 - 5x
x-intercept: 47
y-intercept: 235
The x-intercept means that it takes Kim 47 weeks to pay all of her debt.
The y-intercept means that Kim owes her friend $235.
Step-by-step explanation:
The amount that Kim owes her friend after x weeks is given by the following function:
y = b - ax
In which b is the initial amount she owes and a is how much she pays per week.
Kim owes her friend $235 and plans to pay $5 per week.
So b = 235, a = 5.
The function is: y = 235 - 5x
x-intercept:
Value of x when y = 0, that is, the amount of weeks it takes for her to pay all her debt.
So
235 - 5x = 0
5x = 235
x = 235/5
x = 47
x-intercept: 47
The x-intercept means that it takes Kim 47 weeks to pay all of her debt.
y-intercept:
Value of y when x = 0, that is, the total amount that Kim owes.
235 - 5*0 = 235
y-intercept: 235
The y-intercept means that Kim owes her friend $235.
How would you change 65% to a decimal?
In converting percentage to decimals, you need to divide it by 100.
[tex]\frac{65}{100}=0.65[/tex]The answer is 0.65