Solution:
Given the expression:
[tex]\frac{x^2+5x+2}{2x^2+2x-35}[/tex]A function f(x) has disconituity at x=a if
[tex]\lim_{x\to a}f(x)[/tex]exists and is finite.
The function is thus undefined at x=a or when
[tex]\lim_{x\to a}(f(x))\ne f(a)[/tex]From the given function, we have
[tex]\begin{gathered} \frac{x^2+5x+2}{x^2+2x-35} \\ factorize\text{ the denominator,} \\ \frac{x^2+5x+2}{x^2-5x+7x-35}=\frac{x^2+5x+2}{x(x-5)+7(x-5)} \\ \Rightarrow\frac{x^2+5x+2}{(x-5)(x+7)} \end{gathered}[/tex]The function is undefined at
[tex]\begin{gathered} x-5=0 \\ \Rightarrow x=5 \\ x+7=0 \\ \Rightarrow x=-7 \end{gathered}[/tex]Hence, there is discontinuity at
[tex]x=5,\text{ x=-7}[/tex]what is x^3 - 2x^2 - 4x - 1 divided by x + 1 ?
To answer this question we will use the long division.
Using long division we get:
Therefore:
[tex]\frac{x^3-2x^2-4x-1}{x+1}=x^2-3x-1.[/tex]Answer: Option A.
Mr.Ortiz has to successfully interview 90% of his assigned households. He was assigned 500 households. He has interviewed 430 households so far. Has he met his goal?
90 % of 500 is found by
0.9 * 500 = 450
430 < 450
so he has not met his goal
Ravi had 119 dollars to begin with. He just spent b dollars.using. B, write expression for the number of dollars he has left
Given:
Total money Ravi has to begin with = 119 dollars.
He spent b dollars.
The number of dollars he has left is:
119 - b
Find the length of side x in simplest radical form with a rational denominator.30°х60°12
Ok, to find the lenght of side x we are going to use the sine function:
[tex]\sin (30)=\frac{12}{x}[/tex]Clearing x:
[tex]x=\frac{12}{\sin (30)}=\frac{12}{1/2}=24[/tex]Finally we get that x is equal to 24.
does this represent exponential growth or exponential decay and identify the percent rate of changedetermine whether y= 500(1.08)t represents exponential growth or exponential decay and identify the rate of change.
Given:
[tex]500\mleft(1.08\mright)^t[/tex]To determine whether it represents exponential growth or exponential decay:
Since, the general exponential growth formula is,
[tex]f\mleft(x\mright)=a\mleft(1+r\mright)^x[/tex]Hence, the given represents exponential growth.
Comparing we get,
1+r=1.08
r=0.08
That is, r=8%
Therefore, the percentage rate of change is 8%.
Let c(t) be the number of customers in a restaurant t hours after 8 a.m. Explain the meaning of each statement.c(3)=c(3)
Given:
Here, c(t) be the number of customers in a restaurant t hours after 8 a.m.
The statement is,
[tex]c\left(3\right)=c\left(3\right)[/tex]To find:
The meaning of the given statement.
Explanation:
Since c(t) is the number of customers in a restaurant t hours after 8 a.m.
So, c(3) be the number of customers in a restaurant 3 hours after 8 a.m.
That is,
The number of customers in a restaurant 3 hours after 8 a.m is equal to the number of customers in a restaurant 3 hours after 8 a.m.
Final answer:
The number of customers in a restaurant 3 hours after 8 a.m is equal to the number of customers in a restaurant 3 hours after 8 a.m.
The figure below was made with a scale of 1 unit = 9 cm.Draw the figure with a new scale of 1 unit = 3 cm.You can place your figure anywhere on the grid on the right.9 cmCurrent scale1 unit = 9 cmExplanationCheck3 cmNew scale1 unit = 3 cmI need help with this math problem
We will draw the figure
In a new scale, the new scale is
[tex]1\text{ unit= 3 cm}[/tex]Note that the draw above is a square of side 18cm, therefore in the new scale the side of the square have to be drawn using
[tex]\frac{18cm}{3cm}=6\text{ }units[/tex]That is, if we change the units our new square have a side of 6 units as follows
Three points are shown on the coordinate plane.What is the distance from point A to point B?
Answer:
The distance from point A to point B is;
[tex]5\text{ units}[/tex]Explanation:
Given the points A and B with coordinates as shown on the graph;
[tex]\begin{gathered} A(0,5) \\ B(3,1) \end{gathered}[/tex]Recall that the distance between two points can be calculated using the formula;
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]substituting the coordinates of point A and B. we have;
[tex]\begin{gathered} d=\sqrt[]{(3-0)^2+(1-5)^2} \\ d=\sqrt[]{3^2+4^2} \\ d=\sqrt[]{9+16} \\ d=\sqrt[]{25} \\ d=5 \end{gathered}[/tex]Therefore, the distance from point A to point B is;
[tex]5\text{ units}[/tex]Find the cost for each pound of jelly beans and each pound of almonds
Let 'x' represent the cost for each pound of jelly beans.
Let 'y' represent the cost for each pound of almonds.
For the first statement, the mathematical expression is
[tex]\begin{gathered} 9x+7y=37\ldots\ldots1 \\ \end{gathered}[/tex]For the second statement, the mathematical expression is,
[tex]3x+5y=17\ldots\ldots2[/tex]Combining the two equations
[tex]\begin{gathered} 9x+7y=37\ldots\ldots\text{.}.1 \\ 3x+5y=17\ldots\ldots2 \end{gathered}[/tex]Applying the elimination method to resolve the systems of equation
Multiply the second equation by 3, in order to eliminate x
[tex]\begin{gathered} 9x+7y=37\ldots\ldots\ldots1 \\ 3x+5y=17\ldots\ldots\ldots2\times3 \end{gathered}[/tex][tex]\begin{gathered} 9x+7y=37\ldots\ldots\text{.}.1 \\ 9x+15y=51\ldots\ldots2 \end{gathered}[/tex]Subtract equation 1 from 2
[tex]\begin{gathered} 9x-9x+15y-7y=51-37 \\ 8y=14 \\ \frac{8y}{8}=\frac{14}{8} \\ y=\frac{7}{4}=1.75 \\ \therefore y=1.75 \end{gathered}[/tex]Substitute y = 1.75 into equation 1 in order to solve for x
[tex]\begin{gathered} 9x+7y=37 \\ 9x+7(1.75)=37 \\ 9x+12.25=37 \\ 9x=37-12.25 \\ 9x=24.75 \\ \frac{9x}{9}=\frac{24.75}{9} \\ x=2.75 \end{gathered}[/tex]Hence, the cost for each pound of jelly beans = x = $2.75.
the cost for each pound of almonds = y = $1.75.
What type of model does the data suggest?х01234y2.55102040A ConstantB ExponentialCLinearD) Quadratic
The function for this data can be represented as:
[tex]y=5\times2^{n-2}[/tex]Therefore, it is exponential.
the point M 6,-4 is reflected over the y-axis. what are the cordnates of the resulting point, M?
A reflection over the Y-axis is given by:
[tex](x,y)\rightarrow(-x,y)[/tex]Substitute for (x,y)=(6,-4):
[tex](6,-4)\rightarrow(-6,-4)[/tex]Therefore, the new coordinates of the point after a reflection over the Y-axis, are:
[tex](-6,-4)[/tex]jenelle and hadiya went to lunch,the bill,before sales before sales tax and tip,was 37.50.a sales tax of 8% was added.they added an 18% tip on the amount after the tax was added.a)what was the amount,in dollars,of the sales tax.b)what was the total amount they paid,including tax and tip.
$37.50
tax = 8%
tip = 18%
a) 37.5 ------------------ 100%
x ------------------- 8%
x = (8 x 37.5) / 100
x = 3
Tax = $3
b) Money of lunch plus tax = $40.5
40.5 -------------------- 100
x --------------------- 18
x = (18 x 40.5) / 100
x = 7.29
Total amount paid = 7.29 + 40.5
= $ 47.79
Which answers describe the shape below? Check all that apply.A. SquareB. RhombusC. QuadrilateralD. TrapezoidE. RectangleF. Parallelogram
Recall the following definitions:
A square is a shape that has 4 sides. All of them with the same length. It has 2 pairs of parallel sides and has 4 right angles. Based on this definition, the given shape is a square.
A rhombus is a shape that has 4 sides. It has two pairs of parallel sides and each par has the same length. Based on this definition, it is also a rhombus.
A quadrilateral is closed shape that has 4 sides. Based on this definition, this shape is also a quadrilateral.
A trapezoid is a quadrilateral that has exactly one pair of parallel sides. As in this case we have two pairs of parallel sides, it is not a trapezoid.
A rectangle is a quadrilateral that has a pair of parallel sides of equal length and has 4 right angles. Based on this definition, this shape is also a rectangle.
A parallelogram is a quadrilateral that has two pairs of parallel sides with the same length. Based on this definition, this shape is also a parallelogram
There are two buildings beside a park.
The first building is 165 3/4 ft tall, and
the second building is 114 1/4 ft tall.
By rounding to the nearest whole number,
estimate the difference between the
heights of the buildings.
The difference of the height of the buildings is 51.5 for the first building is 165 3/4 feet tall, and the second building is 114 1/4 feet tall.
Given that,
There are two building side of a park.
The first building is 165 3/4 feet tall, and the second building is 114 1/4 feet tall.
We have to find the difference of the height of the buildings.
We have to subtract the first building is 165 3/4 feet tall, and the second building is 114 1/4 feet tall.
165 3/4- 114 1/4
660+3/4- 456+1/4
663/4-457/4
165.75-114.25
51.5
Therefore, The difference of the height of the buildings is 51.5 for the first building is 165 3/4 feet tall, and the second building is 114 1/4 feet tall.
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Use the figures below. What is the ratio of AD to JM? A.2/3B.6/5C.3/2
Given:
Rectangle ABCD is similar to rectangle JKLM
From the first rectangle, we have:
AB = 15
DC = 6
From the second rectangle, we have:
JM = 10
ML = 5
We know that,
AD ~ JM
DC ~ ML
Thus, we have the ratio as:
[tex]\frac{AD}{JM}=\frac{DC}{ML}[/tex][tex]\begin{gathered} \frac{AD}{JM}=\frac{15}{10}=\frac{3}{2} \\ \end{gathered}[/tex]Therefore the ratio of AD to JM is:
[tex]\frac{3}{2}[/tex]ANSWER:
[tex]C\text{. }\frac{3}{2}[/tex]Solve for 3x/2 -4 = 16what does x equal??
The given equation is expressed as
3x/2 - 4 = 16
The first step is to multiply both sides of the equation by 2. It becomes
3x/2 * 2 - 4 * 2 = 16 * 2
3x - 8 = 32
3x = 32 + 8
3x = 40
x = 40/3
x = 13.33
I need help with this question can you please help me ?
Answer:
Given that,
The product of a number and 6 equals twice the result of the sum of the number and 6.
Let the number be x,
product of a number and 6 is 6x.
sum of the number and 6 is x+6.
we get,
[tex]6x=2(x+6)[/tex]a) The equation could be used to find the number is,
[tex]6x=2(x+6)[/tex]b) On solving the above equation we get,
[tex]6x=2x+12[/tex][tex]6x-2x=12[/tex][tex]4x=12[/tex][tex]x=3[/tex]The number is 3.
Answer is: 3
If x is perpendicular to a and X is perpendicular to b then____X is perpendicular to a A // BA is perpendicular to YX // Y
A house is worth $350,000 when purchased. It was worth $335,000 after the firstyear and $320,000 after the 2ndyear.1. Geometric or Arithmetic and Why?2. Complete a table that shows the value of the house for 5 years.3. Write an explicit and recursive formula for the sequence.4. What is the value of the house after you have lived in it for 10 years?
A house is worth $350,000 when purchased. It was worth $335,000 after the first year and $320,000 after the 2nd year.
So, the difference between initial cost and the cost after one year =
335,000 - 350,000 = -15,000
The difference between the cost after one year and after 2 years =
320,000 - 335,000 = -15,000
As the common difference is constant
so, the cost represents Arithmetic sequence
the first term is 330,000 and the common difference is -15,000
The general form of the sequence is a + d(n - 1)
where a is the first term and d is the common difference and n the number of term
so, a = 335,000 and d = -15,000
so, the general form will be = 335,000 - 15,000(n-1)
So, the value of the house after 5 years = 335,000 - 15,000 * (5-1) = 275,000
-------------------------------------------------------------------------------------------------
1. Geometric or Arithmetic and Why?
Arithmetic
2. Complete a table that shows the value of the house for 5 years.
For 5 years:
first year = $335,000
second year = $320,000
third year = $305,000
fourth year = $290,000
fifth year = $275,000
3. Write an explicit and recursive formula for the sequence.
The formula will be : 335,000 - 15,000(n-1)
4. What is the value of the house after you have lived in it for 10 years?
After 10 years;
the value of the house = 335,000 - 15,000 * (10-1)
= 335,000 - 15,000 * 9 = $200,000
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Hello, I need some assistance with this homework question please for precalculusHW Q15
Solution
The remainder theorems state that when a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x = k, the remainder is given by r = a(k).
Given
[tex]f(x)=4x^3-10x^2+10x-4[/tex]since f(x) is divided by x - 2, the remainder is
[tex]f(2)=4(2)^3-10(2)^2+10(2)-4=4(8)-10(4)+20-4=32-40+20-4=8[/tex]Therefore, the remainder is 8
Evan is going to the 50th state fair this weekend. It costs $10 to enterand each ride is $2. How much will it cost Evan to go to the fair and ride 5rides? **Don't forget the initial cost.**( hint: determine the equation first y =X + and then plug in 5 for x) *
From the question, we are given the following;
Cost of entering the state fair = $10
Amount of each ride = $2
For us to determine the amount it will cost Evan to go to the fair and ride 5 rides, the equation y = $10 + 2x will be used where;
x is the total ride taken = 5 rides
y is the amount it cost evan to enter the state fair and ride 5 rides
Substitute x = 5 into the equation and get y;
y = $10 + 2x
y = $10 + $2(5)
y = $10 + $10
y = $20
Hence it will cost Evans $20 to go to the fair and ride 5 rides
Find the volume of thetriangular prism.24 m7 m3.6 mThe volume of the triangular prism ism3
The volume of a triangle prism formula is shown below.
[tex]\text{Volume of a triangular prism = Base area x Lenght}[/tex]From the figure,
The triangle of base 3.6m and height 24m is the base of the prism.
Therefore, the base area is the area of the triangle.
Area of the triangle = 1/2 x base x height
Area = 1/2 x 24 x 3.6
= 12 x 3.6
= 43.2
The volume = Base area x Length
Length = 7m
Base area = 43.2 meter square
Therefore,
The violume = 43.2 x 7
= 302.4
Final amswer
[tex]\text{Volume = 302.4 m}^3[/tex]how do I multeply Fractions
Multiplying simultaneously numerator by numerator and denominator by denominator.
You can multiply fractions, multiplying simultaneously numerator by numerator and denominator by denominator.
2) Notice that whenever possible, we must simplify it to the lowest possible fraction.
3. Which expression is equivalent to 3(x-2) + Zx?A. -XB. 3xC. 5X-2D. 5X-6marios The cost of
Given an expression below :
[tex]3(x-2)+2x[/tex]The expression can be solved by :
Step 1: Opening the bracket
[tex]\begin{gathered} 3(x-2)+2x \\ 3x-6+2x \end{gathered}[/tex]Step 2: Collect like terms
[tex]\begin{gathered} 3x-6+2x \\ 3x+2x-6 \\ 5x-6 \end{gathered}[/tex]Therefore the correct answer for the expression is 5x - 6
Hence the correct value is Option D
One equation from a system of two linear equations is graphed on the coordinate grid. 51 46 5 4 3 2 1 6 x -1 -21 The second equation in the system of linear equations has a slope of 3 and passes through the point (2,-5). What is the solution to the system of equations? th
First, we need to find the equation for the two equations.
The equation graphed has a y-intercept of 3 and a slope of
[tex]m=\frac{-6}{3}=-3[/tex]therefore, the equation of the line is
[tex]\boxed{y=-\frac{1}{2}x+3.}[/tex]For the second equation, we know what it has a slope of 3; therefore it can be written as
[tex]y=3x+b[/tex]Now, we also know that this equation passes through the point y = -5, x = 2; therefore,
[tex]-5=3(2)+b[/tex]which gives
[tex]-5=6+b[/tex][tex]b=-11[/tex]Hence, the equation of the line is
[tex]\boxed{y=3x-11}[/tex]Now we have the equations
[tex]\begin{gathered} y=-\frac{1}{2}x+3 \\ y=3x-11 \end{gathered}[/tex]equating them gives
[tex]-\frac{1}{2}x+3=3x-11[/tex]adding 11 to both sides gives
[tex]-\frac{1}{2}x+14=3x[/tex]adding 1/2 x to both sides gives
[tex]14=\frac{7}{2}x[/tex]Finally, dividing both sides by 7/2 gives
[tex]\boxed{x=4\text{.}}[/tex]The corresponding value of y is found by substituting the above value into one of the equations
[tex]y=-\frac{1}{2}(4)+3[/tex][tex]y=1[/tex]Hence, the solution to the system is
[tex](4,1)_{}[/tex]Write a coordinate proof of the following theorem:"If a quadrilateral is a kite, then its diagonals are perpendicular."(image attached)thank you ! :)
Given the following coordinate points from the kite
[tex]\begin{gathered} W=(a,4b) \\ X=(2a,b) \\ Y=(a,0) \\ Z=(0,b) \end{gathered}[/tex]For the diagonals to be perpendicular the product of the distance WY and XZ must be zero that is;
[tex]\vec{WY}\cdot\vec{XZ}=0[/tex]Determine the coordinate point WY
[tex]\begin{gathered} \vec{WY}=[(a-a,4b-0)] \\ \vec{WY}=(0,4b) \end{gathered}[/tex]Determine the coordinate point XZ
[tex]\begin{gathered} \vec{XZ}=[(2a-0),(b-b)] \\ \vec{XZ}=(2a,0) \end{gathered}[/tex]Take the dot product of the coordinates
[tex]\begin{gathered} \vec{WY}\cdot\vec{XZ}=(0,4b)\cdot(2a,0) \\ \vec{WY}\cdot\vec{XZ}=[(0)(2a)+(4b)(0))] \\ \vec{WY}\cdot\vec{XZ}=(0,0)=\vec{0} \end{gathered}[/tex]Since the dot product of the coordinates is a zero vector, hence its diagonals are perpendicular.
Which situation is best modeled by the graph? a.) the cost of buying muffinsb.) the distance between the train and the station as the train travels towards the stationc.) the amount of money left in the roll of quarters after paying a roll each dayd.) the distance a runner covers traveling at a steady paste
Notice that the graph plots points that as we move along the horizontal axis, go down in value. The Horizontal axis is most likely representing the time elapsed in each description.
Then, we DISCARD the first answer, since the cost of muffins don't go down as time goes by.
Answer b is a POSSIBLE answer, since the distance as the train approaches the station, is reducing (going down in value) as time goes by.
Answer C is not a good answer (we discard it) since after paying a roll each day, the number of quarters in each roll doesn't go down because we pay with the entire roll.
Answer d is also discarded, since the distance covered by the runner, should be going UP (increasing) as time goes by
Therefore, answer b) is the selected answer.
Can u please help me with This am trying to study but can’t get it
Given:
Following Matrices are given.
[tex]A=\begin{bmatrix}{2} & {1} \\ {3} & {4}\end{bmatrix},B=[\text{ }5\text{ 4 \rbrack, C=}\begin{bmatrix}{4} & {1} & {6} \\ {} & {} & {} \\ {5} & {2} & {7}\end{bmatrix}[/tex]Find:
we have to find which Matrix multiplication can be defined.
Explanation:
For Matrix multiplication, the number of columns of first Matrix should be equal to the number of rows of the second Matrix.
Therefore, the following Matrix multiplication can be defined
BC,Because number of columns of B is 2 and number of rows of C is 2.
AC,Because number of columns of A is 2 and number of rows of C is 2.
BA,Because number of columns of B is 2 and number of rows of A is 2.
Therefore, the multiplications BC,AC,BA can be defined.
Suppose f(x) = x². Find the graph off(x+3).???
If f(x)=x^2
Then f(x+3)=(x+3)^2
[tex](x+3)^2=x^2+6x+9[/tex]Use geogebra to graph the function or calculate the vertex using the equation
x=-b/2a
From the equation we have that
b=6
a=1
x=-6/(2*1)
x=-3
The vertex is on x=-3
Calculate f(-3)=9-18+9=0
The vertex is (-3,0)
y axis cut off point f(0)=0+0+9=9
As "a" is a positive value, parabola open upwards, now you can draw the parabola
This is a sketch, let's use geogebra
The length of a rectangle is 1m more than twice the width, the area of the rectangle is 45m^2
Let l and w be the length and width of the rectangle, respectively; therefore, according to the question
[tex]\begin{gathered} l=2w+1 \\ and \\ l*w=45 \end{gathered}[/tex]Where l and w are in meters.
Substitute the first equation into the second one, as shown below
[tex]\begin{gathered} l=2w+1 \\ \Rightarrow(2w+1)*w=45 \\ \Rightarrow2w^2+w=45 \\ \Rightarrow2w^2+w-45=0 \end{gathered}[/tex]Solve for w using the quadratic formula,
[tex]\begin{gathered} \Rightarrow w=\frac{-1\pm\sqrt{1+4*2*45}}{2*2}=\frac{-1\pm\sqrt{361}}{4}=\frac{-1\pm19}{4} \\ \Rightarrow w=\frac{9}{2},-5 \end{gathered}[/tex]But w has to be positive since it is a measurement; therefore, w=9/2.
Finding l given the value of w=9/2,
[tex]\begin{gathered} w=\frac{9}{2} \\ \Rightarrow l=2(\frac{9}{2})+1=10 \\ \Rightarrow l=10 \end{gathered}[/tex]Thus, the answers are length=10 m, width=4.5m