Answers
The function is continuous at a = 5
Explanation:Given:
[tex]18)\text{ }f(x)\text{ = }\frac{2x^2+3x+1}{x^2+5x};\text{ a = 5}[/tex]To find:
If the function is continuous at a = 5
For a function to be continuous at a point, the limit exists for the point and the value of the function at that point must be equal to the limit at the point.
when x = 5
[tex]\begin{gathered} f(x)\text{ = }\frac{2(5)^2+3(5)+1}{(5)^2+5(5)} \\ \\ f(x)\text{ = }\frac{50\text{ + 15 + 1}}{25\text{ + 25}} \\ \\ f(x)\text{ = }\frac{66}{50} \\ \\ f(x)\text{ = }\frac{33}{25} \end{gathered}[/tex]Finding the limit at the point:
[tex]\begin{gathered} \lim_{a\to5}\frac{2x^2+3x\text{ + 1}}{x^2+5x} \\ \\ To\text{ get the limit at the point a = 5, we will susbtitute x with 5} \\ =\text{ }\frac{2(5)\placeholder{⬚}^2+3(5)+1}{(5)\placeholder{⬚}^2+5(5)} \\ \\ =\text{ }\frac{50+15+1}{25+25}\text{ = }\frac{66}{50} \\ \\ =\text{ }\frac{33}{25} \end{gathered}[/tex]The value of the function at that point is equal to the limit at the point.
Hence, the function is continuous at a = 5
Related Questions
The diagram shows a field.
66 m
140m
102 m
Work out the area of the field.
4
Answers
Answer:
The area of the field will be 60504 Sq. m
Step by Step calculation:
Area of the cuboidal field
A cuboid is a three-dimensional figure bounded by six rectangular planes that have different lengths, widths, and heights. If you look around and see a box, brick, or anything in the shape of a rectangle, it might be a cuboid. A cuboid ([tex]3[/tex]-dimensional) can be seen as composed of rectangles ([tex]2[/tex]-dimensional) of different dimensions when viewed from either end
Total area of block = lh + lh + lb+ lb+ hb+ hb=[tex]2[/tex](lb+bh+hl).......(1)
where l means length h means height and b means the breadth of the cuboid
Put the value of length, breadth, and height in (1)
We get TSA of field as= 2(66*140+140*102+102*66 ) = 60504 m^2
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heyyyy i need help with jumber 2
Answers
We are asked to determine whether the given two polygons are similar or not.
Recall that the two polygons are said to be similar if the ratio of their corresponding sides is equal.
The corresponding sides of the two polygons are
side 3 = side 6
side 4 = side 8
side 5.5 = side 11
Let us check if they are in the same ratio
[tex]\begin{gathered} \frac{3}{6}=\frac{4}{8}=\frac{5.5}{11} \\ \frac{1}{2}=\frac{1}{2}=\frac{1}{2} \end{gathered}[/tex]As you can see, the ratio of the corresponding sides is equal.
Therefore, the given pair of polygons is similar.
Given f(x)
= 3x + 1, solve for x when
f(x) = 7.
Answer:
Answers
Answer:
x=2
Step-by-step explanation:
7=3x+1
6=3x
2=x
Hopes this help please mark brainliest
thanks for the help!!!
Answers
The value of expression cos(A + B) is equivalent to 0.9902.
What is the relation between sinФ and cosФ?The relation between sinФ and cosФ is as follows -
sin²Ф + cos²Ф = 1
Given is sin(A) = -11/61 and sin(B) = 9/41
We have -
sin(A) = -11/61
sin(B) = 9/41
Evaluating the expression -
cos(A + B)
We can write -
cos(A + B) = cos[A] cos[B] - sin[A] sin[B]
Now, we know -
sin²Ф + cos²Ф = 1
cos²A = 1 - sin²A = 1 - 0.033 = 0.97
cos A = 0.98
cos²B = 1 - sin²B = 1 - 0.04 = 0.95
cos B = 0.97
Using the values -
cos(A + B) = cos[A] cos[B] - sin[A] sin[B]
cos(A + B) = 0.98 x 0.97 + 0.18 x 0.22
cos(A + B) = 0.9902
Therefore, the value of expression cos(A + B) is equivalent to 0.9902.
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What is the solution to this equation?4x - 6 + 2x = 18OA. x = 6OB. X= 4OC. X = 2OD. x = 12
Answers
In order to solve this equation, we can do the following steps:
[tex]\begin{gathered} 4x-6+2x=18\\ \\ 6x-6=18\\ \\ 6x=18+6\\ \\ 6x=24\\ \\ x=\frac{24}{6}\\ \\ x=4 \end{gathered}[/tex]Therefore the correct option is B.
the baseball stadium the price for popcorn is $16.20 for 6 bags. If youwanted to buy 5 bags of popcorn, how much would it cost?
Answers
It is given that the cost of 6 bags of popcorn is $16.20
So the cost of 1 bag is:
[tex]\frac{16.20}{6}=2.7\text{ dollars}[/tex]So the cost of 5 bags at $2.70 per bag is:
[tex]2.7\times5=13.5\text{ dollars}[/tex]So the cost of 5 bags of popcorn is $13.5.
a parabola can be drawn given a focus of (4, -7) and a directrix of y=-1
Answers
The equation of parabola is -12(y + 4) = (x-4)² with vertex(4, -7) and Latus rectum 12.
What is Parabola?
A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.
Any point on the parabola is equidistant from the focus an directrix.
Distance of a point (x,y) from y=-1 is (y+1)
Distance of a point (x,y) from (4,-7) say L, then
L² = (x - 4)² + (y+7)²
since, L = y + 1
(y + 1)² = (x - 4)² + (y+7)²
y² + 1 + 2y = (x - 4)² + y² + 49 + 14y
-12y - 48 = (x-4)²
-12(y + 4) = (x-4)²
Therefore, The equation of parabola is -12(y + 4) = (x-4)² with vertex(4, -7) and Latus rectum 12.
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iif there is 3 kids and they wanted to share one cup of celery and one cupof carrots how many cups doe each kid get
Answers
Each kid will get the fraction 1/3 of a cup of carrots .
A common fraction is a number that represents a rational number. The same number may be expressed as a decimal, percent, or negative exponent.
For instance, the numbers 0.01, 1%, and 102 are equal to the fraction 1/100. The term "set of rational numbers" refers to the collection of all numbers that can be expressed in the form a / b, where a and b are integers and b is not zero. This collection is represented by the letter Q, which stands for quotient. A denominator of one can be considered to be inherent in an integer. A number is said to be logical when it can be stated in that manner (i.e., as a common fraction).There is 1 cup of the carrots and it is to be divided among 3 kids.
therefore each kid will get:
1÷3 = 1/3 cups of carrot.
Hence the kids will each have 1/3 cups of carrot .
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Nancy went to the mall on Saturday to buy clothes. She paid $14.95 on pants and
$4.05 on a jacket with a $20 bill. How much money did Nancy get in change?
Answers
Answer:
$1.00
Step-by-step explanation:
Total cost = $14.95 + $4.05 = $19.00
Change = $20.00 - $19.00 = $1.00
find the unit price of 16 oz of candy with sells for $4.82
Answers
The price of 16 oz candy is $4.82.
Determine the unit price of candy.
[tex]\begin{gathered} s=\frac{4.82}{16} \\ =0.30125 \end{gathered}[/tex]Find the area and perimeter of the following rectangle guru angad education
Answers
1.
[tex]A=l\times w=11\times8=88\operatorname{cm}\text{ }[/tex][tex]P=2l+2w=2(11)+2(8)=22+16=38\text{ cm}[/tex]2.
[tex]\begin{gathered} A=11\times11=121 \\ P=2(11)+2(11)=22+22=44 \end{gathered}[/tex]3.
[tex]\begin{gathered} A=8\times6=48 \\ P=2(8)+2(6)=16+12=28 \end{gathered}[/tex]4.
[tex]\begin{gathered} A=7\times2=14 \\ P=2(7)+2(2)=14+4=18 \end{gathered}[/tex]5.
[tex]\begin{gathered} 35=7\times w \\ \frac{35}{7}=\frac{7w}{7} \\ w=5 \\ P=2(7)+2(5)=14+10=24\text{ units} \end{gathered}[/tex][tex]\begin{gathered} 25=l\times5 \\ \frac{25}{5}=\frac{5l}{5} \\ l=5 \\ P=2(5)+2(5)=10+10=20\text{ units} \end{gathered}[/tex]6.
[tex]P=11+18+9+3+3+8+5+7=64[/tex]4.) Rotate 90° counterclockwise about the origin.Original NewCoordinates: Coordinates:A: (___) A: ()YAON+COB:(_)B': ()2D2CC: (-)C':(___)D: (___)D:(__)
Answers
The Solution:
Rule:
When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
The original coordinates of the given points are as follows:
[tex]\begin{gathered} A(-4,3)_{} \\ B(2,3) \\ C(2,-1) \\ D(-4,-1) \end{gathered}[/tex]So, the new coordinates of the given points are below:
[tex]A^{\prime}(-3,-4)[/tex][tex]B^{\prime}(-3,2)[/tex][tex]C^{\prime}(1,2)[/tex][tex]D^{\prime}(1,-4)[/tex]Jeanette wants to raise $3, 200 in a marathon fundraiser. Her sponsers will donate
$35 for each (whole) kilometer she runs this summer.
The minimum amount Jeanette will have to run to reach her goal of $3, 200 is
kilometers.
It’s not 92
Answers
Jeanette need to run 91.42 km to get $3,200
How to calculate the distance :
The amount Jeanette wants to raise = $3,200
Amount her sponsers donate = $35 per KM
To find total distance she need to run is divide 3,200 by 35
so we get the distance which she need to cover.
Distance Jeanette need to run = 3200/35 = 91.42 km
The basic operation applied is division.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.There are four important terms used in division. These are dividend, divisor, quotient and remainder.Dividend: The number to be divided by another number is called the dividend.Divisor: The number by which we divide another number (dividend) into equal parts is called the divisor.Quotient: The result of division is called a quotient.Remainder: The leftover number after division is called the remainder.To learn more about division refer :
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What is the cardinal number of the set H={}?
Answers
The set is empty that is null set, so the cardinal number is zero.
The cardinal number of a finite set A is the number of distinct members present in the set and it is denoted by n(A). The cardinal number of the empty set, Ø, is 0 because Ø has zero members or no members. so n(Ø) = 0. And the cardinal number of an infinite set, cannot be found because such a set has countless members.
for example
i) If A = (-3,-2,-1,0,1,2,3) then n(A)=7.
ii) If A = (x/x is a letter of the word HYDERABAD) then n(A) = 7 because writing in the tabular form, A = (H,Y,D,E,R,A,B)
Here, the set is empty that is null set, so the cardinal number is zero.
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Graph the inequality on the numberlineA + 5/3 > 1/2
Answers
Okay, here we have this:
Let's solve first A + 5/3 > 1/2:
[tex]\begin{gathered} A+\frac{5}{3}>\frac{1}{2} \\ A>-\frac{7}{6} \end{gathered}[/tex]So, according with this we obtain the following in the number line:
Classify each angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. <1 and <3 <3 and <7 <8 and <10<4 and <14<6 and <14<2 and <3
Answers
EXPLANATION:
To make a correct classification we must do the following:
First we must know the following terms:
-Corresponding angles:
They are on the same side of the parallels and on the same side of the transversal.
For example: <1 <3 ; <6 and <14
-Alternate interior:
They are found within the parallel lines and on the opposite sides to the transversal
For example: <3 and <7 ; <8 and <10
-Alternate Exterior:
they lie outside the parallel lines and on the opposite sides to the transversal.
For example: <4 and <14
-Consecutive interior angles:
They are the pairs of angles on one side of the transversal that are between the lines.
For example: <2 and <3
What is the word for added and subtracted parts of an expression
Answers
Answer:
Step-by-step explanation:
answer: terms
hope that is what you mean!
how many solutions does 2(x+4)=4(x+2)
Answers
lets solve the equation!
[tex]\begin{gathered} 2(x+4)=4(x+2) \\ x+4=\frac{4}{2}(x+2) \\ x+4=2(x+2) \\ x+4=2x+4 \\ 4-4=2x-x \\ x=0 \\ \\ \text{Thus there is only ONE solution, and it is x=0} \end{gathered}[/tex]A circle has a radius of 4 in find the length s of the arc
Answers
The rule of the length of an arc is
[tex]s=r\theta[/tex]r is the radius of the circle
Cita is the central angle subtended by this arc in radian measure
Since the radius of the circle is 4 inches, then
[tex]r=4[/tex]Since the measure of the central angle is 1.9 radian, then
[tex]\theta=1.9[/tex]Substitute them in the rule above
[tex]\begin{gathered} s=4\times1.9 \\ s=7.6\text{ inches} \end{gathered}[/tex]The length of the arc is 7.6 inches
Simplify this question for me thanks!
Answers
Answer:
2[tex]x^{\\2}[/tex][tex]y^{5}[/tex][tex]\sqrt{x} 7xy^{3}[/tex]
Step-by-step explanation:
Answer:
2x[tex]2x^{2} \sqrt[5]{7xy} }^{38}[/tex]
Step-by-step explanation:
Determine if the pair of solids are similar. If NO explain
Answers
Given:
There are given that the two solid to find the similar or not.
Explanation:
To determine whether the solid pair are similar or not, we need to set their dimension with proportion.
So,
From the dimensions of solid:
The radius of the given solids is 14 yd and 4 yd.
The height of the solids is 20 yd and 6 yad.
Now,
We need to set the proportion:
[tex]\begin{gathered} \frac{14}{4}=\frac{7}{2} \\ \frac{20}{6}=\frac{10}{3} \end{gathered}[/tex]So,
[tex]\frac{7}{2}\ne\frac{10}{3}[/tex]Final answer:
Hence, the given pair of solid is not similar because their proportion has not equal.
Mr. Pryor's second period consists of 25 students. The mean grade on the first exam was 80, the median was also 80, and the standard deviation was 6.07. Find the standardized scores (z-scores) for each of the following students. Interpret each value in context.
a) Katie, who scored 93.
b) Norman, who scored 72
c) Ted, who scored an 80.
d) Jenny earned an 82 on Mr. Goldstone's chemistry test. Mr. Goldstone told the class that the distribution was fairly symmetric with a mean of 76 and a standard deviation of 4. She scored an 86 in Mr. Pryor's exam, on which test did Jenny perform better relative to the class? Justify your answer.
Answers
Answer:
See explanation
Step-by-step explanation:
a. (93-80)/6.07=
13/6.07=2.14
b. (72-80)/6.07=
8/6.07=1.317957
1.317957=1.32
c. (80-80)/6.07=
0/6.07=0
d. (82-76)/4=
6/4=1.5
(86-80)/6.07=
6/6.07=0.988
1.5>0.98, so Jenny did better on Mr. Goldstone's test.
a rectangle measures 12 inches by 20 inches. what size squares can tile the rectangle completely? choose all that apply
Answers
Therefore, supplying 4X4 square tiles can tile the rectangle completely with the help of the HCF concept.
What is HCF?
The greatest number that totally divides two numbers is known as the Highest Common Factor (HCF).
HCF for 12 and 20 is equal to 4. Factors of 12 & 20 = 1, 2, 3, 4, 6, and, respectively, 1, 2, 4, 5, 10, 20. In this case, 4 is the biggest number that can be found in the factors for 12 and 20.
We interpret the study released as the component of the product factors in order to determine the HCF by listing common factors in prime factorization.
Consequently, 12 and 20 can be written as;
12 equals 2 × 2 × 3
20 equals 2 × 2 × 5
2 and 2 are frequent prime factors for 12 and 20.
Therefore,
HCF (12, 20) equals 2 × 2 = 4
Therefore, supplying 4X4 square tiles can tile the rectangle completely with the help of the HCF concept.
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Kristen make $16 per hour and worked 34 hours last week. How many dollars she made : Mark make $14 per hour and worked 46 hours last week. How many dollars he make :How many hours must Kristen and mark work in order for their pay/savings to be equal ?If Kristen and mark combine their saving how many they will have ?
Answers
first question
Kristen make $16 per hour
last week he worked for 34 hours
1 hour ==== $16
35 hours ==== $x
cross multiplication
x * 1 = 16 x 34
x = $544
Second question
for mark
make $14 per hour
he worked 46 hours last week
total amount made
1 hour ===== $14
46 hours =====$x
1 * x = 14 x 46
x = $644
Mark make $644 last week
for the fourth question
if mark and kristen combined their savings
mark make $644 and kristen make $544
their saving combines is
$644 + $544
= $1,188
Their saving combines is $1, 188
if mark works for 46 hours and make $644
if marks works for 34 hours and make $544
how many hours will they work
let the number of hours be x
equating the two equation
Predict using the equation of the trend line y=25X+150 what will the y value be when x =23?
Answers
Given the equation of the line :
[tex]y=25X+150[/tex]We need to find the value of y when x = 23
So, substitute with x = 23 at the given equation
[tex]\begin{gathered} y=25\cdot23+150 \\ y=575+150 \\ \\ y=725 \end{gathered}[/tex]So, the answer is : y = 725
Answer:
725
Step-by-step explanation:
Hello!
You can substitute 23 for x in the equation y = 25x + 150, to find the predicted y-value.
Solve for y
y = 25x + 150; x = 23y = 25(23) +150y = 575 + 150y = 725The value of y at x = 23 is 725.
all you need is in the photo please don't put the step by step ANSWER FAST
Answers
The given expression is
[tex]3x^2+12x-15=0[/tex]First, we factor our the number 3.
[tex]3(x^2+4x-5)=0[/tex]Then,
[tex]x^2+4x-5=0[/tex]Now, we look for two numbers whose product is 5, and whose difference is 4, those numbers are 5 and 1.
[tex](x+5)(x-1)=0[/tex]Hence, the solutions are x = -5 and x = 1.1. If(x)= 5x-2, find(-3)a. -13b. 13c. -17d. 172. If(x)= 5x-2, find x such that f(x)= -3a. -1/5b. 1/5c. -1(Also explain what's the difference between the questions)
Answers
1. f ( -3 ) = 5 ( -3 ) - 2 = - 15 - 2 = -17
2. f (x) = 5x - 2 = -3
5x = -3 + 2
5x = -1
x = -1/5 ( dividing both sides by 5 )
The difference between the equations is that -3 is the value for the variable x in the first equation but the function is equal to -3 in the second.
Will picks a Marble random puts it back and then picks another Marble at random are these 2 events depended or independent
Answers
When Will puts back the marble, the number of marbles in the sample space has not changed. This is similar to having a replacement marble. The event therefore, is independent.
(05.01)Neil has been running a tutoring business since 2005. He charges a monthly fee for weekly tutoring sessions and a phone help line. Each year, he has increased his fee by the same amount. The table shows what Neil charged each customer for two given years of his business:YearAnnual Tutoring Fee2005$12002008$1350A. What is the rate of change and initial value for Neil’s business? How do you know?B. Write an equation in slope-intercept form to represent the fees that Neil charges each year.
Answers
Solution:
Given that, the initial year (2005), the tutoring fee is $1200. Three years later (2008), the tutoring fee is $1350.
Thus, the rate of change, m, is;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ x_1=0,y_1=1200,x_2=3,y_2=1350 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{1350-1200}{3-0} \\ \\ m=\frac{150}{3} \\ \\ m=50 \end{gathered}[/tex]Then, the rate of change for Neil's business is 50 and the initial value is $1200.
(b) The slope-intercept form is written as;
[tex]\begin{gathered} y=mx+b \\ \\ \text{ Where }m\text{ is the rate of change, }b\text{ is the initial value;} \\ y\text{ is the annnua tutoring fee,}x=year \end{gathered}[/tex]ANSWER:
[tex]y(x)=50x+1200[/tex]I need help solving this problem.( I had a tutor helping a min ago, but Brainly crashed)
Answers
See graph below
Explanation:Given:
Rate water is added = 30 l/min
The initial amount in the pond = 600l
To find:
The equation relating the amount of water in the pond to the number of minutes the water is being added
W = amount of water in the pond
T = number of minutes that water has been added
Amount of water in the pond = rate water is added (number of minutes that water has been added) + the initial amount in the pond
[tex]\begin{gathered} W\text{ = 30\lparen T\rparen + 600} \\ W\text{ = 30T + 600 \lparen equation\rparen} \end{gathered}[/tex]Graphing the equation:
To graph the equation, we will assign values to T
when T = 0, W = 600
when T = 2, W = 660
when T = 4, W = 720
when T = 6, W = 780
