Answers
These are the conditions of the continuity in a function:
First, the value of x must have an image.
Second, the lateral limits must be equal:
[tex]\lim_{x\to a^+}f(x)=\lim_{x\to a^-}f(x)[/tex]Finally, the value of the limit must be equal to the image of x. This means that:
[tex]f(a)=\lim_{x\to a^}f(x)[/tex]In this case, we must find a value of k that can make the two lateral limits equal in x =3:
[tex]\lim_{x\to3^+}x^2+k=\lim_{x\to3^-}kx+5[/tex]We can solve these two limits easily by replacing the x with the value of 3
[tex]3^2+k=3k+5[/tex][tex]\begin{gathered} 9+k=3k+5 \\ 4=2k \\ k=2 \end{gathered}[/tex]Finally, we can see that the answer is k=2.
Related Questions
You randomly draw a marble from a bag of marbles that contains 7 blue marbles 2 green marbles and 1 red marbles
Answers
Given the following:
7 blue marbles
2 green marbles
1 red marbles
We to find the probability of not drawing a blue marble.
We will be solving it in two ways.
First let's get the total marbles
Total Marble = 7 + 2 + 1 = 10
recall that probablity is number of favourable outcome divide by number of total outcome.
So,
probablity of Drawing a Blue Marble is = 7/10
probability of not Drawing Blue Marbles = 1 - Probability of Drawing Blue Marbles
= 1 - 7/10
= 10 - 7
10
= 3/10
OR
Probability of not Drawing Blue Marbles = Probablity of drawing Green or Red Marbles.
= 2/10 + 1/10
= 3/10
Therefore, the probability of not Drawing Blue Marbles is 3/10.
I have 5 digits in my number. I do not have any tens. My digits add upto the product of 2 and 6. My biggest place has a value of 30,000. Myhundreds and thousands place adds up to three. The value of mythousands place is bigger than my hundreds. I only have one 0 in mynumber. The sum of my ten thousands, thousands, and hundredsequals the value of my ones place.
Answers
Let's begin by listing out the information given to us:
I have 5 digits in my number means the number is XXXXX (10,000 - 99,999)
No tens: the place value of 'tens' is zero
My digits add up to the product of 2 and 6: 2 * 6 = 12
[tex]\begin{gathered} \Sigma X=2\cdot6=12 \\ \Sigma X=12 \end{gathered}[/tex]My biggest place has a value of 30,000: this restricts the number to lie between 10,000 - 30,000
My hundreds and thousands place adds up to three: this can either be 2 + 1 or 1 + 2 or 0 + 3 or 3 + 0
The value of my thousands place is bigger than my hundreds: this implies that it is 2 + 1 or 3 + 0
I only have one 0 in my number: this cannot be in the 'ten thousands' place, it is the 'tens' place value (I do not have any tens)
The sum of my ten thousands, thousands, and hundreds equals the value of my ones place: the value of the 'ones' place is 6, the value of the 'ten thousands' is 2, the value of the 'thousands' is 3, the value of the 'hundreds' is 1
Hence, the number is 23,106 (remember that "My biggest place has a value of 30,000")
Question 3(Multiple Choice Worth 2 points)
(01.06 MC)
Simplify √√-72-
--6√√2
6√-2
6√√2i
061√2
Answers
Answer:
[tex]6i\sqrt{2}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt{-72}[/tex]
Rewrite -72 as the product of 6 · -1 · 2:
[tex]\implies \sqrt{36 \cdot -1 \cdot 2}[/tex]
Apply the radical rule [tex]\sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies \sqrt{36} \sqrt{-1} \sqrt{2}[/tex]
Carry out the square root of 36:
[tex]\implies 6\sqrt{-1}\sqrt{2}[/tex]
Apply the imaginary number rule [tex]\sqrt{-1}=i[/tex] :
[tex]\implies 6i\sqrt{2}[/tex]
A student worked 51 hr during a week one summer. The student earned $5. 10 per hour for the first 40 hr and $7.65 per hour for overtime. How much did the student earn during the week?
Answers
We will determine the earnings for the week as follows:
[tex]W=40(5.10)+11(7.65)\Rightarrow W=288.15[/tex]So, the student earned $288.15 that week.
7.5 is 15% of what number?
Answers
Let the number be x. So equation for x is,
[tex]\begin{gathered} \frac{15}{100}\cdot x=7.5 \\ x=\frac{7.5\cdot100}{15} \\ =\frac{750}{15} \\ =50 \end{gathered}[/tex]The number is 50.
Dilate trianglesDraw the image of AABC under a dilation whose center is A and scale factor is
Answers
Since the dilation is centered at vertex A, the coordinates of A' are the same of A.
Then, to find the coordinates of B, let's multiply the distance AB by the scale factor:
[tex]\begin{gathered} AB=12.6\\ \\ A^{\prime}B^{\prime}=12.6\cdot\frac{1}{4}=3.15 \end{gathered}[/tex]Doing the same for AC, we have:
[tex]A^{\prime}C^{\prime}=AC\cdot\frac{1}{4}=11.3\cdot\frac{1}{4}=2.825[/tex]The points B' and C' are on the sides AB and AC, respectively.
Knowing this, let's draw the image A'B'C':
Since AB = BC, we also have A'B' = B'C' = 3.15.
2) Katie and Jacob are enlarging pictures in a school yearbook on the copy machine. The ratio of the width to the length of the enlarged photo will be the same as the ratio of the width to the length of the original photo. 25 points One of the photographs that they want to enlarge is a 3" x 4"photo. katie says that she can enlarge the photo to a 9" x 12", but Jacob disagrees. He says it will be 11" x 12". Who is correct? Explain your reasoning in words. * Enlarged Photo Original Photo 3 inches 4 inches
Answers
The original picture Katie and Jacob want to enlarge is 3 by 4 photographs
This means that the initial length of the photograph is 3 and the intial width of the photographs is 4
If both of them want to enlarge the photograph, then the scaling factor must be the same for both the width and length
Katie enlarge the photo to a 9 x 12
The ratio of the original photograph is 3 to 4
That is, 3 : 4
Katie enlarge the photo to a 9 x 12
Ratio of the enlarged photo by katie is 9 to 12
That is, 9 : 12
Equate the two ratio together
3/4 = 9/12
Introduce cross multiplication
We have,
3 x 12 = 4 x 9
36 = 36
Therefore, the ratio which katie enlarged the photo results to a proportion
For Jacob
Jacob enlarged the photo to 11 x 12
Equating the two ratios
3/4 = 11/12
3 x 12 = 4 x 11
36 = 44
This does not give us a proportion
Therefore, Katie is correct while Jacob is wrong
v+1.6>-5.5
nnnnnnnnnnnn
Answers
Answer:
v > -7.1
Step-by-step explanation:
Find the volume of a pyramid with a square base, where the side length of the base is
11 in and the height of the pyramid is 15.1 in. Round your answer to the nearest
tenth
Answers
Answer:
53.7 cubic inches
Step-by-step explanation:
Use the volume formula for a square pyramid:
[tex]V = \dfrac{1}{3} (A_{\mathrm{base}} \cdot h)\\\\\mathrm{or} \\\\A = \dfrac{l^2h}{3}[/tex]
where l is the side length of the base and h is the height of the pyramid.
Now substitute in the given values:
[tex]V = \dfrac{1}{3}((11 \, \mathrm{in})^2 \cdot 15.1 \, \mathrm{in})[/tex]
[tex]V = \dfrac{1}{3}(121 \, \mathrm{in}^2 \cdot 15.1 \, \mathrm{in})[/tex]
[tex]V = \dfrac{1}{3}(1,821 \, \mathrm{in}^3)[/tex]
[tex]V = 53.7 \, \mathrm{in}^3[/tex]
So, the volume of the pyramid is 53.7 cubic inches.
New York City is a popular field trip destination. This year the senior class at High School A and
the senior class at High School B both planned trips there. The senior class at High School A
rented and filled 2 vans and 6 buses with 244 students. High School B rented and filled 4 vans
and 7 buses with 298 students. Every van had the same number of students in it as did the buses.
Find the number of students in each van and in each bus.
Answers
There are eight students in each van and 38 students are in each bus.
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
Let the number of students fit into a van would be v
And the number of students fit into a bus would be b
School A:
2v + 6b = 244 ...(i)
2v = 244 - 6b
v = 122 - 3b
School B:
4v + 7b = 298 ...(ii)
Substitute the value of v = 122 - 3b in the equation (ii),
4(122 - 3b) + 7b = 298
Solve for b to get b = 38.
Substitute the value of b = 38 in equation (i),
2v + 6(38) = 244
2v + 228 = 244
2v = 16
v = 8
Therefore, eight students are in each van and 38 students are in each bus.
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Graph the solution to the following system of inequalities.y>3x+7y≤−3x-8
Answers
Step 1. Graphing the first inequality.
The first inequality is:
[tex]y>3x+7[/tex]to graph this, we need to graph the line 3x+7, which compared with the slope-intercept equation
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept, the line
[tex]y=3x+7[/tex]is a line with a slope of 3 and a y-intercept at 7:
SInce the inequality is:
[tex]y>3x+7[/tex]The solution just for this inequality are the values greater than the red line, but not including the red line so we represent is a dotted line and a shaded part above:
Step 2. Graph the second inequality.
The second inequality is:
[tex]y\le-3x-8[/tex]As we did with the first inequality, we graph the line -3x-8 first.
comparing -3x-8 with the slope-intercept equation:
[tex]y=mx+b[/tex][tex]y=-3x-8[/tex]we can see that the slope m is -3 and the y-intercept b is -8. This line is shown in blue in the following diagram along with our results for the previous inequality:
Since the inequality form is:
[tex]y\le-3x-8[/tex]We shade the values below this blue line:
The final solution will be the intersection between the red part and the blue part:
Do the following lengths form an acute, right, or obtuse triangle? 99 90 39 O Acute, 7921 < 7921 Right, 7921 = 7921 Obtuse, 7921 > 7921
Answers
As we can see the interior angles of this triangle are less than 90° , therefore this triangle is an ACUTE TRIANGLE
A bakery makes and sells hot cocoa bombs during the holidays. The first 12 hot cocoa bombs of an order cost is $4.00 each. Each of the next 6 hot cocoa bombs cost $3.50 each. For orders exceeding 18, the cost drops to $3 each. The function C(x) represents the bakery's pricing.
Answers
Solution
Step 1
Given data for C(x), the bakery's pricing
[tex]\begin{gathered} F\text{or this range 0}\leq x\leq12ofhotcocoabombs\text{ we use C(x) =4x} \\ \text{For this range }1218,ofhotcocoabombs\text{ we useC(x) = }3x+15 \end{gathered}[/tex]Required
Step 1
To find the cost of 8 hot cocoa bombs
[tex]\begin{gathered} C(8)\text{ lies in the range 0}\leq x\leq12 \\ \text{Hence we use 4x where x = 8} \\ \text{The cost of 8 hot cocoa bombs = 4(8) = \$32} \end{gathered}[/tex]Step 2
To find the cost of 18 hot cocoa bombs
[tex]\begin{gathered} C(18)\text{ lies in the range 12}Step 3To find the C(30)
[tex]\begin{gathered} C(30)\text{ lies in the range x}\ge18 \\ \text{Hence we use 3x +15, where x = 30} \\ C(30)\text{ = 3(30) + 15 = 90 + 15 = \$105} \\ \end{gathered}[/tex]Step 4
What C(30) represents.
C(30) represents the cost of ordering 30 hot cocoa bombs which is $105
Describe the transformation of f(x) that produce g(x). f(x)= 2x; g(x)= 2x/3+7Choose the correct answer below.
Answers
The vertical translation involves shifting the graph either up or down on the y axis. For example.
[tex]\begin{gathered} y=f(x) \\ \text{translated upward }it\text{ will be } \\ y=f(x)+k \end{gathered}[/tex]When a graph is vertically compressed by a scale factor of 1/3, the graph is also compressed by that scale factor. This implies vertical compression occurs when the function is multiplied by the scale factor. Therefore,
[tex]\begin{gathered} f(x)=2x \\ \text{The vertical compression by a scale of }\frac{1}{3}\text{ will be} \\ g(x)=\frac{1}{3}(2x)=\frac{2}{3}x \end{gathered}[/tex]Finally, the vertical translation up 7 units will be as follows
[tex]g(x)=\frac{2}{3}x+7[/tex]The answer is a. There is a vertical compression by a factor of 1/3 . Then there is a vertical translation up 7 units.
What is 58 divided into 7275
Answers
Answer:125.431034
Step-by-step explanation:
Find P (A and B) for the following. P(A) = .65 and P(B) =.69 and P(A and B) =.48P(A and B)
Answers
We know that
[tex]\begin{gathered} P(A)=0.65 \\ P(B)=0.69 \end{gathered}[/tex]The probability of the intersection of the two events is:
[tex]P(AandB)=0.48[/tex]Answer:
GIven , P(A) = 0.65 P(B) = 0.69
Suppose that $2000 is invested at a rate of 2.8%, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 5 years.Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
Solution:
Given the amount invested, P; the rate, r, at which it was invested and the time, t, it was invested.
Thus,
[tex]\begin{gathered} p=2000, \\ \\ r=2.8\text{ \%}=0.028 \\ \\ t=5 \end{gathered}[/tex]Then, we would solve for the total amount, A, using the formula;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ Where; \\ n=4 \end{gathered}[/tex]Thus;
[tex]\begin{gathered} A=2000(1+\frac{0.028}{4})^{(4)(5)} \\ \\ A=2000(1.007)^{20} \\ \\ A=2299.43 \end{gathered}[/tex]ANSWER: $2,299.43
how many ones equal 4 tens
Answers
We have to find the number of ones in 4 tens.
As we know that, there are 10 ones in a 10.
Therefore, in 4 tens, the total number of ones would be 1 x 4 x 10 = 40
An airplane travels at 550 mph. How far does the airplane travel in 5 1/2 hours
Answers
Answer:
At a speed of 550mph, the airplane covers 3,025 miles in 5 1/2 hours.
Explanation:
Given:
• The speed of the airplane = 550 miles per hour
,• Time taken = 5 1/2 hours
We want to find out how far the airplane travels.
The distance covered is calculated using the formula:
[tex]Distance=Speed\times Time[/tex]Substitute the given values:
[tex]Distance=550\times5\frac{1}{2}[/tex]Simplify:
[tex]\begin{gathered} Distance=550\times\frac{11}{2} \\ =275\times2\times\frac{11}{2} \\ =275\times11 \\ =3025\text{ miles} \end{gathered}[/tex]The airplane covers 3,025 miles in 5 1/2 hours.
Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.
Answers
The probability that a randomly selected passenger have a waiting time greater than 2.25 minutes is .
in the question ,
it is given that
the waiting time is randomly distributed between 0 and 6 minutes .
Since it is uniformly distributed , the Uniform distribution have two bounds a and b .
The probability of finding the value greater than x can be calculated using the formula .
P(X>x) = (b-x)/(b-a)
Given that , the waiting time is Uniformly distributed 0 and 6 minutes , we get a=0 and b=6,
Substituting the values in the Probability formula , we get
P(X>2.25) = (6-2.25)/(6-0)
= 3.75/6
= 0.625
Therefore , the probability that a randomly selected passenger have a waiting time greater than 2.25 minutes is 0.625.
The given question is incomplete , the complete question is
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.
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I have the area of the circle but having trouble find the area of the triangle
Answers
To calculate the area of the triangle we need the length of the base and the height, being the height perpendicular to the base.
The base of the triangle has a length that is equal to the diameter of the circle. It can also be expressed as 2 times the radius r. So the base is:
[tex]b=2\cdot r=2\cdot4=8\operatorname{cm}[/tex]The height is the segment perpendicular to the base that goes up to the vertex at the top. as it goes from the center of the circle to the border of the circle, it has a length that is equal to the radius r:
[tex]h=r=4\operatorname{cm}[/tex]Then, we can calculate the area of the triangle as:
[tex]A=\frac{b\cdot h}{2}=\frac{8\cdot4}{2}=\frac{32}{2}=16\operatorname{cm}^2[/tex]We can calculate the area of the circle as:
[tex]A_c=\pi r^2\approx3.14\cdot4^2=3.14\cdot16=50.24[/tex]The probability that a randomly selected point within the circle falls in the white area is equal to the ratio of white area to the area of the circle.
The white area is equal to the area of the circle minus the area of the triangle.
Then, we can calculate the probability as:
[tex]p=\frac{A_w}{A_c}=\frac{A_c-A_t}{A_c}=\frac{50.24-16}{50.24}=\frac{34.24}{50.24}\approx0.68=68\%[/tex]Answer: The probability is p=0.68.
Find the lateral surface area and volume of the object in picture below
Answers
So first of all we have to find the lateral surface of the truncated pyramid. This surface is composed of 4 equal trapezoids. The are of a trapezoid is given by half the sum of its bases multiplied by its height. The large base of these faces are 6' long, the short base are 5' long and their height are 2.1' long. Then the area of each trapezoid is:
[tex]\frac{(6^{\prime}+5^{\prime})}{2}\cdot2.1^{\prime}=11.55in^2[/tex]Then the total lateral surface is:
[tex]11.55in^2\cdot4=46.2in^2[/tex]Then we need to find the volume of the truncated pyramid. This is given by the following formula:
[tex]\frac{1}{3}h(a^2+ab+b^2)[/tex]Where a and b are the bottom and top side of its two square faces and h is the height of the pyramid i.e. the vertical distance between bases. The lengths of the bases is 5' and 6' whereas the height of the pyramid is 2' then its volume is given by:
[tex]\frac{1}{3}\cdot2^{\prime}\cdot(5^{\prime2}+6^{\prime}\cdot5^{\prime}+6^{\prime2})=60.7in^3[/tex]In summary, the lateral surface is 46.2in² and the volume is 60.7in³.
which of the following liner equations passes through points (-1,5) and (1,5)?
Answers
Hence, the correct option is Option D. None of the choices are correct.
4(px+1)=64The value of x when p is -5 is ?
Answers
Answer:
x = -3
Explanation:
Given the equation:
[tex]4\left(px+1\right)=64[/tex]We are required to find the value of x when p is -5.
[tex]\begin{gathered} 4\left(px+1\right)=64\colon p=-5 \\ 4\left(-5x+1\right)=64 \\ -20x+4=64 \\ -20x=64-4 \\ -20x=60 \\ \text{Divide both sides by -20} \\ x=\frac{60}{-20} \\ x=-3 \end{gathered}[/tex]find the slope of the line that passes through (10,2) and (2,10)
Answers
The distance to the nearest exit door is less than 200 feet.
Answers
ANSWER
d < 200
EXPLANATION
If d is the distance to the nearest exit door, and this distance is less than 200 feet, then the inequality to represent this situation is d < 200.
The change in the value of a stock is represented by the rational number -5.90 describe in words what this means
Answers
The change in the value of a stock which is represented by the rational number -5.90 means that the stock decreased by 5.90 units.
Whenever we use negative value to describe change, it means that the value of that particular entity that been decreased by that number.
On the contrary, If we are using positive value to describe change, it means that the value of that particular entity that been increased by that number.
For example:- The change in total money possessed by Daniel is $ 50 means there is an increase of $ 50 in the money with Daniel.
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Hello! I need some help with this homework question, please? The question is posted in the image below. Q7
Answers
SOLUTION
Since -3 is a zero of the function then x=-3
This implies
x+3 is a factor of the polynomial
Following the same procedure, since 2 and 5 are zeros then
x-2 and x-5 are factors
Hence the polynomial can be written as
[tex]y=a(x+3)(x-2)(x-5)[/tex]Since the graph passes through the point (7,300)
Substitute x=7 and y=300 into the equation
This gives
[tex]300=a(7+3)(7-2)(7-5)[/tex]Solve the equation for a
[tex]\begin{gathered} 300=a(10)(5)(2) \\ 300=100a \\ a=\frac{300}{100} \\ a=3 \end{gathered}[/tex]Substitute a into the equation of the polynomial
[tex]y=3(x+3)(x-2)(x-5)[/tex]Therefore the answer is
[tex]y=3(x+3)(x-2)(x-5)[/tex]In ΔVWX, m∠V=(6x−4, m∠W=(x+12), and m∠X=(3x+2. Find m∠W.
Answers
The measure of angle W in the triangle is 29 degrees
How to determine the measure of angle W?The definition of the angles are given as
m∠V=(6x−4, m∠W=(x+12), and m∠X=(3x+2)
Where the triangle is given as
Triangle VWX
The sum of angles in a triangle is 180 degrees
This means that
V + W + X = 180
Substitute the known values in the above equation
So, we have
6x - 4 + x + 12 + 3x + 2 = 180
Evaluate the like terms
10x = 170
Divide by 10
x = 17
Substitute x = 17 in m∠W=(x+12)
So, we have
m∠W=(17+12)
Evaluate
m∠W = 29
Hence, the angle W is 29 degrees
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I NEED HELP WITH THIS ASAP ILL MARK YOU BRAINLIEST Put each set of numbers from greatest to least
Answers
Every number is equivalent to:
[tex]\begin{gathered} 7.18\times10^{-3}=0.00718 \\ \sqrt{\frac{25}{49}}=\frac{5}{7}=0.7143 \\ \frac{7}{10}=0.7 \\ 0.\bar{8}=0.8888 \\ \frac{3}{4}=0.75 \\ 80\text{ \% = 0.8} \end{gathered}[/tex]So, each number from greatest to least is:
[tex]0.\bar{8},80\text{ \%, }\frac{3}{4},\sqrt{\frac{25}{49}},\frac{7}{10},7.18\times10^{-3}[/tex]