What is the radius of Earth, in meters, written as a single-digit number multiplied by a power of 10?
Answers
Given:
The Radius of earth = 6,378,100 meters
To find:
The radius of earth in single-digit number multiplied by power of 10.
Step by step solution:
R = 6,378,100 meters
R = 6.3781 × 10^6
From here we have calculated the value of the radius in terms of single digit number.
Related Questions
14. Log(x)=2meansa. x=10b. x=2^10c. x=10^2d. x=0e. none of the above
Answers
Can you help me with this, I’ve already completed the assignment but trying to go back and figure out what I missed and what I did wrong
Answers
OK
the base in this case is an hexagone
we can find the area of the base with the following formula
[tex]A=\frac{3\sqrt{3}S^2}{2}[/tex]where S represent the side of the hexagone
s=20
[tex]A=\frac{3\sqrt{3}*20^2}{2}[/tex][tex]A=600\sqrt{3}=1039.23[/tex]Perimiter is given by 6*S
P=6*20=120
h=22
Given the following formula for the hexagone
[tex]A=\frac{p*a}{2}[/tex][tex]600\sqrt{3}=\frac{120*a}{2}[/tex]solving for a
[tex]a=\frac{2*600\sqrt{3}}{120}=10\sqrt{3}=17.32[/tex]applying pythagoras theorem
[tex]l^2=a^2+h^2[/tex][tex]l^2=(10\sqrt{3})^2+22^2[/tex][tex]l=\sqrt{784}=28[/tex]Lateral surface
[tex]LS=\frac{p*l}{2}[/tex][tex]LS=\frac{120*28}{2}=1680[/tex]Total surface
[tex]TS=LS+A[/tex][tex]TS=1680+600\sqrt{3}[/tex][tex]TS=2719.23048[/tex]Volume
[tex]V=\frac{1}{3}A*h[/tex][tex]V=\frac{1}{3}600\sqrt{3}*22[/tex][tex]V=4400\sqrt{3}=7621.02[/tex]Find the exact coordinates of the HOLE in this rational function: R (x)=×+1/×+(-1)
Answers
Four different stores have the same digital camera on sale. The original price and discounts offered by each store are listed below. Rank the stores from the cheapest to most expensive sale price of the camera.
Store A: price $99.99 and discount of 15%
Store B: price $95.99 and discount of 12%
Store C: price $90.99 and discount of 10%
Store D: price $89.99 and successive discounts of 5% and 5%
Answers
D<C<B<A; This is the correct ranking of the given stores in the order of cheapest to most expensive sale price of the camera as the definition of ascending order says, "Ascending order means to arrange numbers in increasing order, that is, from smallest to largest."
What is ascending order?The arrangement of numbers or other things in increasing order from smallest to largest is known as ascending order. Ascending order is demonstrated by numbers on a number line, which are listed from left to right. Usual representations include using commas or the "less-than symbol (<)" between numbers. For instance, 1, 2, 3, 4, or 5; or 1<2 <3 <4 <5.
Here,
Store A:
Price=$99.99
Discount=15%
Discount in dollar=$14.9985
Discounted price=$84.9915
Store B:
Price=$95.99
Discount=12%
Discount in dollar=$11.5188
Discounted price=$84.4712
Store C:
Price=$90.99
Discount=10%
Discount in dollar=$9.099
Discounted price=$81.891
Store D:
Price=$89.99
Discount=5% and after that 5%
net price after discount=$81.215
The price of store D is minimum that is $81.215.
According to the definition of ascending order, "Ascending order means to arrange numbers in increasing order, that is, from smallest to largest," this ranking of the given stores in order of cheapest to most expensive sale price of the camera is correct; D<C<B<A.
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What is the total paymentrequired to pay off a promissorynote issued for $700.00 at 12%ordinary interest and a 180-dayterm?A. $760.00B. $742.00C. $712.00D. $721.60
Answers
Given:
Promissory note issued for $700 at 12%.
[tex]P\text{ayment of 12\% for 700=}\frac{700\times\frac{6}{12}\times12}{100}[/tex][tex]\text{Payment for 12\% for 700= \$}42[/tex][tex]\text{Total payment required to pay off=}700+42[/tex][tex]\text{Total payment required to pay off= \$742}[/tex]Therefore, Option B is the correct answer.
Hello, I'm stuck on this.Question: Calculate the slant height of this come, identified by letter X. Give your answer to the nearest whole number.
Answers
The right triangle formed is shown below
To find the slant height, x, we would apply the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
Looking at the triangle,
hypotenuse = x
one leg = 12
other leg = 7
By applying the pythagorean theorem,
x^2 = 12^2 + 7^2 = 144 + 49 = 193
x = square root of 193
x = 13.89
Rounding to the nearest whole number,
x = 14
There can be no more than 100 people in the movie theater. There are already 22 people in the movie theater.What inequality represents the number of additional people, p, that can enter the movie theater?Drag and drop the appropriate symbols to correctly complete the inequality.
Answers
Answer:
[tex]p\text{ + 22}\leq\text{ 100}[/tex]Explanation:
Here, we want to drop the appropriate symbols
When we add the given number 22 to p, it would give a number which is at most 100
That means the number must be less than or equal to 100
mathematically, we have that as:
[tex]p\text{ + 22}\leq\text{ 100}[/tex]48. Mrs. Dalton is selling pieces of cake at the school carnival. She baked 8 cakes and cut them
each into 12 pieces. If she sold 81 slices of cake, how many total cakes does she have left?
Circle the correct option.
Answers
Total number of cakes left is 1.25 i.e. 1 and quarter.
Given,
Number of cakes = 8
Number of pieces of each cake =12
Number of slices sold = 81
Then,
Total number of slices of cake = [tex]12*8=96[/tex]
Now,
number of remaining slices =[tex]96-81=15[/tex]
To find number of remaining cake left, divide number of remaining slices to the pieces of each cake.
Number of remaining cake = [tex]\frac{15}{12} =1.25[/tex]
Thus, total number of cakes left is 1.25 i.e. 1 and quarter.
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Write the following ratio as a fraction in lowest terms. 36 to 38
Answers
Given:
Write the following ratio as a fraction in the lowest terms.
36 to 38
the ratio will be as follows:
[tex]36\text{ }to\text{ }38=\frac{36}{38}=\frac{2*18}{2*19}=\frac{18}{19}[/tex]So, the answer will be: 18/19
can anyone give me an example of plotting points with a real life word problem
Answers
Let's have an example of a seller that sells phones.
His salary have a fixed part of $50, and it increases by $2 by each phone he sells.
We want to find out how much will be his salary if he sells 5, 10 and 15 phones.
If we use the variable x to represent the number of phones sold, his salary (variable y) will be defined by the equation:
[tex]y=50+2x[/tex]Now, using the values of x we want to calculate, we have that:
[tex]\begin{gathered} x=5\colon \\ y=50+2\cdot5=50+10=60 \\ \\ x=10\colon \\ y=50+2\cdot10=50+20=70 \\ \\ x=15\colon \\ y=50+2\cdot15=50+30=80 \end{gathered}[/tex]We can plot these points to see how much his salary increases for each phone sold, and also we can have an idea of any point we want to find out:
Deon had $25 then he spent $15 on lunch. What percentage of his money did deon spend on lunch
Answers
Initial amount = $25
Amount spent on lunch = $15
The percentage of money spent on lunch
[tex]\frac{Amount\text{ spent}}{Initial\text{ amount}}\text{ x 100\%}[/tex][tex]\frac{15}{25}\text{ x 100 \%}[/tex][tex]\begin{gathered} \frac{1500}{25}^{} \\ =\text{ 60\%} \end{gathered}[/tex]Entrance Ticket on Translations Sarah graphed a triangle with vertices X (3,3) Y (4,1) Z (1,1). She asked her classmate Paul to translate the triangle (x-4) (y+2). Paul stated that the triangle will move down by 4 and right by 2 putting the triangle in the 4th quadrant. Graph the translation to see if Paul is correct? Explain your reasoning. Your explanation should include: • What is a translation? • Is Paul correct? Why or why not • Which direction should you move the triangle? • Which quadrant is the translation located?
Answers
The coordinates of the triangle XYZ are:
X(3,3)
Y(4,1)
Z(1,1)
The translation to perform is (x-4) and (y+2)
Translations are rigid transformations of a figure, this means that the triangle will move but won't change its shape or size.
A translation over the x axis results in a horizontal movement.
If you subtract a factor k x-coordinate, the movement will be to the left.
If you add the factor k x-coordinate, the movement will be to the rigth.
In this example the translation over the x-coordinate is (x-4) → 4 unit are being subtracted to the x-coordinate of each point, this results in a horizontal movement 4 units to the left
A translation over the y axis results in a vertical movement.
If you subtract a factor m from the y-coordinate, the movement will be downwards.
If you add the factor m from the y-coordinate, the movement will be upwards
In this example the translation over the y-coordinate is (y+2)→ 2 units were added to the y-coordinate, this results in a vertical movement 2 units up.
Paul moved the triangle 4 units down and 2 units right, he performed the wrong translation.
THe triangle was moved "left" and "up", the translation will be located in the second quadrant
High school band perform a concert on four different days bandsaw tickets each day as a fun raiser below the table shows the number of tickets sold in the amount collection of from sales slove with tablesHELPPP PLEASSEEEEEE
Answers
From the table given, Let's consider the third day
On the third day, 62 tickets were sold and $ 341 was collected
Then we can obtain the cost of a single ticket, which will be =
[tex]\frac{341}{62}[/tex]= $ 5.5
So 1 ticket cost $5.5
Then we can fill in the table
PART A
PART B
The equation that can be used to find y, the amount of money collected can be obtained since we know the cost of a single ticket which is $ 5.5
[tex]\begin{gathered} y\text{ = 5.5x} \\ \text{where x is the number of tickets sold} \end{gathered}[/tex]PART C
A dependent variable represents a quantity whose value depends on how the independent variable is manipulated.
From the equation
y = 5.5 x
y = Amount of money collected
x = Number of tickets
Since y (Amount collected) depends on x (the number of tickets sold)
y is the dependent variable
x is the independent variable
Part D
The relationship is that:
The amount of money that will be collected is dependent on the number of tickets sold.
since each ticket costs $5.5, then the amount realized is $5.5 multiplied by the number of tickets
Can you please help me with 28 Please give all end behavior such as limits and as_,_
Answers
We must describe the local and end behaviour of the function:
[tex]f(x)=\frac{x^2-4x+3}{x^2-4x-5}.[/tex]First, we rewrite the polynomials in numerator and denominator in terms of their roots:
[tex]f(x)=\frac{(x-1)\cdot(x-3)}{(x+1)\cdot\mleft(x-5\mright)}\text{.}[/tex]Local behaviour
We see that f(x) has a zero in the denominator for x = -1 and x = 5. The function f(x) has vertical asymptotes at these values. To analyze the local behaviour, we must compute the lateral limits for x → -1 and x → 5.
Limit x → - 1 from the left
Computing the limit from the left when x → -1, is equivalent to replacing x by -1 - ε and computing the limit when ε → 0:
[tex]\begin{gathered} \lim _{x\rightarrow-1^-}f(x)=\lim _{\epsilon\rightarrow0}f(-1-\epsilon) \\ =\lim _{\epsilon\rightarrow0}\frac{(-1-\epsilon-1)\cdot(1-\epsilon-3)}{(-1-\epsilon+1)\cdot(-1-\epsilon-5)} \\ =\lim _{\epsilon\rightarrow0}\frac{(-2)\cdot(-2)}{(-\epsilon)\cdot(-6)}\rightarrow+\infty. \end{gathered}[/tex]In the last step, we can't throw the ε in the parenthesis different to zero.
Limit x → - 1 from the right
Computing the limit from the left when x → -1, is equivalent to replacing x by -1 + ε and computing the limit when ε → 0:
[tex]\begin{gathered} \lim _{x\rightarrow-1^+}f(x)=\lim _{\epsilon\rightarrow0}f(-1+\epsilon) \\ =\lim _{\epsilon\rightarrow0}\frac{(-1+\epsilon-1)\cdot(1+\epsilon-3)}{(-1+\epsilon+1)\cdot(-1+\epsilon-5)} \\ =\lim _{\epsilon\rightarrow0}\frac{(-2)\cdot(-2)}{(+\epsilon)\cdot(-6)}\rightarrow-\infty. \end{gathered}[/tex]In the last step, we can't throw the ε in the parenthesis different to zero.
Limit x → 5 from the left
Computing the limit from the left when x → 5, is equivalent to replacing x by 5 - ε and computing the limit when ε → 0:
[tex]\begin{gathered} \lim _{x\rightarrow-1^-}f(x)=\lim _{\epsilon\rightarrow0}f(-1-\epsilon) \\ =\lim _{\epsilon\rightarrow0}\frac{(5-\epsilon-1)\cdot(5-\epsilon-3)}{(5-\epsilon+1)\cdot(5-\epsilon-5)} \\ =\lim _{\epsilon\rightarrow0}\frac{(+4)\cdot(+2)}{(+4)\cdot(-\epsilon)}\rightarrow-\infty. \end{gathered}[/tex]In the last step, we can't throw the ε in the parenthesis different to zero.
Limit x → 5 from the right
Computing the limit from the left when x → 5, is equivalent to replacing x by 5 + ε and computing the limit when ε → 0:
[tex]\begin{gathered} \lim _{x\rightarrow-1^-}f(x)=\lim _{\epsilon\rightarrow0}f(-1-\epsilon) \\ =\lim _{\epsilon\rightarrow0}\frac{(5+\epsilon-1)\cdot(5+\epsilon-3)}{(5+\epsilon+1)\cdot(5+\epsilon-5)} \\ =\lim _{\epsilon\rightarrow0}\frac{(+4)\cdot(+2)}{(+4)\cdot(+\epsilon)}\rightarrow+\infty. \end{gathered}[/tex]In the last step, we can't throw the ε in the parenthesis different to zero.
End behaviour
To describe the end behaviour of the function, we must compute the limits of the function when x → -∞ and x → +∞.
Limit x → -∞
[tex]\begin{gathered} \lim _{x\rightarrow-\infty^{}}f(x)=\lim _{x\rightarrow-\infty^{}}\frac{x^2-4x+3}{x^2-4x-5} \\ =\lim _{x\rightarrow-\infty}\frac{x^2-4x+3}{x^2-4x-5}=\frac{\lim _{x\rightarrow-\infty}\frac{x^2-4x+3}{x^2}}{\lim _{x\rightarrow-\infty}\frac{x^2-4x-5}{x^2}}=\frac{1}{1}=1. \end{gathered}[/tex]To compute the limit we have divided numerator and denominator by x² and distributed the limit. The result of each limit is given by the leading term, which has the highest power of x.
Limit x → +∞
[tex]\begin{gathered} \lim _{x\rightarrow+\infty^{}}f(x)=\lim _{x\rightarrow+\infty^{}}\frac{x^2-4x+3}{x^2-4x-5} \\ =\lim _{x\rightarrow+\infty}\frac{x^2-4x+3}{x^2-4x-5}=\frac{\lim_{x\rightarrow+\infty}\frac{x^2-4x+3}{x^2}}{\lim_{x\rightarrow+\infty}\frac{x^2-4x-5}{x^2}}=\frac{1}{1}=1. \end{gathered}[/tex]To compute the limit we have divided numerator and denominator by x² and distributed the limit. The result of each limit is given by the leading term, which has the highest power of x.
AnswersLocal behaviour
The function f(x) has vertical asymptotes at x = -1 and x = 5.
[tex]\begin{gathered} \lim _{x\rightarrow-1^-}f(x)=+\infty \\ \lim _{x\rightarrow-1^+}f(x)=-\infty \\ \lim _{x\rightarrow5^-}f(x)=-\infty \\ \lim _{x\rightarrow5^+}f(x)=+\infty \end{gathered}[/tex]End behaviour
[tex]\begin{gathered} \lim _{x\rightarrow-\infty^{}}f(x)=1 \\ \lim _{x\rightarrow+\infty^{}}f(x)=1 \end{gathered}[/tex]Write an equation for the line parallel to g(x)= -2x-6 and passing through the point (7, 4) Write the answer in slop intercept form.
Answers
The slope-intercept form is:
[tex]y=mx+c[/tex]So first we will find the gradient:
Parallel lines have the same gradient:
[tex]\begin{gathered} g(x)=-2x-6 \\ \text{The gradient from the equation above is -2} \end{gathered}[/tex]So now that we know the gradient of the line as -2, we will then find the equation of the line using the formula below as it passes through (7,4):
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{From (7,4)} \\ x_1=7,y_1=4 \\ y-4=-2(x-7) \\ y-4=-2x+14 \\ y=-2x+14+4 \\ y=-2x+18 \end{gathered}[/tex]Use the data in the following table, which shows the results of a survey of 2000 gamers concerning their favorite home video game systems, organized by age group. If a survey participant is selected at random, determine the probability of the following. Round to the nearest hundredth.The participant prefers the Nintendo Wii U system.
Answers
0.30
Explanations:What is probability?Probability is the likelihood or chance that an event will occur. Mathematically:
[tex]Probability=\frac{n(E)}{n(S)}[/tex]where:
• n(E) is the ,expected outcome
,• n(S) is the ,total outcome
Since the results shows a total survey of 2000 gamers, hence the total outcome is 2000.
Determine the total participant that prefers Nintendo Wii U system
Total participant that refers Nintendo Wii U system = 64 + 103 + 246 + 193
Total participant that refers Nintendo Wii U system n(E) = 606
Determine the required probability
[tex]\begin{gathered} Pr(participant\text{ prefers the Nintendo})=\frac{606}{2000} \\ Pr(participant\text{ prefers the Nintendo})=0.303 \\ Pr(participant\text{ prefers the Nintendo})\approx0.30 \end{gathered}[/tex]Hence the probability the participant prefers the Nintendo Wii U system is 0.30
If you were to solve the following system by substitution, what would be the best variable to solve for and from what equation? 3x + 6v=9 2x – 10v=13
Answers
The best variable to solve is x=3-2v, after dividing the first equation by 3.
x=4, and v=-1/2
1) Solving that system by Substitution
2) Making then
x=3-2v
2x-10v=13
3) Plugging into the 2nd equation
2(3-2v)-10v=13
6-4v -10v=13
6-14v=13
-14v=13-6
-14v=7
v=-1/2
Plugging into the first equation
x=3-2v
x=3-2(-1/2)
x=3+1
x=4
Question 1.) d.) how to find instantaneous rate of change if x= 2pi
Answers
Explanation
We are given the following function:
[tex]f(x)=3\cos2x[/tex]We are required to determine the instantaneous rate of change at x = 2π.
This is achieved thus:
[tex]\begin{gathered} f(x)=3\cos2x \\ \frac{\triangle f(x)}{\triangle x}=3\cdot-2\sin2x \\ \frac{\operatorname{\triangle}f(x)}{\operatorname{\triangle}x}=-6\sin2x \\ \text{ At the point }x=2\pi \\ \frac{\operatorname{\triangle}f(x)}{\operatorname{\triangle}x}=0 \end{gathered}[/tex]Hence, the answer is:
[tex]\frac{\operatorname{\triangle}f(x)}{\operatorname{\triangle}x}=0[/tex]Area of Triangles What is the area of this triangle? bh A 0 24 in? 8 in O 30 in 48 in 96 in
Answers
Given the triangle:
We're going to find its area.
To do this, we just multiply the base of the triangle by its height and then divide this result by 2:
[tex]A=\frac{6in\cdot8in}{2}=24in^2[/tex]Therefore, the area equals 24 in2.
1)Lin solved the equation incorrectly. Find all the errors in her solution. (Select all appropriate answers.)Given to Step 1: Lin calculated 4 - 17 incorrectly; should be -13.Step 1 to Step 2: Lin distributed 8(x - 3) incorrectly; should be 8x - 3.Step 2 to Step 3: Lin calculated 8x - 24 + 7 incorrectly; should be 8x - 31.Step 3 to Step 4: Lin should have subtracted 8x from each side; should be 18x.What should Lin's answer have been ?8 ( x - 3 ) + 7 = 2x ( 4 - 17 )answer choices :x = 3/2 x = 1/2x = 1/5x = 1/3
Answers
Answer:
Given to Step 1: Lin calculated 4 - 17 incorrectly; should be -13.
Step 3 to Step 4: Lin should have subtracted 8x from each side; should be 18x.
Lin's answer should be x = 1/2
Explanation:
The initial expression is:
8(x - 3) + 7 = 2x(4 - 17)
So, the first error is in step 1, because 4 - 17 = - 13, then step 1 should be:
8(x - 3) + 7 = 2x(-13)
Then, we can apply the distributive property as:
8x - 8(3) + 7 = -26x
8x - 24 + 7 = -26x
We need to add similar terms:
8x - 17 = - 26x
Then, we can subtract 8x from both sides as follows:
8x - 17 - 8x = - 26x - 8x
-17 = -34x
Finally, we can divide by -34 as follows:
-17/(-34) = -34x/(-34)
1/2 = x
Therefore, the answers are:
Given to Step 1: Lin calculated 4 - 17 incorrectly; should be -13.
Step 3 to Step 4: Lin should have subtracted 8x from each side; should be 18x.
Lin's answer should be x = 1/2
Without graphing, identify the vertex, axis of symmetry, and transformations from the parent function f(x)= |x|y = |x-5|-1
Answers
Answer:
• Vertex: (5, –1)
,• No symmetry
,• Transformations: 5 units to the right, and 1 unit down.
Explanation
We are given the parent function f(x)= |x| and the transformed function:
[tex]y=|x-5|-1[/tex]Thus, we can get the vertex considering that a function in the form:
[tex]y=|x\pm a|\pm b[/tex]has a vertex at (+a, ±b).
Therefore, our vertex is at (5, –1). Additionally, as an absolute function has the form of a 'v', and as the vertex is at (5, –1) then it has no symmetry about the x-axis, nor y-axis, and nor about the origin, meaning it has no symmetry.
Finally, the transformation from the parent function is a shift 5 units to the right and one unit down.
Answer:
Answer:
• Vertex: (5, –1)
,
• No symmetry
,
• Transformations: 5 units to the right and 1 unit down.
Explanation
We are given the parent function f(x)= |x| and the transformed function:
Thus, we can get the vertex considering that a function in the form:
Has a vertex at (+a, ±b).
Therefore, our vertex is at (5, –1). Additionally, as an absolute function has the form of a 'v', and as the vertex is at (5, –1) then it has no symmetry about the x-axis, nor y-axis, nor about the origin, meaning it has no symmetry.
Finally, the transformation from the parent function shifts 5 units to the right and one unit down.
Step-by-step explanation:
For a given geometric sequence, the common ratio, r, is equal to 5, and the 7th term, an, is equal to -43. Find the value of the 9thterm, a9. If applicable, write your answer as a fraction.a9=
Answers
Given:
it is given that common ration of a geometric sequence is r = 5 and 7th term is - 43.
Find:
we have to find the value of 9th term.
Explanation:
we know the formula for nth term of a geometric sequence is
[tex]a_n=ar^{n-1}[/tex]since, 7the term is - 43,
Therefore, we have
[tex]\begin{gathered} a_7=-43 \\ ar^{7-1}=-43 \\ ar^6=-43 \\ a(5)^6=-43 \\ a(15625)=-43 \\ a=-\frac{43}{15625} \end{gathered}[/tex]The 9the term of the geometric sequence is
[tex]\begin{gathered} a_9=-\frac{43}{15625}\times(5)^{9-1} \\ =-\frac{43}{15625}\times(5)^8 \\ =-\frac{43}{(5)^6}\times(5)^8 \\ =-43\times25 \\ a_9=-1075 \end{gathered}[/tex]Therefore, 9th term of given geometric sequence is -1075.
The list price for a case of medicine is $275.49 Your pharmacy will receive a 18% trade discount. What is the amount of the discount? b) What is the net cost of the case of medicine?
Answers
The amount of the discount is $49.59, and the net cost after the discount is applied is $225.90.
What is the amount of the discount?If we have a original price P and we apply a discount of X, where X is a percentage, the amount of the discount is given by the formula:
D = P*(X/100%)
In this case, the original price is $275.49 and the discount is of 18%, then the amount of the discount is:
D = $275.49*(18%/100%) = $275.49*0.18 = $49.59
b) To get the net cost we need to take the difference between the original price and the amount of the discount, we will get:
net cost = $275.49 - $49.59 = $225.90
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i need help with question 2
Answers
To find the vertex (h,k), we have to find h using the following formula
[tex]h=-\frac{b}{2a}[/tex]Where a = 1 and b = -10.
[tex]h=-\frac{-10}{2\cdot1}=5[/tex]Then, we find k by evaluating the function when x = 5.
[tex]y=5^2-10\cdot5+9=25-50+9=-16[/tex]Hence, the vertex is (5,-16).The axis of symmetry is given by the h coordinate of the vertex.
Hence, the axis of symmetry is x = 5.The y-intercept is found when x = 0.
[tex]y=0^2-10\cdot0+9=9[/tex]The y-intercept is (0,9).The x-intercepts are found when y = 0.
[tex]x^2-10x+9=0[/tex]To solve this expression, we have to look for two numbers which product is 9, and which addition is 10. Those numbers are 9 and 1.
[tex](x-9)(x-1)=0[/tex]Then, we use the zero product property to express both solutions
[tex]\begin{gathered} x-9=0\rightarrow x=9 \\ x-1=0\rightarrow x=1 \end{gathered}[/tex]Hence, the x-intercepts are (9,0) and (1,0).The minimum value is defined by the k coordinate of the vertex.
Therefore, the minimum value of the function is -16.The domain of the function would be all real numbers because quadratic functions don't have any domain restrictions.
[tex]D=(-\infty,\infty)[/tex]The range of the function is determined by the vertex, given that the parabola opens upwards, then the range is
[tex]R\colon\lbrack-16,\infty\rbrack[/tex]Can you please help me
Answers
Step 1
A rectangle is a quadrilateral with the parallel opposite two sides being equal and with each vertex being 90°. The sum of angles in a rectangle is 360°. It has 2 diagonals.
Step 2
Derive an answer from the statement in step 1
The consecutive sides are perpendicular is the only right option.
Hence option D
Lauren uses1/3cup of carrot juice for every2/3cup of apple juice to make a fruit drink.Enter the number of cups of carrot juice Lauren uses for 1 cup of apple juice,
Answers
1/3 cup of carrot juice ---------------------------------->2/3 cup of apple juice
x cups of carrot juice ----------------------------------->1 cup of apple juice
Using cross multiplication:
[tex]\frac{\frac{1}{3}}{x}=\frac{\frac{2}{3}}{1}[/tex]solve for x:
[tex]\begin{gathered} x=\frac{\frac{1}{3}}{\frac{2}{3}} \\ x=\frac{3}{6} \\ x=\frac{1}{2} \end{gathered}[/tex]She uses 1/2 cups of carrot juice for 1 cup of apple juice
If anyone can answer this question I will be surprised
Answers
A reflection through x-axis is the property to get a point and transform it like this:
[tex]\begin{gathered} P\rightarrow P^{\prime} \\ (x,y)\rightarrow(x,-y) \end{gathered}[/tex]If we have point P = (3,4), its reflexion through x-axis will be:
[tex]\begin{gathered} P\rightarrow P^{\prime} \\ (x,y)\rightarrow(x,-y) \\ (3,4)\rightarrow(3,-4) \end{gathered}[/tex]So our final answer will be:
[tex](3,-4)[/tex]write the er exponent expression forty-one to the seventh power
Answers
Write the exponential expression, forty one to the seventh power;
[tex]41^7[/tex]List each real zero of f according to the behavior of the graph at the x-axis near that zero. Zero(s) where the graph crosses the x-axis:Zero(s) where the graph touches, but does not cross the x-axis:
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In the graph, there are 2 zeros, one for each type.
The zero where the graph crosses the x axis is 1. When x=1, the function intercepts the x axis and crosses it.
The zero where the graph touches but does not cross the x axis is -1. When x=-1, the function touches x axis but goes back to the quadrant.
HiThe scatter plot shows a hiker's elevation above sea level during a hike from the base to the
top of a mountain. The equation of a trend line for the hiker's elevation is y = 7.96x +676, where x
represents the number of minutes and y represents the hiker's elevation in feet. Use the equation of
the trend line to estimate the hiker's elevation after 170 minutes.
Answers
Answer:
2029.2 ft
Step-by-step explanation:
If x represents the number of minutes, then all you have to do is plug in 170 ( the number of minutes ) into the equation.
y = 7.96 (170) + 676
y = 1353.2 + 676
y = 2029.2
y represents the hiker's elevation in feet, so the answer would be 2029.2 ft.
let me know if anything is confusing :-))