The sun's diameter as described in the task content is; ; 1.09 × 10⁵ times the earth's diameter.
This follows from the given premise that; the diameter of the sun is approximately 1.4x10⁹ Km and the diameter of Earth is approximately 1.28x10⁴ Km
By how much is the sun's diameter greater than the earth's diameter?According to the task content; The diameter of the sun is approximately 1.4x10^9 Km and the diameter of Earth is approximately 1.28x10^4 Km.
The number of times by which the sun's diameter is greater than the earth's diameter can be evaluated as follows;
= 1.4 × 10⁹/1.28 × 10⁴
= 1.09 × 10⁵
Ultimately, The sun's diameter as described in the task content is; 1.09 × 10⁵ times the earth's diameter.
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F(x)=x-5 and g(x)=x2 - 1 find
The value of the given functions are:
(i) f + g = x² + x - 6
(ii) f - g = -x² + x - 4
(iii) f . g = x³ - 5x² - x + 5
(iv) f/g = ( x - 5)/(x +1)(x - 1)
(v) g(f(x)) = x² - 10x + 24
The two functions are given that
f(x) = x - 5
g(x) = x² - 1
We have to find
(i) f + g
f(x) + g(x) = ( x-5) + (x² - 1)
= x² + x -5 -1
= x² + x -6
(ii) f - g
f(x) - g(x) = (x-5)- (x² - 1)
= -x² + x -5 +1
= -x² + x -4
(iii) f . g
f(x) . g(x) = (x-5)(x²-1)
=x(x² - 1) -5(x² - 1)
= x³ - x - 5x² + 5
= x³ - 5x² - x + 5
(iv) f/g
f(x) / g(x) = (x-5) / ( x² - 1)
= (x - 5) / (x+1)(x-1)
(v) g(f(x)) = - 1 + ( -5 + x )²
= -1 + 25 + x² - 10x
= x² - 10x + 24
Therefore we get the value of the function, (i) f + g = x² + x - 6, (ii) f - g = -x² + x - 4,(iii) f . g = x³ - 5x² - x + 5, (iv)f/g = ( x - 5)/(x +1)(x - 1), (v) g(f(x)) = x² - 10x + 24.
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The complete question is:
F(x)=x-5 and g(x)=x2 - 1 find (i) f + g , (ii) f-g, (iii) f. g (iv) f/g (v) g(f(x)).
A linear function, f(x)+2x+3, is transformed to g)x)=2x-5 . What transformation occurred?
Step-by-step explanation:
The function f was shifted 8 units to the right to obtain g.
√80 in the number line
√80 on the number line would be marked at (8.94, 0) on the number line.
Hope this graph helps!
Given right triangle ABC, what is the value of tan(A)?
5/13
12/13
12/5
13/12
Answer: 13/12 times 12/4 is the answer
Express the inequality using interval notation.
161 6.)
Interval Notation:
-7 < x < -4
8
The inequality using interval notation are (-7, -4).
What is defined as the interval notation?An interval is represented on a number line using interval notation.
In those other sayings, it is a method of writing real number line subsets. An interval is made up of numbers that fall between two specific data set.For instance, the set of digits x satisfying 0 ≤ x ≤ 8 is an interval containing 0, 8, as well as all numbers between 0 and 8.Open intervals: The endpoints of a inequality are not included in this type of interval. This is written in open interval notation: (-3, 1).closed intervals: The endpoints of a inequality are included in this type of interval. This is written in closed interval notation as [-3,1].For the given expression;
-7 < x < -4
As, x > -7; x is not equal to -7.
x < -4; here also x is not equal to -4.
So, the is a condition of open interval where both vales are not taken.
Thus, the intervals are written as; (-7, -4).
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Find the first order differential eqn of y
dy/dx = y(x² + 1)
Answer:
[tex]\large\text{$y=ke^{\frac{1}{3}x^3+x}$}[/tex]
Step-by-step explanation:
Given differential equation:
[tex]\large\text{$\dfrac{\text{d}y}{\text{d}x}=y(x^2+1)$}[/tex]
Rearrange the equation so that all the terms containing y are on the left side, and all the terms containing x are on the right side:
[tex]\large\text{$\implies \dfrac{1}{y}\;\text{d}y=(x^2+1)\;\text{d}x$}[/tex]
Integrate both sides, remembering to add the constant of integration (C):
[tex]\large\begin{aligned}\implies \displaystyle \int\dfrac{1}{y}\;\text{d}y & =\int(x^2+1)\;\text{d}x\\\ln y & = \dfrac{1}{3}x^3+x+\text{C}\end{aligned}[/tex]
Rewrite C as ln k:
[tex]\large\text{$\implies \ln y = \dfrac{1}{3}x^3+x+\ln k$}[/tex]
Solve for y, applying:
[tex]\textsf{Log rule}: \quad e^{\ln a}=a[/tex][tex]\textsf{Exponent rule}: \quad \:a^{b+c}=a^ba^c[/tex][tex]\large\text{$ \implies e^{\ln y} =e^{\frac{1}{3}x^3+x+\ln k}$}[/tex]
[tex]\large\text{$ \implies y=e^{\ln k} \cdot e^{\frac{1}{3}x^3+x}$}[/tex]
[tex]\large\text{$\implies y=ke^{\frac{1}{3}x^3+x}$}[/tex]
Integration rules
[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Integrating $\frac{1}{x}$}\\\\$\displaystyle \int \dfrac{1}{x}\:\text{d}x=\ln |x|+\text{C}$\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5.1 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\\\(where $n$ is any constant value) \end{minipage}}[/tex]
Answer:
[tex]{ \tt{ \frac{dy}{dx} = y( {x}^{2} + 1) }} \\ [/tex]
- Simplify by collecting each term according to its corresponding d
[tex]{ \tt{ \frac{dy}{y} = ( {x}^{2} + 1) \: dx}} \\ [/tex]
- Integrate both sides;
[tex]{ \tt{ \int \frac{1}{y} \: dy = \int ( {x}^{2} + 1) \: dx }} \\ \\ { \tt{ ln(y) = \frac{1}{3} {x}^{3} + x + c }}[/tex]
- To make y the subject, you must remove the natural log;
[tex]{ \tt{ log_{e}(y) = \frac{1}{3} {x}^{3} + x + c }} \\ \\ { \tt{y = {e}^{( \frac{1}{3} {x}^{3} + x + c) } }} \\ [/tex]
If a cat went 7/16 actoss the yard how much further does it have to go to reach the gate
Using proportions, it is found that the cat has to go 9/16 further to reach the gate.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
An entire distance is represented by the proportion of 1 = 100%. The cat has gone 7/16 of the distance, hence the fraction corresponding to the remaining distance that he has to go is given by:
1 - 7/16 = 16/16 - 7/16 = 9/16.
Hence the cat has to go 9/16 further to reach the gate.
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hello help me with question b
[tex] \bf\longrightarrow \large\frac{ \frac{ \frac{a( {r}^{4} - 1)}{ \cancel{r - 1}} }{a( {r}^{2} - 1) } }{ \cancel{r - 1}} = 10 \\ [/tex]
[tex]\bf\longrightarrow {r}^{4} - 1 = {10r}^{2} - 10[/tex]
[tex]\bf\longrightarrow {r}^{4} - {10r}^{2} + 9 = 0[/tex]
Put a = r²[tex]\bf\longrightarrow \: {a}^{2} - 10 {a}^{2} + 9 = 0[/tex]
[tex]\bf\longrightarrow \: a = \frac{10± \sqrt{100 - 36} }{2} = \frac{10±8}{2} [/tex]
a = 9 or a = 1r = 3 or r = 1 but r ≠ 1
[tex]\therefore[/tex] r = 3
[tex]\bf\longrightarrow \: a_3 = 54 \\ \bf\longrightarrow \: a {r}^{2} = 54 \\ \bf\longrightarrow \: a = \frac{54}{9} = 6[/tex]
How do you break apart the factor 56 using place
values
Answer:
Step-by-step explanation:
go
Find the area of the circle.
Use 3.14 for π. Do not round your answer.
Hint: A = πr²
6 inches
Area = [?] inches²
Enter the number that
belongs in the green box.
Answer:
28.26 inches^2
Step-by-step explanation:
The area of a circle is given by the formula [tex]A = \pi r^2[/tex].
We know that the diameter of the circle is 6 inches, therefore, its radius 3 inches (the radius is exactly one half of the circle's diameter).
Substituting into the formula
[tex]A = \pi r^2 \\ \\\to A = \pi \times 3^2 \\ \\\to A = \pi \times 9 = 28.26[/tex]
Which of the functions below could have created this graph?
+
OA. F(x)=x2
OB. F(x)=-¹-4
O C. F(x)=x²+2x-2
OD. F(x)=3x³ +2x²
Answer:
only D is negative on the leading term
Step-by-step explanation:
even roots bounce at (0,0)
negative leading coefficient: initial graph descending to right, curve up
4 local extremes means remaining 5 degree of the function
A car salesman sells cars with prices ranging from $5,000 to $45,000. The histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years.
The salesman has observed that many students are looking for cars that cost less than $5,000. If he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years, how will the distribution be affected?
Answer:
The mean will move to the left as more affordable vehicles are introduced.
Step-by-step explanation:
It is given that a car salesman sells cars with prices ranging from $5,000 to $45,000. The histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years.
We need to find how will the distribution be affected if he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years.
Now, let us understand what is meant by mean;
What is the Mean ?
The mean of a set of data is its average value.
Further, It is given that the car salesman sells cars with prices ranging from $5,000 to $45,000.
Additionally, the salesperson has noticed that a lot of students are searching for vehicles around $5,000.
If he chooses to sell vehicles as well and anticipates selling 200 of them over the following ten years,
The histogram will deviate from its mean if cards with values less than $5,000 are also included in the data set.
The mean will move to the left as more affordable vehicles are introduced.
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lim
T-44
√x+5-7
x - 44
[tex]\displaystyle \lim_{x\to 44}~\cfrac{\sqrt{x+5}-7}{x-44}\hspace{5em}\stackrel{\textit{L'Hopital's rule}}{\lim_{x\to 44}~\cfrac{ ~~ \frac{d}{dx}[\sqrt{x+5}-7] ~~ }{\frac{d}{dx}[x-44]}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{d}{dx}[\sqrt{x+5}-7]\implies \cfrac{1}{2}(x+5)^{-\frac{1}{2}}(1)\implies \cfrac{1}{2\sqrt{x+5}} \\\\\\ \cfrac{d}{dx}[x-44]\implies 1 \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{x\to 44}~\cfrac{\sqrt{x+5}-7}{x-44}\implies \lim_{x\to 44}~\cfrac{ ~~ \frac{1}{2\sqrt{x+5}} ~~ }{1}\implies \lim_{x\to 44}~\cfrac{1}{2\sqrt{x+5}}\implies \cfrac{1}{2\sqrt{44+5}} \\\\\\ \cfrac{1}{2\sqrt{49}}\implies \cfrac{1}{2(7)}\implies \cfrac{1}{14}[/tex]
angelina determined that her father’s age is 4 less than 3 times her age. If x represents angelina’s age, write an expression for her father’s age
Answer:
4 - 3x
Step-by-step explanation:
please mark me as brainliest
Answer:
3x-4= Y
Y= her dad's age.
There are 52 candies in a packet, about how many packets would 22 packets contain? Estimate the answer by rounding off the numbers to the nearest ten.
After rounding, we can say that there are about 1,140 candles in the 22 packets.
About how many packets would 22 packets contain?First let's get the exact number, and then round it as we need to do.
We know that each packet contains 52 candles, and there are 22 packets, so the total number of candles is given by the product between these two values, which gives:
C = 52*22 = 1,144 candles.
Now we want to round it to the nearest ten, to do so, we need to look at the digit at the right of the tens unit (in this case the ones digit) and see, if it is 5 or more, we round up, if it is 4 or less, we round down.
We can see that it is a 4, so we round down here:
C = 1,140
There are about 1,140 candles in the 22 packets.
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Even counting numbers less than 10
Answer:
2, 4 6, 8
Step-by-step explanation:
The counting numbers are the set of numbers: 1,2,3,4,... It follows that pattern forever. No, 1/2 or .0745.
Answer:
2 4 6 8 is the answer for your question
On a spring day the temperature outside is 68 degrees F. What is this in Celsius? (Write your answer
as a whole number.)
Question
Find the rate if a principal of $5,875 earned $1,645 interest in 4 years. Round to the nearest whole percent.
The yearly interest rate percentage is 7%
The rate of interest can be found dividing the interest and the product of the principal and time period which can be written as
R = I / PT
where R is the Rate of interest
I is the Interest
P is the Principal amount
T is the time period.
Given values are
P = $5,875
I = $1,675
T = 4 years
Then,
R = I/PT
= 1,645/(5,875 x 4)
= 1645 / 23500
= 0.07
The Yearly interest rate percentage is
=0.07 x 100
= 7%
Therefore, the yearly rate percentage is 7%
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A truck can be rented from Company A for $120 a day plus $0.50 per mile. Company B charges $80 a day plus $0.60 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
what is the equation for the line with slope (rate of change) 2/3 and y-intercept 9
Answer:
y = 2/3x + 9
Step-by-step explanation:
The equation of a line is defined as y = mx + b
with m being the slope, and b being he intercept.
So to figure out the equation for the line with a slope of 2/3 and an intercept of 9, we can just plug those values into our line equation!
So take y = (slope)*x + *(intercept)
and plug your values in and you get...
y = 2/3 * x + 9
Answer: the answers for the quiz are
1. What is the slope (rate of change) of the line in the graph show below? Answer is A. -2
2. Find the slope (rate of change) of a line that passes through (-2, -3) and (1, 1). Answer is D. 4/3
3. constant of variation of -4y=8x answer is B. -2
4 the value of y when x=10 answer is B. 30
5. the equation for the line with slope 2/3 and y-intercept 9 answer is C. y=2/3x+9
6 is the equation in slope intercept form for the line that passes through the points (1, -3) and (3, 1) answer is D. y=2x-5
Step-by-step explanation:
What is the slope of the line?
Answer:
Slope = (-7/4)
Step-by-step explanation:
Point 1: (-3, 4); Point 2: (1, -3)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -3 - 4 -7 -7
m = ----------- = ----------- = ----------- = ------
x₂ - x₁ 1 - (-3) 1 + 3 4
I hope this helps!
Choose the symbol that makes the statement true
A. >
B. <
C. =
PLEASE HELP THANK YOU :)))
Answer:
C. =
Step-by-step explanation:
This is because 18% is 18/100. You could find the answer one of two ways. Divide by two or multiply by 2.
The scale from a playground to this drawing is 5 ft to 1 cm. The scale from the same playground to another drawing is 8 ft to 1 cm. What are the side lengths of the playground in the other scale drawing?
The scale from a playground to this drawing is 5 ft to 1 cm. The scale from the same playground to another drawing is 8 ft to 1 cm. What are the side lengths of the playground in the other scale drawing?
The side lengths of the playground in the other scale drawing is [tex]\frac{5a}{8}[/tex].
By using geometry we answer this question.
Geometry is nothing but the branch of mathematics which deals with measurements of shapes.
Here, we take the scale from a playground to this drawing as "a" and The scale from the same playground to another drawing as "b".
First, we see the scale from a playground to this drawing.
[tex]\frac{a}{l}= \frac{1}{5}[/tex]
[tex]l=5a[/tex]
Now we see the scale from the same playground to another drawing.
[tex]\frac{b}{l} =\frac{1}{8}[/tex]
[tex]b=\frac{l}{8}\\[/tex]
Here, l=5a then
[tex]b=\frac{5a}{8}[/tex]
Therefore, the side lengths of the playground in the other scale drawing is [tex]\frac{5a}{8}[/tex].
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please help!! thank you
Step-by-step explanation:
when a line intersects with 2 (or more) parallel lines, the angles at the intersection points are the same for each parallel line.
therefore,
5 + 10x = 85
10x = 80
x = 8
so, B is the right answer option.
NO LINKS!!
Please help me with this graphs
Answer:
triangle: 18.81 unitsparallelogram: 17.21 unitsStep-by-step explanation:
You want the perimeter of each of the figures defined by the coordinates of their vertices. You are told to use the distance formula as necessary.
TriangleThe first attachment shows the graph of the triangle. The distance formula is needed only for the length of the diagonal segment:
d = √((x2 -x1)² +(y2 -y1)²)
d = √((3 -(-2))² +(-3 -3)²) = √(5² +(-6)²) = √61 ≈ 7.81
The lengths of the horizontal and vertical legs of the triangle are the difference of their x- and y-coordinates, respectively.
CB = 3 -(-2) = 5
CA = 3 -(-3) = 6
The perimeter is the sum of the side lengths:
P = CA +CB +AB = 6 +5 +7.81 = 18.81
The perimeter of the triangle is 18.81 units.
ParallelogramThe second attachment shows the graph of the parallelogram. As with the triangle, we only need to use the distance formula for the length of the diagonal side. Here is the length of ML.
d = √((4 -2)² +(1 -(-2))²) = √(2² +3²) = √13 ≈ 3.606
The length of the horizontal legs is the difference of their x-coordinates.
KL = 4 -(-1) = 5
Opposite sides are congruent, so the perimeter is double the length of two adjacent sides.
P = 2(3.606 +5) ≈ 17.21
The perimeter of the parallelogram is about 17.21 units.
Answer:
1. 18.81 units
2. 17.21 units
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Question 1Given vertices of ΔABC:
A = (-2, 3)B = (3, -3)C = (-2, -3)Plot the vertices on the given graph paper and join with line segments to create the triangle.
As points B and C share the same y-coordinate:
[tex]\implies BC = |x_B-x_C|=|3-(-2)|=5\:\: \sf units[/tex]
As points A and C share the same x-coordinate:
[tex]\implies AC = |y_A-y_C|=|3-(-3)|=6\:\: \sf units[/tex]
Use the distance formula to find the length AB:
[tex]\begin{aligned}AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(3-(-2))^2+(-3-3)^2}\\& =\sqrt{(5)^2+(-6)^2}\\& =\sqrt{25+36}\\& =\sqrt{61}\\\end{aligned}[/tex]
The perimeter of a two-dimensional shape is the distance all the way around the outside.
[tex]\begin{aligned}\textsf{Perimeter of $ABC$} & = AB + BC + AC\\& = \sqrt{61}+5+6\\& = 11+\sqrt{61}\\& = 18.81\:\: \sf units\:(nearest\:hundredth)\end{aligned}[/tex]
Question 2Given vertices of polygon KLMN:
K = (-1, 1)L = (4, 1)M = (2, -2)N = (-3, -2)Plot the vertices on the given graph paper and join with line segments to create the polygon.
As the y-coordinate of points K and L, and M and N are the same, KL and MN are parallel line segments.
As the difference between the x-coordinates of K and N, and L and M is 2 units, KN and LM are parallel line segments.
Therefore, the polygon is a parallelogram.
A parallelogram has two pairs of opposite sides that are equal in length.
Therefore, KL = NM and KN = LM.
As points K and L share the same y-coordinate:
[tex]\implies KL = |x_K-x_L|=|-1-4|=5\:\: \sf units[/tex]
Use the distance formula to find the length KN:
[tex]\begin{aligned}KN & =\sqrt{(x_N-x_K)^2+(y_N-y_K)^2}\\& =\sqrt{(-3-(-1))^2+(-2-1)^2}\\& =\sqrt{(-2)^2+(-3)^2}\\& =\sqrt{4+9}\\& =\sqrt{13}\\\end{aligned}[/tex]
The perimeter of a two-dimensional shape is the distance all the way around the outside.
[tex]\begin{aligned}\textsf{Perimeter of $KLMN$} & = 2\:KL + 2 \:KN\\& = 2 \cdot 5 + 2\cdot \sqrt{13}\\& =10 + 2\sqrt{13}\\& = 17.21\:\: \sf units\:(nearest\:hundredth)\end{aligned}[/tex]
Find the square root of 1000 000 base two
Answer: Here's the answer step by step
Step-by-step explanation: First, find the square root of 1000000 base to and leave your answer in base two
find the square root of 111 in base 2
simplify 342+134-233 in base 5
divide 100001 by 11 in base 2
convert 123.12 in base 3 to a number in base 10 and make sure you leave your answer in base 2
Last step: convert 3.875 in base 10 to a number in base 2
6.139 rounded to the nearest hundredth?
Answer:
Step-by-step explanation: 6.140
slove please and thanks
Can someone please help me this is geometry
Answer:
Step-by-step explanation:
[tex]\displaystyle\\\boxed {M_{AB}=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2} ) }[/tex]
1) E(-5,-3) F(3,7) M(x,y)=?
[tex]\displaystyle\\M(x,y)=(\frac{-5+3}{2} ),\frac{-3+7}{2})\\\\ M(x,y)=(\frac{-2}{2},\frac{4}{2} )\\\\ M(x,y)=(-1,2)\\\\Thus, \ M(-1,2)[/tex]
2) L(-8,11) N(-3,12) M(x,y)=?
[tex]\displaystyle\\M(x,y)=(\frac{-8+(-3)}{2} ,\frac{11+12}{2} )\\\\M(x,y)=(\frac{-11}{2},\frac{23}{2})\\\\ M(x,y)= (-5.5,11.5)\\\\Thus, M(-5.5,11.5)[/tex]
3) A(-4,6) B(2,4) M(x,y)=?
[tex]\displaystyle\\M(x,y)=(\frac{-4+2}{2},\frac{6+4}{2})\\\\ M(x,y)=(\frac{-2}{2},\frac{10}{2})\\\\ M(x,y)=(-1,5)\\\\ Thus,\ M(-1,5)[/tex]
(a) Determine the net change between the indicated points on the graph.
b) determine the average rate of change between the indicated points on the graph.
The function which passes from (1,4) and (5,1) is y= -7/20x² + 27/20x +3
and the net change between the indicated points is -3, whereas the average rate change is -3/4.
Given, from the graph, the function passes (1,4) and (5,1).
Let y = ax² + bx + 3
from point 1.
the equation is: a + b+ 3 = 4 eq(1)
from point 2.
the equation is 25a + 5b + 3 = 1 eq(2)
solving equation 1 and equation 2.
we get, 20b = 99-72
20b = 27
b = 27/20
substitute b value in equation 1.
a + 27/20 + 3 = 4
20a = -7
a = -7/20
hence y = -7/20x² + 27/20x +3
(a) net change = change in y coordinates.
net change = y₂ - y₁
net change = 1 - 4
= -3
(b) Average rate = change in y coordinates / change in x coordinates
= 1 - 4/5-1
= -3/4
hence we get the required answers.
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