Answers
Answer: B
Step-by-step explanation:
The horizontal change is 6.
The vertical change is 5.
So, the distance is [tex]\sqrt{6^2 + 5^2}=\sqrt{61}[/tex]
Related Questions
X2 +1/2x+____=2+____?
Answers
Answer:
[tex]x^{2}+\frac{1}{2} x + \frac{33}{16}= 2 + (x + \frac{1}{4})^2[/tex]
Step-by-step explanation:
[tex]x^{2}+\frac{1}{2} x=x^{2}+2 \times \frac{1}{4} \times x +(\frac{1}{4})^2 - (\frac{1}{4})^2[/tex]
[tex]=[x^{2}+2 \times \frac{1}{4} \times x +(\frac{1}{4})^2] - (\frac{1}{16})[/tex]
[tex]=[x + \frac{1}{4}]^2 - (\frac{1}{16})[/tex]
____________________
then
[tex]x^{2}+\frac{1}{2} x = [x + \frac{1}{4}]^2 - (\frac{1}{16}) -2 + 2[/tex]
then
[tex]x^{2}+\frac{1}{2} x = [(x + \frac{1}{4})^2 - (\frac{1}{16}) -2] + 2[/tex]
then
[tex]x^{2}+\frac{1}{2} x = [(x + \frac{1}{4})^2 - (\frac{33}{16}) ] + 2[/tex]
then
[tex]x^{2}+\frac{1}{2} x = (x + \frac{1}{4})^2 - \frac{33}{16} + 2[/tex]
then
[tex]x^{2}+\frac{1}{2} x + \frac{33}{16}= (x + \frac{1}{4})^2 + 2[/tex]
then
[tex]x^{2}+\frac{1}{2} x + \frac{33}{16}= 2 + (x + \frac{1}{4})^2[/tex]
I need help
Please help ASAP
Answers
Answer:
The volume of the solid is [tex]1,021m^3[/tex]
Step-by-step explanation:
1. Cylinder
For find the volume of a cylinder we use the next formula:
[tex]V_{cylinder} = \pi h r^2 = \pi \cdot 9m\cdot (5m)^2 \approx 706.86m^3[/tex]
Then the volume of the cylinder is equal to [tex]706.86m^3[/tex]
2. Cones
For find the volume of a cone we use the next formula:
[tex]V_{cone} = \pi \frac{h}{3} r^2 = \pi \cdot \frac{6m}{3} \cdot (5m)^2 \approx 157.08m^3[/tex]
However there are two cones so we have to multiply the volume of one cone for two and we get the total volume for the cones which is [tex]314.16m^3[/tex]
3. Sum of the volumes
Finally we sum the volumes of the cylinder and the cones for get the final result
[tex]V_{cylinder} + V_{cones} = 706.86m^3 + 314.16m^3 \approx 1021m^3[/tex]
So approximating the result is [tex]1021m^3[/tex]
What’s the slope please help
Answers
By secant line formula, the slope of the line represented in the table is equal to - 2.
How to determine the slope of a linear function based on a table
In this problem we must determine the slope of a function based on the secant line formula. After a quick glance at the table, we find that the slope formula can be used as Δx and Δy are constant at every pair consecutive points. Then, the slope of the line is:
m = (- 3 - 9)/(9 - 3)
m = - 12/6
m = - 2
By secant line formula, the slope of the line represented in the table is equal to - 2.
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Buns,cost 40p each. Cakes cost 55p each. I spend exactly £4.35 on buns and cakes.
How many of each did I buy?
Someone pls help me, I’m so stuck lol
Answers
By solving a linear equation, we conclude that you bought 4 buns and 5 cakes.
How many of each did I buy?
We will define the two variables:
x = number of buns bought.y = number of cakes bought.We know that you spent exactly £4.35, then we only need to solve the linear equation:
x*0.40 + y*0.55 = 4.35
We need to solve that equation for x and y, such that the values of x and y can only be positive whole numbers.
We can rewrite the equation as:
y*0.55 = 4.35 - x*0.40
y = (4.35 - x*0.40)/0.55
Now we only need to evaluate it in different values of x, and see for which value of x, the outcome y is also a whole number.
We will see that for x = 4, we have:
y = (4.35 - 4*0.40)/0.55 = 5
So you bought 4 buns and 5 cakes.
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40p + 55p = 95p
435p ÷ 95p = 4.57...
So, the sum of the two pairs can go into £4.35 four times.
That meant if I increase the buns & cakes four times, it will help me get closer to the sum of £4.35 & work out which was extra
(40 x 4 = 160) & (55 x 4 = 220)
160 + 220= 380p or £3.80
Adding them up I get 380 pence & that's 55p short to getting to the sum of 435p or £4.35
(435-380=55p)
Thus, the extra is the cake, meaning you bought 4 buns and 5 cakes.
Hope this helps!
What is the area of the actual square window
shown in the scale drawing?
Answers
Answer:
2.25m²
Step-by-step explanation:
if 1in = 2m then 0.5in = 1m
so 0.75in = 1.5m
area = 1.5 x 1.5
a = 2.25m²
Donna has a $300 loan through the bank she is charged a simple rate The total interest she paid on the loan was $63 As a percentage what was the annual interest rate on her loan
Answers
The annual interest rate is 21%
How to determine the annual interest rate?The given parameters are
Loan Amount, P = $300
Interest, I = $63
Number of years, T = 1
The annual interest rate is calculated as
I = PRT
Substitute the known values in the above equation
63 = 300 * R * 1
Evaluate the product
300R = 63
Divide through by 300
R = 21%
Hence, the annual interest rate is 21%
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A Big Year
By Bob Kowalski
Would you go to the ends of the earth to see a bird? What if it were a really special bird: one with beautiful feathers, an entrancing call, or a silly dance? What if seeing that one special bird would allow you to win a contest?
If that contest doesn't get you on television or win you any cash prizes, would you still do it? For those who participate in the "Big Year," the honor of beating the previous record is the only reward they get or even want.
A "Big Year" is a year in which a person attempts to see as many different species of birds as possible within a particular region. For most in North America who participate in a "Big Year," this region is the lower 48 American states, plus Alaska, Canada, and a couple of French islands off the Canadian coast.
You may be thinking that looking at birds is silly, but just think about the numbers of the recent record holders and the commitment it takes to get these numbers. One recent "Big Year" winner managed to see 744 birds in one year, missing the record by just one bird. Big Year birders travel by train, plane, boat, car, bicycle, and of course, by foot. They can cover over 150 thousand miles to get numbers of sightings this high. They can also spend a small fortune.
Just to clarify, the birds these contestants are counting are the number that they see in a particular year. You see, the contest is based on an honor system. No pictures or other evidence is required as proof of a sighting. Most birders take great pride in their reputation and their abilities to see or hear and then identify a bird. Usually, important sightings of the rare birds needed to get counts in the 700s are visited by hundreds of birders. It is pretty hard to cheat your way to a record-breaking year, but in general, few are interested in cheating.
This honesty comes from the fact that most people who want to break such a record know the greatest rewards are not necessarily in winning. Such rewards are in being able to commit a year of your life to doing something you love. Rewards are found in seeing amazing, inspiring creatures like the California Condor or the Magnificent Frigate bird. Rewards also come in spending time with people who, like you, want to spend their time looking to the skies and trees for glimpses of emerald, crimson, or cerulean blue feathered jewels.
You don't have to be able to travel a continent to have a big birding experience though. Have a big month. Or a big weekend. Set a personal record, learn to identify the species that live in your part of the world, or try to learn the calls of just two species of birds. You will soon find looking at birds isn't such a strange way to spend your time.
Extra! Extra! Backyard Birding
Many schools, families, and young birders across the country participate in the "Great Backyard Bird Count." While not as long as a "Big Year," the "Great Backyard Bird Count" happens every year. It depends on birders and families across the country to watch feeders and other areas in their yards and count the number of birds they see. Unlike the "Big Year," the goal is not to see who can count the most birds. Instead, participants in this event work together to help bird experts get a good idea of how birds are doing. Participants are given checklists and enter their sightings on a website. Called a "citizen-science" project, this event is open to anyone, requires no travel, and happens every year over one weekend in February.
Read this sentence from the article:
You may be thinking that looking at birds is silly, but just think about the numbers of the recent record holders and the commitment it takes to get these numbers.
Why would the author suggest that looking at birds is silly?
To create a sense of doubt in the reader
To distance himself from what seem to be rather strange people
To show readers that some people do not think birding is interesting
To suggest he has never birded himself but might someday
Ill give brainliest
Answers
The inference is that the author suggest that looking at birds is silly A. to create a sense of doubt in the reader.
What is an inference?It should be noted that that an inference simply means the conclusion that can be deduced based on the information given in a story.
In this case, A Big Year" is a year in which a person attempts to see as many different species of birds as possible within a particular region. For most in North America who participate in a "Big Year," this region is the lower 48 American states, plus Alaska, Canada, and a couple of French islands off the Canadian coast.
The inference is that the author suggest that looking at birds is silly is to create a sense of doubt in the reader. Therefore, the correct option is A.
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What percent of 50 is 15?
A. 0.3%
B. 7.5%
C. 30%
D. 35%
Answers
Answer:30%
Step-by-step explanation:
10% of 50 is 50/10 so 10% is 5
15/5=3 so its three lots of 10%
3*10%=30%
Step by step.
What percent of 50 is 15?
So
what percent of (means multiply)
50 is (means equal) 15.
So
50x = 15
Solve for “x” by dividing both sides by 50.
X= .30
To turn a decimal into a percent, multiply by 100 = 30%.
Help I can’t figure out anything with this question
Answers
Answer: Look in step-by-step explanation
Step-by-step explanation:
Area has a unit of cm^2 or m^2, whilst Volume has a unit of cm^3 or m^3
Using this information, we can see that we have to square both sides of the similarity ratio for the area ratio and cube both sides of the similarity ratio for the volume ratio
For example, question 2 states that the similarity ratio is 3:6, so the area ratio is 3^2:6^2 or 9:36 and the volume ratio is 3^3:6^3 = 27:216
You can do the rest from here
Write 2.154 × 10∧5 in decimal form.
Answers
The decimal notation for the given value in scientific notation is 215400.
How to convert from scientific to decimal notation?Very large or very small numbers are denoted in scientific notation to simplify complex calculations.
The scientific notation is represented by: a × 10ⁿ
Wher a - any number or decimal number
n - the power of 10; it is an integer number
To convert this into decimal notation,
If the value of n is positive, then the decimal point in the 'a' moves right. (OR)If the value of n is negative, then the decimal point in the 'a' moves left.Calculation:The given number is in the scientific notation,
2.154 × 10⁵
Since the power of 10 is positive, the decimal point in the number 2.154 moves towards the right. I.e,
2.154 × 10⁵ = 215400
Here power is 5. So, the decimal point moved five places to the right.
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Newton's Law of Cooling states that the rate of change of the temperature of an object, T, is proportional to the difference of T and the temperature of the region, TR or dT over dt equals k times the quantity T minus T sub R end quantity. An object with core temperature of 1200°F is removed from a fire and placed in a region with a constant temperature of 80°F. After 1 hour, its core temperature is 830°F. What is the object's core temperature 4 hours after it is taken off the fire? (1 point)
Answers
Answer:
305 °F
Step-by-step explanation:
The core temperature of the object after 4 hours can be found using an exponential decay formula to model the decay of the difference between core temperature and ambient.
Cooling ModelThe solution to the differential equation described by Newton's law of cooling is the exponential equation ...
y = ab^t +c
where 'a' is the initial core temperature difference from ambient, 'b' is the decay factor of that difference in 1 unit of time period t. 'c' is the ambient temperature.
For this problem, the ambient temperature is c=80, and the differences of interest are ...
a = 1200 -80 = 1120
b = (830 -80)/1120 = 75/112
Using these values in the model gives ...
y = 1120(75/112)^t +80 . . . . . . where y(t) is the core temperature at time t
Note that units of time are hours.
ApplicationWe want y when t=4.
y = 1120(75/112)^4 +80 ≈ 1120(0.20108) +80 ≈ 305.212
The core temperature after 4 hours is about 305 °F.
__
Additional comment
The differential equation will have a solution of the form ...
[tex]T-T_R=(T_0-T_R)e^{kt}[/tex]
where k = ln(75/112) ≈ -0.40101
In the above, we defined b = e^k = 75/112. Accuracy with this fraction can be better than using a truncated value of k.
In how many possible ways can this be accomplished if there are 25 members on the board of directors
Answers
Explanation:
There are 25 choices for president. Then we have 25-1 = 24 choices for the secretary, and 24-1 = 23 choices for treasurer. This countdown (25,24,23) is because any given person cannot serve in more than one position.
Multiply out those values: 25*24*23 = 13800
Side note: you could use the nPr permutation formula as an alternative path. Plug in n = 25 and r = 3.
a tree 20 feet tall with a circumference of 3 ft has a vine wound around 7 times. How long is the vine?
Answers
The length of the vine is 21 ft
what is the circumference of a circle?
the circumference is the perimeter of a circle
the perimeter of the circle = 2πr = 3 ft
the vine is 7 times the perimeter
length of vine = 7×3= 21 ft
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If the tree is 20 feet tall with circumference 3 feet then the length of vince is around 21 feet.
Given the height of tree is 20 feet and the circumference of tree is 3 feet.
We have to find the length of vine.
Circumference is the perimeter of a circular object. Because the trunk of a tree is in shape of circle so the perimeter of the trunk is 2πr.
We have been given the circumference of tree be 3 feet.
Circumference=2πr
Because vine is 7 times the circumference so the length of vine being:
Length of vine=7*3
=21 feet.
Hence if the tree is 20 feet tall with circumference 3 feet then the vince is around 21 feet long.
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(x+ 3/8 ) 2 + y 2 =1
what is the radius & units?
Answers
The radius of the circle of the circle equation (x + 3/8)^2 + y^2 = 1 is 1 unit
How to determine the radius of the circle?The circle equation of the graph is given as:
(x + 3/8)^2 + y^2 = 1
The general equation of a circle is represented using the following formula
(x - a)^2 + (y - b)^2 = r^2
Where the center of the circle is represented by the vertex (a, b) and the radius of the circle is represented by r
By comparing the equations (x - a)^2 + (y - b)^2 = r^2 and (x + 3/8)^2 + y^2 = 1, we have the following comparison
(x - a)^2 = (x + 3/8)^2
(y - b)^2 = y^2
1 = r^2
Rewrite the last equation as follows:
r^2= 1
Take the square root of both sides of the equation
√r^2 = √1
Evaluate the square root of 1
√r^2 = 1
Evaluate the square root of r^2
r = 1
Hence, the radius of the circle of the circle equation (x + 3/8)^2 + y^2 = 1 is 1 unit
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what is the length of the interval of solutions to the inequality 1≤3-4x≤9?
Answers
Answer: -3 ≤ x ≤ -1
Step-by-step explanation:
1 ≤ 3 - 4x ≤ 9
1 + 3 ≤ - 4x ≤ 9 + 3; Add 3 on all sides
4 ≤ -4x ≤ 12
1 ≤ -x ≤ 3; Divide 4 on all sides
-1 ≥ x ≥ -3; Multiply -1 on all sides(FYI: When multiplying or dividing negative numbers in inequalities, make sure to reverse the signs as well)
Answer:
2
Step-by-step explanation:
1≤3-4x≤9
subtract 3
1-3≤3-4x-3≤9-3
-2≤-4x≤6
divide by 2
-1≤-2x≤3
multiply by -1
1≥2x≥-3
or
-3≤2x≤1
divide by 2
[tex]-\frac{3}{2} \leq \frac{2x}{2} \leq \frac{1}{2} \\-\frac{3}{2} \leq x\leq \frac{1}{2} \\[/tex]
length of interval
[tex]=\frac{1}{2} -(\frac{-3}{2} )\\=\frac{1}{2} +\frac{3}{2} \\=\frac{1+3}{2} \\=\frac{4}{2} \\=2[/tex]
z=2cispi/3 in rectangular form
Answers
The conversion of "z = 2(cos(π/3))" in polar form to rectangular form is equal to 1.
What is a polar coordinate?A polar coordinate can be defined as a two-dimensional coordinate system, wherein each point on a plane is typically determined by a distance (r) from the pole (origin) and an angle (θ) from a reference direction (polar axis).
How to transform polar coordinates to rectangular coordinates?In geometry, the relationship between a polar coordinate (r, θ) and a rectangular coordinate (x, y) based on the conversion rules is given by the following polar functions:
a = rcos(θ) ....equation 1.
b = rsin(θ) ....equation 2.
Where:
θ is the angle.r is the radius of a circle.Note: The exact value of cos(π/3) is equal to ½.
Substituting the given parameters into the formula, we have;
z = 2(½)
z = 2/2
z = 1.
In conclusion, we can logically deduce that the conversion of "z = 2(cos(π/3))" in polar form to rectangular form is equal to 1.
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Complete Question:
Convert z = 2(cos(π/3)) in rectangular form
An older person is 9 years older than four times the age of a younger person the sum of their ages is 24 find their ages
Answers
Step-by-step explanation:
let the younger person be x and older be y
4x + 9 = 24
4x = 15
x = 3.75
y = 24 - 3.75
y = 20.25
△ABC has vertices A(-2, 0), B(0,8), and C(4,2) Find the equations of the three altitudes of △ABC
Answers
The equations of the three altitudes of triangle ABC include the following:
3y - 2y - 4 = 0.y + 3x - 8 = 0.4y + x - 6 = 0.What is a triangle?A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to determine a slope?Mathematically, the slope of a straight line can be calculated by using this formula;
[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Also, the point-slope form of a straight line is given by this equation:
y - y₁ = m(x - x₁)
Assuming the following parameters for triangle ABC:
Let AM be the altitudes on BC.Let BN be the altitudes on CA.Let CL be the altitudes on AB.For the equation of altitude AM, we have:
Slope of BC = (2 - 8)/(4 - 0)
Slope of BC = -6/4
Slope of BC = -3/2
Slope of AM = -1/slope of BC
Slope of AM = -1/(-3/2)
Slope of AM = 2/3.
The equation of altitude AM is given by:
y - y₁ = m(x - x₁)
y - 0 = 2/3(x - (-2))
3y = 2(x + 2)
3y = 2x + 4
3y - 2y - 4 = 0.
For the equation of altitude BN, we have:
Slope of CA = (2 - 0)/(4 - (-2))
Slope of CA = 2/6
Slope of CA = 1/3
Slope of BN = -1/slope of CA
Slope of BN = -1/(1/3)
Slope of BN = -3.
The equation of altitude BN is given by:
y - y₁ = m(x - x₁)
y - 8 = -3(x - 0)
y - 8 = -3x
y + 3x - 8 = 0.
For the equation of altitude CL, we have:
Slope of AB = (8 - 0)/(0 - (-2))
Slope of AB = 8/2
Slope of AB = 4
Slope of CL = -1/slope of AB
Slope of CL = -1/4
The equation of altitude CL is given by:
y - y₁ = m(x - x₁)
y - 2 = -1/4(x - 4)
4y - 2= -(x - 4)
4y - 2= -x + 4
4y + x - 2 - 4 = 0.
4y + x - 6 = 0.
In conclusion, we can infer and logically deduce that the equations of the three altitudes of triangle ABC include the following:
3y - 2y - 4 = 0.y + 3x - 8 = 0.4y + x - 6 = 0.Read more on point-slope form here: brainly.com/question/24907633
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What is the value of 2 + (- 2/3)^2 ÷ 1/3 ?
16
3
-2
0
Answers
Answer:
3
Step-by-step explanation:
2+ (-2/3)^2 ÷ 1/3
make -2/3 postive because its being raised by an even exponent
you never divide by fractors so make 1/3 into 3 and make it multiplication
2+ (2/3)^2 × 3
raise the fraction to the power of 2
2+ (4/9)× 3
cancel out the GCF
2+ 4/3
add
10/3
simplify
3.3 ≅ 3
A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 729 cubic feet. The concrete for the base cost $8 per square foot, The material for the roof costs $3 Per square foot, and the material for the sides costs $5.50 Per square foot. Find the dimensions of the most economical shed.
Answers
The dimensions of the most economical shed are 9 ft in length, 9 ft in width, and 9 ft in height if the storage shed is to be built in the shape of a box with a square base.
What is volume?It is defined as a three-dimensional space enclosed by an object or thing.
It is given that:
A storage shed is to be built in the shape of a box with a square base.
It is to have a volume of 729 cubic feet.
Let x be the length of the base
Let y be the height of the box.
V = 729 cubic feet
The base is square:
l = w = x
V = x²y
y = 729/x²
Cost of the base = $8x²
Cost of the roof = 3x²
Cost of the sides = 4(5.50)xy
= 22xy
Total cost
C= 8x² + 3x² + 22xy
C = 11x² + 22x(729/x²)
C = 11x² + 16038/x
Find the first derivative:
dC/dx = 22x - 16038/x²
Equate; dC/dx = 0
22x - 16038/x² = 0
22x = 16038/x²
22x³ =16038
x³ = 729
x = 9
y = 729/(9)² = 9
Length of base = 9 ft
Width of base = 9 ft
Height of box = 9 ft
Thus, the dimensions of the most economical shed are 9 ft in length, 9 ft in width, and 9 ft in height.
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A right pyramid has a height of 3 inches and a square base with side length of 5 inches. What is the volume of the pyramid?
The volume of this pyramid is ______
cubic inches.
PLEASE MY LAST QUESTION
Answers
Answer: 25 in³
Step-by-step explanation:
We can calculate the volume of the pyramid by first calculating the volume of a prism with the same dimensions, and then dividing by 3 (all pyramids a volume that's [tex]\frac{1}{3}[/tex] of the volume of a prism with the same dimensions).
The volume of a prism is its base area times its height. The base would be a square, so its area is 5², which is 25. The height is 3 inches, making the prism's volume 75 in³.
The volume of the pyramid would be one-third of this value, which is 75[tex]75\div3[/tex] which is 25 in³.
urgently need help please help
Answers
Answer: 40
Step-by-step explanation:
Sub x=4 into 3x²-2x+1
∴ 3(4)²-2(4)+1
=3(16)-8+1
=48-8+1
=40
Answer:
41
Step-by-step explanation:
substitute the x to 4
so 3(4)² - 2(4) + 1 = 41
please help jajajajaja
Answers
If segment IG and segment JL are parallel then angle IGK is congruent to angle LJK by alternate interior angles theorem
giving brainliest!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer: [tex]\pm1,\pm3,\pm5, \pm15[/tex]
Step-by-step explanation:
We can list the possible rational roots of this polynomial using the Rational Root Theorem. This theorem states that all the possible rational roots of an equation follow the structure [tex]\frac{p}{q}[/tex], where p is any of the factors of the constant term and q is any of the factors of the leading coefficient.
In this example, -15 is the constant term and 1 is the leading coefficient ([tex]x^4[/tex] has a coefficient of 1).
The factors of -15 are [tex]\pm1,\pm3,\pm5, \pm15[/tex], while the factors of 1 are [tex]\pm1[/tex]. p is can be any one of the factors of -15, while q can be any of the factors of 1.
[tex]\frac{\pm1,\pm3,\pm5, \pm15}{\pm1}[/tex]
The possible roots can be any of the numbers on the top divided by any of the numbers on the bottom. Since dividing by 1 or -1 won't change any of the numbers on the top, the rational roots of this function are [tex]\pm1,\pm3,\pm5, \pm15[/tex].
(2 Fruit juice A is composed of 2 parts apple juice and 1 part grape juice.
Fruit juice B is composed of 1 part apple juice and 2 parts grape juice.
When A and B are mixed, the new mixture has 10 kg of apple juice and
8 kg of grape juice. How many kilograms does each type of original
fruit juice weigh
Answers
The amount of kilograms of each type of original fruit juice weighs; 12 kg of Apple and 6 kg of grape
How to Solve Algebra Word Problems?
The concentrations of apple and grape juice in the two different juice types are given as;
Juice A:
(2/3) apple
(1/3) grape
Juice B:
(1/3) apple
(2/3) grape
Let a be how much juice A is in the mixture;
Let b be how much juice B is in the mix.
Thus;
²/₃a + ¹/₃b = 10 ------(eq 1)
¹/₃a + ²/₃b = 8 ------(eq 2)
Solving both equations simultaneously gives us;
a = 12 and b = 6
Thus, the amount of kilograms of each type of original fruit juice weighs; 12 kg of Apple and 6 kg of grape
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1.
Berkley is flying a kite. The string is all the way out, which means it is 425 meters away. Berkley is looking up at the kite at an angle of 42°. Berkley's dog is watching the kite too and the angle from Berkley to the dog to the kite is 87°. How would you find the distance between the kite and the dog? Is it possible? Explain your answer using the law of sines.
Answers
Using the law of sines, it is found that the distance between the kite and the dog is of 284.77 meters.
What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A is a.The length of the side opposite to angle B is b.The length of the side opposite to angle C is c.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
For the situation described, we have that:
The height is opposite to the angle of 42º.The 425 meters are opposite to the angle of 87º.Hence:
[tex]\frac{\sin{42^\circ}}{h} = \frac{\sin{87^\circ}}{425}[/tex]
Applying cross multiplication:
[tex]h = 425\frac{\sin{42^\circ}}{\sin{87^\circ}}[/tex]
h = 284.77 meters.
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Find f. f ″(x) = x^−2, x > 0, f(1) = 0, f(6) = 0
Answers
If you do in fact mean [tex]f(1)=f(6)=0[/tex] (as opposed to one of these being the derivative of [tex]f[/tex] at some point), then integrating twice gives
[tex]f''(x) = -\dfrac1{x^2}[/tex]
[tex]f'(x) = \displaystyle -\int \frac{dx}{x^2} = \frac1x + C_1[/tex]
[tex]f(x) = \displaystyle \int \left(\frac1x + C_1\right) \, dx = \ln|x| + C_1x + C_2[/tex]
From the initial conditions, we find
[tex]f(1) = \ln|1| + C_1 + C_2 = 0 \implies C_1 + C_2 = 0[/tex]
[tex]f(6) = \ln|6| + 6C_1 + C_2 = 0 \implies 6C_1 + C_2 = -\ln(6)[/tex]
Eliminating [tex]C_2[/tex], we get
[tex](C_1 + C_2) - (6C_1 + C_2) = 0 - (-\ln(6))[/tex]
[tex]-5C_1 = \ln(6)[/tex]
[tex]C_1 = -\dfrac{\ln(6)}5 = -\ln\left(\sqrt[5]{6}\right) \implies C_2 = \ln\left(\sqrt[5]{6}\right)[/tex]
Then
[tex]\boxed{f(x) = \ln|x| - \ln\left(\sqrt[5]{6}\right)\,x + \ln\left(\sqrt[5]{6}\right)}[/tex]
Juan bought a table on sale for $459. This price was 32% less than the original price. What was the original price?
Answers
Answer:
675
Step-by-step explanation:
100%-32%=68%
459/0.68= 675
Hope this helps! :)
. Which of the following statements is not true?
a. If x = 1, then x² = 1.
b. If x²= 1, then x = 1.
c. If x=-1, then x² = 1.
d. x² = 1.if and only if x = 1 or x = -1.
Answers
Answer:
If x^2 = 1, then x = 1 is NOT true because x can also be -1.
solve the simultaneous equation 2x+y=22 =12, x + 24+2 = 18, 2x -y +22=16
Answers
The solution for the simultaneous equations 2x + y - 2z = 12, x + 2y +z =18 and 2x - y + 2z =16 are x = 7, y = 4 and z = 3
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the solution to the simultaneous equations?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2x + y - 2z = 12,
x + 2y +z =18
2x - y + 2z =16
Eliminate y and z in the equations by adding the first and the third equation together
This gives
2x + y - 2z = 12,
+
2x - y + 2z =16
--------------------------
4x = 28
Divide both sides by 4
x = 7
Substitute x = 7 in x + 2y +z =18 and 2x - y + 2z =16
7 + 2y +z =18
2(7) - y + 2z =16
This gives
2y + z = 11
-y + 2z= 2
Multiply -y + 2z= 2 by 2
-2y + 4z= 4
Add -2y + 4z= 4 and 2y + z = 11
5z = 15
Divide by 5
z = 3
Substitute z = 3 in -y + 2z= 2
-y + 2*3= 2
Evaluate
y = 4
Hence, the solution for the simultaneous equations 2x + y - 2z = 12, x + 2y +z =18 and 2x - y + 2z =16 are x = 7, y = 4 and z = 3
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