A measurement that is closest to the the distance between point B and point D is 6√5 or 13.42 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-1 - 5)² + (3 + 9)²]
Distance = √[(-6)² + (12)²]
Distance = √[36 + 144]
Distance = √180
Distance = 6√5 or 13.42 units.
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When you roll two number cubes, what are the odds in simplest form against getting two numbers greater than 4?
A. 4:1
B. 1:4
C. 1:8
D. 8:1
The odds in simplest form against getting two numbers greater than 4 is 1 : 4.
What are the odds?Probability determines the odds that a random event would happen. The odds the event occurs is 1 and the probability that the event does not occur is 0.
The odds of getting two numbers greater than 4 = 2 x (numbers greater than 3 in a cube / total number of sides in a cube)
2(3/6)
2 x 1/2 = 1 : 4
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From the top of a 16 m tall building, the angle of depression to a car on the road is 35°. To the nearest metre, how far is the car from the base of the building?
The distance of the car to the base of the building is 23 metres.
How to find the distance of the car from the building using angle of depression?The situation will form a right angle triangle.
Therefore, the distance of the car to the base of the building is the adjacent side of the right angle triangle formed.
Therefore,
tan 35 = opposite / adjacent
tan 35 = 16 / x
x tan 35 = 16
x = 16 / tan 35
Therefore,
x = 16 / 0.70020753821
x = 22.8506141103
x = 23 meters
Therefore, the distance of the car to the base of the building is 23 metres.
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Consider the function f(x) = x² + 10x + 25 for x ≥ -5.
What is the value of f-¹(x) when x = 4?
Answer:
-3
Step-by-step explanation:
On the way to visit her grandmother, Sally drove at an average speed of 85 mph. On the way home (taking the same route) she only averaged 65 mph. If the total round trip took 18 hours, how many hours did it take Sally to drive to her grandmother's? Write your answer as a decimal.
Answer:
7.8 hours
Step-by-step explanation:
We will use the formula:
distance =rate×time
We don't know the distance but it is the same distance going and returning. Two rate×time calculations will both equal that distance from Sally's to Grandma's. See image.
The volume of the oceans on Earth is approximately 1,386 million km^3. As the Earth's temperature rises, the ice in the polar icecaps melts into the oceans, increasing the volume of the oceans. If 1 cm^3 of ice melts, it turns into approximately 0.92 cm^3 water.
1) There are approximately 3,800 cm^3 in a gallon. If 1.9 m^3 of ice melts, how many gallons of water does this produce? (Round your answer to the nearest gallon.)
2) Scientists estimated that the addition of 1,000 km^3 of water would increase sea levels by 364 cm. Greenland's ice sheet is especially vulnerable to melting. Recent reports indicate a melting average of 195 km^3 of ice per year from Greenland, resulting in additional yearly 179.4 km^3 of water. If melting continues at this rate, how many centimeters would the sea increase after 6 years? (Round your answer to the nearest centimeter.)
Answer:
460 gallons392 cmStep-by-step explanation:
The necessary units conversion can be accomplished by multiplying by appropriate conversion factors. Quantity can be found by multiplying rate by time.
1)The number of gallons of water produced by melting 1.9 m³ of ice is ...
[tex]1.9\text{ m$^3$ (ice)}\times\left(\dfrac{100\text{ cm}}{1\text{ m}}\right)^3\times\dfrac{0.92\text{ cm$^3$ (water)}}{1\text{ cm$^3$ (ice)}}\times\dfrac{1\text{ gal}}{3800\text{ cm$^3$}}\\\\=\dfrac{1.9\times10^6\times0.92}{3800}\text{ gal}=\boxed{460\text{ gal}}[/tex]
2)Multiplying the melting rate by time and converting to height, we have ...
[tex]\dfrac{179.4\text{ km$^3$}}{1\text{ yr}}\times\dfrac{364\text{ cm}}{1000\text{ km$^3$}}\times6\text{ yr}\approx\boxed{392\text{ cm}}[/tex]
__
Additional comment
The area of the world's oceans is about 361e6 km², so addition of 1000 km³ of water might be expected to increase the water level by (1000/361)e-6 ≈ 2.77e-6 km = 0.277 cm. Something seems a little off in this problem statement.
BRAINLIEST TO CORRECT ANSWER
There is a pair of parallel sides in the following shape.
what is the area
The area of the given figure is 38 square units
Area of a trapezoidThe area of the given trapezoid is expressed as:
A = 0.5(a+b)h
where
a and b are the sides
h is the height
Substitute
A = 0.5(9+10) * 4
A = 19 * 2
A = 38 square units
Hence the area of the given figure is 38 square units
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What is the range of the function f(x) = |x – 3| + 4?
R: {f(x) ∈ ℝ | f(x) ≥ 4}
R: {f(x) ∈ ℝ | f(x) ≤ 4}
R: {f(x) ∈ ℝ | f(x) > 7}
R: {f(x) ∈ ℝ | f(x) < 7}
Answer: R: {f(x) ∈ ℝ | f(x) ≥ 4}
Step-by-step explanation:
[tex]|x-3| \geq 0[/tex] for all real x, so the range is [tex]f(x) \geq 4[/tex].
Which search method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line
The wide-area search method employs the use of markers such as knots at regular intervals along the search line.
Given the method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line.
In order to locate, relieve distress, and preserve the life of a person who has been reported missing or is believed to be lost, stranded, or is considered a high-risk missing person, wide area search and rescue refers to activities occurring within large geographic areas. It also refers to the removal of any survivors to a safe location.
Hence, the wide-area search method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line
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the height of a can of coke is in 11 cm and the radius is 6 cm calculate the total surface area of the can in cm^3 assuming that the
can is a closed cylinde
Answer:
The total surface area of the the cylinder is 640.56cm², surface are is always give in cm² not in cm³ b/c cm³ indicates the volume of the cylinder not the surface area.
Step-by-step explanation:
Hello!
. SA=2πr(r+h) ,or 2πr²+h(2πr)
SA=2(3.14)(6cm)(6cm+11cm)SA=6.28(6cm)(17cm)SA=37.68cm(17cm)SA=640.56cm²Answer:
204π cm^2
which is 640.88 cm^2 to the nearest hundredth.
Step-by-step explanation:
Surface area = 2 * area of the base + area of the curved side.
= 2*π *r^2 + 2*π*r*h
= 2π(6)^2 + 2π(6)(11)
= 72π + 132π
= 204π cm^2.
I need help cancelling units
Answer:
60:1
Step-by-step explanation:
60:1 = 366:x
60x = 366
x = 6.1
366 minutes is equivalent to 6.1 hours.
Convert 366 minutes to hours.
Knowing that in 60 minutes = 1 hour.[tex]\boldsymbol{\sf{Therefore \ \to \ 366 \not{m}*\dfrac{1 \ hr}{60\not{m}}=6.1 \ hr }}[/tex]
We conclude that a time of 366 minutes is equal to 6.1 hours
There are 60 minutes in 1 hour. To convert from minutes to hours, divide the number of minutes by 60. For example, 120 minutes equals 2 hours because 120/60=2.
What is the slope of a line that is parallel to the line y = 3/4x+2?
Answer: 3/4
Step-by-step explanation:
Parallel lines have the same slope.
If the parabola of equation y=k−x2 is tangent to the line of the equation y=x then what is the value of k ?
The value of k is 1/4.
According to the statement
we have given
The equation of parabola is y=k−x2
And tangent to the line of equation is y = x
and we have to find the value of K.
So, let y=k−x2 -(1)
and let y = x -(2)
(2) is the tangent to the (1) then
therefore they cut at
y=k−x2 -(1)
y = x -(2)
so, put (2) in the (1) then
x = k- (x)^2
(x)^2 + x = k
The above written equation has one real number then for this D =0
so, (x)^2 + x - k = 0
-1 -1*4*k = 0
-1 - 4k = 0
-4k = 1
The value of k is -1/4.
So, The value of k is 1/4.
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find the equation of the line y=mx+b form with the slope 3 that passes through the point (5,19)
The equation of the line that has a slope of 3 and that passes through the point (5,19) is y = 3x + 4
Equation of a straight lineFrom the question, we are to determine the equation of the line that has a slope of 3 and that passes through the point (5,19)
Using the point-slope form of an equation of a line
y - y₁ = m(x - x₁)
Where m is the slope
and (x₁, y₁) is a point on the line
From the given information
m = 3
x₁ = 5
y₁ = 19
Putting the parameters into the equation, we get
y - 19 = 3(x - 5)
y - 19 = 3x - 15
y = 3x -15 + 19
y = 3x +4
Hence, the equation of the line that has a slope of 3 and that passes through the point (5,19) is y = 3x + 4
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Decrease 100kg by 30%
Answer:
70
Step-by-step explanation:
the 30/100 of 100 is 30
So 100-30=70
Answer:
70kg
Step-by-step explanation:
30% of 100kg is
--> 100 x 30/100 which is 30kg.
If you want to decrease 100kg by 30%, you can take away 30kg from 100kg.
--> 100 - 30 = 70
So 70kg is the remainder.
Find the midpoint of a and b when a has coordinates (2,3) and b has coordinates (8,9)
The midpoint of co-ordinate is (5, 6)
Add both "x" coordinates, and divide by 2.
Add both "y" coordinates, and divide by 2.
Given that;
Coordinates of A = (2,3)
Coordinates of B = (8,9)
Find:
Midpoint of co-ordinate
Computation:
Midpoint of co-ordinate = [(x1 + x2) / 2], [(y1 + y2) / 2]
Midpoint of co-ordinate = [(2 + 8) / 2], [(3 + 9) / 2]
Midpoint of co-ordinate = [10 / 2], [12 / 2]
Midpoint of co-ordinate = (5, 6)
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Find the 8th term of the geometric sequence 5, -15, 45
Answer:
a₈ = - 10935
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 5 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-15}{5}[/tex] = - 3 , then
a₈ = 5 × [tex](-3)^{7}[/tex] = 5 × - 2187 = - 10935
A rectangle measures 3.5 ft by 7 ft. It is enlarged by a scale factor of two. What is the area of the enlarged rectangle? T a m a
Answer:
98
Step-by-step explanation:
Solution 1, (quick)
When enlarging by a scale factor, the shape's area is multiplied by the scale factor squared.
3.5*7*2^2=98
This works because for a rectangle width x and length y, width 2x and length is 2y, area is 4xy compared to area xy originally.
Solution 2, (technical)
Scale factor of 2 means multiplying by 2
3.5^2=7
7*2=14
7*14=98
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answer:
the following 3 equations are equivalent :
• x + 1 = 4
• 2 + x = 5
• -5 + x = -2
Step-by-step explanation:
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
-5 + x = - 2
Let’s take this equation :
x + 1 = 4
=======
By Adding 1 to both sides of the equation we get :
x + 1 + 1 = 4 + 1
⇔ x + 2 = 5
⇔ 2 + x = 5
Then the equations x + 1 = 4 and 2 + x = 5 are equivalent.
…………………………………………………………………
On the other hand ,if we subtract 6 from both sides
of the equation x + 1 = 4 we get :
x + 1 - 6 = 4 - 6
⇔ x - 5 = -2
⇔ -5 + x = -2
Then the equations x + 1 = 4 and -5 + x = -2 are equivalent.
Answer:
A. 2 + x = 5
B. x + 1 = 4
E. -5 + x = -2
Step-by-step explanation:
right on edg, hope it helps ya'll.
Janice bought 30 items each priced at 30 cents, 2 dollars, or 3 dollars. If her total purchase price was $\$$30.00, how many 30-cent items did she purchase
she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.
According to the statement
Janice bought total items = 30
Price of items are 30 cents, 2 dollars, or 3 dollars.
Total purchase price of Janice = 30$
If we let she bought 10 items at price of 3$, Then it is not possible
So, Number of items which are bought by her at price of $3 is less than 10. Similarly Number of items which are bought by her at price of $2 is less than 10.
we know that 1 CENT = 0.01 $
We also know that 10 30-cents will worth 3 dollars, so the number of cents which are bought by her at price of $0.01 is greater than 10.
Now, Let she bought 20 items at price of 0.01$
Then 20*0.3 = 6$
It means 30$-6$ = 24$
24$ are left to purchase the things which are at price of 2$ and 3$.
If we let she purchase 4 items at cost $3 then
Then 4*$3 = 12$
It means 24$-12$ = 12$
Now, with remaining money she bought 6 items at cost $2.
So, she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.
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she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.
According to the statement
Janice bought total items = 30
Price of items are 30 cents, 2 dollars, or 3 dollars.
Total purchase price of Janice = 30$
If we let she bought 10 items at price of 3$, Then it is not possible
So, Number of items which are bought by her at price of $3 is less than 10. Similarly Number of items which are bought by her at price of $2 is less than 10.
we know that 1 CENT = 0.01 $
We also know that 10 30-cents will worth 3 dollars, so the number of cents which are bought by her at price of $0.01 is greater than 10.
Now, Let she bought 20 items at price of 0.01$
Then 20*0.3 = 6$
It means 30$-6$ = 24$
24$ are left to purchase the things which are at price of 2$ and 3$.
If we let she purchase 4 items at cost $3 then
Then 4*$3 = 12$
It means 24$-12$ = 12$
Now, with remaining money she bought 6 items at cost $2.
So, she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.
Please help me with this
Answer:A or C
Step-by-step explanation: i guessed plus 19 hours ago
Find the mean for the given set of data.
-4, -3,-1,-1, 0, 1
-1 1/3
-1
-3/4
Answer:Find the mean for the given set of data.
-4, -3,-1,-1, 0, 1
-1 1/3
-1
-3/4
Answer is -1 1/3
Step-by-step explanation:
1) A school has an enrollment of 1500 students. The student population is expected to increase at a rate of 2.6% each year for the next 5 years.
a) A What is the growth factor as a decimal?
b) Estimate the number of students enrolled 10 years from now. Round to the nearest student.
Show your work!!
The growth factor as a decimal is 1.026 and the number of students enrolled 10 years from now is 1939
How to determine the growth factor?The given parameters are
Initial value of enrollment, a = 1500
Rate, r = 2.6%
The growth factor is then calculated as:
Growth factor = 1 + Rate
This gives
Growth factor = 1 + 2.6%
Evaluate the sum
Growth factor = 1.026
Hence, the growth factor as a decimal is 1.026
The number of students enrolled 10 years from nowAs a general rule, the number of students enrolled t years from now is
Students = Initial value * Growth factor^Number of years
This is represented as
Students = 1500(1.026)^t
10 years from now means t = 10
So, we have
Students = 1500(1.026)^10
Evaluate
Students = 1939
Hence, the number of students enrolled 10 years from now is 1939
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How many solutions does this nonlinear system of equations have? NEED HELP ASAP!
Answer:
Step-by-step explanation:
two
Someone please help me
Step-by-step explanation:
Part A: [tex]u^6[/tex] can be written as the square of u³, or [tex](u^3)^2[/tex]. Similarly, [tex]v^6=(v^3)^2[/tex]. Hence, we can write this as a difference of two squares by writing it as
[tex](u^3)^2-(v^3)^2[/tex]
Part B:
Difference of Two SquaresWe can first factor a difference of two squares a² - b² into (a+b)(a-b). Here, a would be u³ and b would be v³.
[tex](u^3+v^3)(u^3-v^3)[/tex]
Sum and Difference of Two CubesWe can factor this further by the use of two special formulas to factor a sum of two cubes and a difference of two cubes. These formulas are as follows:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)\\a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
Since u³ + v³ is a sum of two cubes, let's rewrite it.
[tex]u^3+v^3=(u+v)(u^2-uv+v^2)[/tex]
Since u³ - v³ is a difference of two cubes, we can rewrite it as well.
[tex]u^3-v^3=(u-v)(u^2+uv+v^2)[/tex]
Now, let's multiply them together again to get the final factored form.
[tex]u^6-v^6=(u+v)(u^2-uv+v^2)(u-v)(u^2+uv+v^2)[/tex]
Part C:
If we want to factor [tex]x^6-1[/tex] completely, we can just see that x to the sixth power is just [tex]x^6[/tex] and 1 to the sixth power is just 1. Hence, x can substitute for u and 1 can substitute for v.
[tex]x^6-1=(x+1)(x^2-x(1)+1^2)(x-1)(x^2+x(1)+1^2)\\x^6-1=(x+1)(x^2-x+1)(x-1)(x^2+x+1)[/tex]
We can repeat this for [tex]x^6-64[/tex], as 64 is just 2 to the sixth power.
[tex]x^6-64=(x+2)(x^2-x(2)+2^2)(x-2)(x^2+x(2)+2^2)\\x^6-64=(x+2)(x^2-2x+4)(x-2)(x^2+2x+4)[/tex]
The population mean is symbolized as ________________, whereas the sample mean is symbolized as __________________. Group of answer choices n; N N; n
The population mean is symbolized as μ. The sample mean is symbolized M.
What is a Population?
A population in statistics, is a the total number of people of a group that shares similar characteristics that are of interest to a researcher. Example of population a researcher can understudy include:
Sixth grade students taking mathApple watch usersPeople who patronize a shopping mall, etc.What is a Sample?A sample is a subset of a population, which is drawn using any sampling technique. An example of a sample is 100 randomly selected persons who patronize a shopping mall.
What is the Population Mean?The population mean can be defined as the average data value of a particular group characteristics that is measured by the researcher. The symbol for population mean is: μ.
What is the Sample Mean?
The sample mean can be defined as the average data value of the sub-group of an entire population that having characteristics that are of interest to a researcher. The symbol for sample mean is: M.
In summary, the population mean is symbolized as μ. The sample mean is symbolized M.
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The temperature was -20.5°F at 5 A.M. and rose 5 degrees per hour for the next 5 hours. Melissa says the temperature at 10 A.M. was -5.5°F. Which statement identifies Melissa’s error and the correct answer?A.Melissa multiplied incorrectly. The correct answer is -0.5°F.B.Melissa multiplied incorrectly. The correct answer is 9.5°F.C.Melissa added incorrectly. The correct answer is 4.5°F.D.Melissa added incorrectly. The correct answer is 5.5°F.
The statement which identifies Melissa’s error and the correct answer is; Melissa added incorrectly. The correct answer is 4.5°F
TemperatureInitial temperature = -20.5°FChange in temperature per hour = 5°FNumber of hours = 5New temperature = Initial temperature + (Change in temperature per × Number of hours)
= -20.5°F + (5°F × 5)
= -20.5°F + (25°F)
= 4.5°F
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Answer:
C
Step-by-step explanation:
Solution
We can start with the pythagorean theorem:
(leg 1)² + (leg 2)² = (hypotenuse)²
Substitute the values we know.
15² + x² = 32²
Solve for x.
X =
Answer:
28.26658805 (I included every digit in case your teacher needs you to round)
Step-by-step explanation:
In order to find x, we need to isolate x by subtracting 15^2 and taking the square root of both sides.
Thus, we have:
[tex]15^2+x^2=32^2\\x^2=32^2-15^2\\\sqrt{x^2} =\sqrt{(32^2-15^2)} \\\sqrt{x^2}=\sqrt{799} \\x=28.26658805[/tex]
What are the center and radius of the circle given by x^2 + y^2 - 16x + 8y + 4 = 0?
The center of the circle = (8, -4)
The radius of the circle = [tex]\sqrt{76}[/tex]
Finding the center and radius of a circle from the equationThe given equation of the circle is:
[tex]x^2+y^2-16x+8y+4=0[/tex]
The equation can be expressed and simplified as:
[tex]x^2-16x+y^2+8y=-4\\\\x^2-16y+8^2+y^2+8y+4^2=-4+8^2+4^2\\\\(x-8)^2+(y+4)^2=-4+64+16\\\\(x-8)^2+(y+4)^2=76[/tex]
The general equation of a circle is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
Comparing the two equations:
The center, (a, b) = (8, -4)
The radius, r = [tex]\sqrt{76}[/tex]
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A couple purchased a home and signed a mortgage contract for $900,000 to be paid with half-yearly payments over a 25-year period. the interest rate applicable is j2 = 5.5% p.a. applicable for the rst ve years, with the condition that the interest rate will be increased by 12% every 5 years for the remaining term of the loan.
A mortgage payment is typically made up of four components: principal, interest, taxes, and insurance. The Principal portion is the amount that pays down your outstanding loan amount. Interest is the cost of borrowing money. The amount of interest you pay is determined by your interest rate and your loan balance.
The term “loan” can be used to describe any financial transaction where one party receives a lump sum and agrees to pay the money back. A mortgage is a type of loan that's used to finance a property. A mortgage is a type of loan, but not all loans are mortgages. Mortgages are “secured” loans.
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Meena’s father’s present age is six times Meena’s age. Five years from now she will be one-third of her father’s present age. What are their present ages?
Answer:
Meena age = 5 yrs Meenas father = 30
Step-by-step explanation:
let,
meena's age = x
meena's father's age = 6x
Five years from now
meena's age will be 1/3(6x)
meena's father's age will be 6x+5
A/Q
x+5+6x+5=2x+6x+5
=x+6x-2x-6x=5-5-5
= -x =-5
= x =5
meena's age = 5
meena's father's age = 6x
= 6×5
= 30