Answer:
(∞,-3) and (1,-∞)
Step-by-step explanation:
Decreasing means going down or in math terms, going toward the negatives.
When you are talking intervals in math, you only want to use the x-axis for the interval points. We write the interval as if it was a coordinate point though.
Looking at the graph it looks like it is going from infinity to -3 or written as (∞,3) and from 1 to negative infinity or written as (1, -∞)
The interval(s) for which the function shown below is decreasing are (∞,-3) and (1,-∞).
What is a function?A function is a relationship between two sets of values in mathematics where each input value (or "argument") corresponds to a certain output value.
In most cases, the input values come from a set referred to as the function's domain, while the output values come from a set referred to as the function's range.
Declining is the mathematical phrase for decreasing or moving towards the negatives.
Mathematicians only use the x-axis to represent interval points when discussing intervals. Yet, we express the interval as if it were a coordinate point.
If you look at the graph, it appears to be traveling from infinity to -3, which is written as (,3), and from one to negative infinity, which is written as (1, -).
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What is the sum of the first eight terms in this series?
2 + 10 + 50 + 250 + …
Answer:
195312
Step-by-step explanation:
Using the formula for the sum of a geometric sequence,
[tex]\frac{2(1-(5)^8)}{1-5}=195312[/tex]
What is the value of x?
The required value of x is 3 in the given equilateral triangle.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
The triangle given in the figure is an equilateral triangle.
We know that all sides are equal in the equilateral triangle.
As per the given figure,
side AB = side AC
6x - 3 = 3x + 6
6x - 3x = 6 + 3
Apply the arithmetic operation,
3x = 9
x = 9/3
x = 3
Therefore, the required value of x is 3 in the given equilateral triangle.
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marie bought 1/2 gallon of milk which she finished after 6 days if she drank the same amounteach day how many gallons a day did she drink
She drinks 1/12 gallons of milk each day
How to determine how many gallons a day did she drink?From the question, we have the following parameters that can be used in our computation:
Size of milk = 1/2 gallons
Number of days = 6 days
These parameters can be represented as
(x, y) = (6, 1/2)
The number of gallons a day she drinks can then be represented as the slope/unit rate and the unit rate is then calculated as
unit rate = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 0) and (6, 1/2)
Substitute the known values in the above equation
So, we have the following equation
Slope = (1/2 - 0)/(6 - 0)
Evaluate the quotient
Slope = 1/12
Hence, the number of gallons she drinks a day is 1/12
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Triangle PQR is isosceles, Q being the right angle. If the hypotenuse is 38.47cm, find: i. Lengths of sides PQ and QR. ii. The size of angle QPR
The size of angle QPR is 45° and the length of sides PQ and QR are both 27.20cm
What are Isosceles triangle?An isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal angle,
since ∆PQR is a right angle isosceles triangle then, if angle Q is 90^°, QPR = PRQ=x( angles of an isosceles triangle).
Therefore 90+x+x= 180°
2x= 90
x= 45°
To find line PQ and QR, we use trigonometry ratio
cos 45°= adj/hyp
I/√2= QR/38.47
QR= 38.47/√2
= 27.20cm
QR= PQ= 27.20
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In a photo contest, two judges are giving scores to each photo. Each judge gives a score for impact (worth 40%), composition (worth 30%), lighting (worth 20%), and color balance (worth 10%). Lester entered a photo in the contest and received the following scores: Impact: 8 and 9 Composition: 7 and 7 Lighting: 8 and 7 Color balance: 5 and 7 Enter a number in each box to create an expression that represents Lester's final score.
Lester's final score from the two Judges is 7.6
How to calculate Lester's final scoreThe scores of the judges are in percentage and this will be converted to decimal by dividing by 100
impact (worth 40%) = 0.4
composition (worth 30%) = 0.3
lighting (worth 20%) = 0.2
color balance (worth 10%) = 0.1
Average score from the Judges will be used to multiply the percentages
Impact: 8 and 9
= 8.5 * 0.4 = 3.4
Composition: 7 and 7
= 7 * 0.3 = 2.1
Lighting: 8 and 7
= 7.5 * 0.2 = 1.5
Color balance: 5 and 7
= 6 * 0.1 = 0.6
sum of the scores gives Lester's final score as 7.6
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water faucet leaked 3/5 liters of water over the course of 2/5 hours. How many liters would it have leaked in 1 hour please tell me the answer
Answer:
1.5 liters
Step-by-step explanation:
what fraction of the numbers from 1 to 20 contain the digit 7
Approximately 72% of persons living in Cape Town who are aged 70 to 84 live in elderly care facilities. If four persons are randomly selected from this population, what is the probability that exactly two of the four live in elderly care facilities?
Select one:
The probability that exactly two of the four live in elderly care facilities is; 0.244
How to solve Binomial Probability Distribution?The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.
The general formula of binomial probability distribution is;
P(X = x) = nCx * p^(x) * (1 - p)^(n - x)
where;
Px = the probability of exactly x events occurring.
x = the number of expected successful outcomes.
p is probability of success
n is sample size
We are given;
p = 72% = 0.72
n = 4
Thus;
P(X = 2) = 4C2 * (0.72)^(2) * (1 - 0.72)^(4 - 2)
P(X = 2) = 0.244
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Eve and Patty swam fewer laps than Maureen. Patty swam more laps than Eve, and Maureen swam fewer laps than Raymond. Who swam the most laps?
Answer:
Raymond
Step-by-step explanation:
1 ) Eve and Patty swam fewer laps than Maureen so...
Eve and Patty < Maureen
2 ) Patty swam more laps than Eve...
Patty > Eve
3 ) Maureen swam fewer laps than Raymond...
Maureen < Raymond
4 ) We can eliminate Eve and Patty since they swam fewer laps than Maureen. The ones who are left are...
Maureen and Raymond
5 ) We know that Maureen swam fewer laps than Raymond so we can eliminate Maureen.
Raymond
6 ) This mean that the one who swam the most laps is...
Raymond
Hope this helps! :)
Which one is triangle a and b
In both triangle one angle is larger than 90 degree . so these triangles are obtuse triangles.
What is Obtuse triangle?
When one of the interior angles of a triangle is more than 90 degrees, the triangle is said to have obtuse angles. The sum of the other two angles in an obtuse triangle is less than 90° if one angle in the triangle is greater than 90°.Degrees with obtuse angles include 110°, 135°, 150°, 179°, 91°, and more. Therefore, all angles that fall between 90° and 180° are obtuse angles.Triangle B = Obtuse triangle
Triangle C = Obtuse triangle
in both triangle one angle is larger than 90 degree . so these triangles are obtuse triangles.
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PLEASE HELP!!
F(n)=3n-4
find term 3
The third term of F(n)=3n-4 is 5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
F(n)=3n-4
F of n equal to three times of n minus four.
We need to find the third term.
To find third term we need to plug 3 in place of n.
F(3)=3(3)-4
Three times three minus four
F(3)=9-4
Nine minus four gives 5
F(3)=5
Hence, the third term of F(n)=3n-4 is 5.
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Subtract.
Your answer should be a polynomial in standard form.
(6a³ + 7a²) - (5a³ + 9a² + a) =
Step-by-step explanation:
=6a^3+7a^2-5a^3-9a^2-a
=a^3-2a^2-a this is the final answer.
Which points are on the axes 5 units from the origin
Answer: X
Step-by-step explanation:
you just start at 0 since that is the origin and go up 5
damian bought a new game station for $774 using the stores zero intrest finace plan. He will pay$43 a month for 18 months. Which equation csn he use ti fund out how much money he still owes
The equation Damian can use to found out how much money he still owes is -
y = - 43x + 774
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
We have the following problem -
Damian bought a new game station for $774 using the stores zero interest finance plan. He will pay $43 a month for 18 months.
We can represent the equation he can use to found out how much money he still owes using a straight line as follows -
y = 774 - 43x
y = - 43x + 774 [x] is the number of month
Therefore, the equation Damian can use to found out how much money he still owes is -
y = - 43x + 774
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35. Rosa plants rows of flowers with exactly the same number
in each row. Each row has more than one flower. She has
28 flowers. What is the largest number of rows she can make?
A 4
B
7
12
D 14
Answer: 10 rows of rose plants
Step-by-step explanation:
The number of rose plants in first, second third,..., and last row are respectively.
23,21,19,....,5.
number of rose plants: n
The sequence 23,21,19,....,5 is an A.P. with first term a(=23), common difference d(=−2) and n
=a+(n−1)d
⟹5=23+(n−1)×−2
⟹5=23−2n+2⟹20=2n⟹n=10
3. Plumbers deal with measurements in inches and common fractions of an inch, while surveyors use feet and decimal
fractions of a foot. Often one trade needs to interpret the measurements of the other.
(a) A drain has a run of 52 ft at a grade of 1/8 in./in. The high end of the drain has an elevation of 126.30 ft. What is the elevation at the low end?
(b) The elevation at one end of a lot is 84.12 ft, and the elevation at the other end is 94.67 ft. Express the difference in elevation in feet and inches and rounded to the nearest 1/8 in
The elevation at the lower end of a drain is 119.8 feet. For the second drain difference in feet will be 10.55 feet and in inches will be 126.6 inch.
What is elevation?The height above or below a fixed reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation. A vertical surface is depicted in an elevation when viewed from a point perpendicular to the viewer's picture plane. You are looking at the front elevation, for instance, if you are standing directly in front of a building and viewing its front. The height between a point and a horizontal surface is known as HEIGHT. The height of a point above (or below) sea level is known as its ELEVATION.
Here,
a. The length of drain= 52 feet
the gradual decrease=0.125 ft
elevation at high end=126.30 feet
elevation at low end,
=126.3-(52*0.125)
=126.3-6.5
=119.8 feet
b. The elevation at one end=94.67 feet
The elevation at other end=84.12 feet
The difference in elevation,
=94.67-84.12
=10.55 feet
=10.55*12
=126.6 inches
The elevation of a drain's lower end is 119.8 feet. The second drain will differ by 10.55 feet in feet and 126.6 inches in inches.
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Carl is making accessories for the soccer team. He uses 773.85 inches of fabric on headbands for 29 players and 4 coaches. He also uses 279.56 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
23.45 inches fabric was used on a headband and 9.64 inches fabric was used on a wristband for each player.
No. of players = 29
No. of coaches = 4
Total fabric used for headbands = 773.85 inches
Total no. of people for headbands = 29 + 4
= 33
Fabric used for headband for 1 person = 773.85/33
= 23.45 inches
Total fabric used for wristbands = 279.56 inches
Total no. of people for wristbands = 29
Fabric used for headband for 1 person = 279.56/29
= 9.64 inches
Hence, fabric for headband is 23.45 inches and for wristband is 9.64 inches.
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9.8 x 100 =
0.040 x 1,000 =
61 divide 10 =
8.909 x 100 =
Answer:
9.8 * 100 = 980
0.040 * 1000 = 40
61 / 10 = 6.1
8.909 * 100 = 890.9
Step-by-step explanation:
Find the values of x, y, and z. The diagram is not to scale.
Answer:
x= 68 z= 180 y=38
Step-by-step explanation:
How many times greater is 5.96 × 10^4 then 2.98 × 10^3?
A. 20
B. 500
C. 50
D. 200
The number 5.96 × 10⁴ is 20 times greater than 2.98 × 10³ , the correct option is (a) .
In the question ,
it is given that
the number is 5.96 × 10⁴ ,
we have to find that how many times greater is 5.96 × 10⁴ then 2.98 × 10³ .
to find that the number is how many times greater ,
we divide 5.96 × 10⁴ by 2.98 × 10³ .
So , on dividing the numbers we get
= ( 5.96 × 10⁴ ) / ( 2.98 × 10³ )
= 5.96/2.98 × 10⁴⁻³
= 2 × 10¹
= 20 times
Therefore , The number 5.96 × 10⁴ is 20 times greater than 2.98 × 10³ .
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Graph the line with slope 1 passing through the point (-2 , -5)
Graph the line.
The equation of the line is y = x -3. The graph of the line is attached below.
What is a line?
A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.
Given that the slope of the line is 1.
Assume that the equation of the line is y = mx +c, where m is the slope of the line and c is y-intercepts.
Putting m = 1 in y = mx +c:
y = 1 × x +c
y = x +c
Since the line passes through the point (-2, -5), thus the point satisfies the given equation of line.
Putting x = -2 and y = -5 in y = x +c
-5 = -2 + c
c = -3
The equation of line is y = x - 3.
The points on the line are
(-2, -5), (0, -3), (3, 0).
Plot the points and join them:
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A straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form. 8 in. 5 in. 5 in.
The length of the straw fitted in the box is 10.67 inches.
What is cuboid?A cuboid is a solid three-dimensional object which has six faces that are rectangular with eight vertices, and twelve edges.
Given that, a straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner,
Diagonal of a cuboid = √ l² + w² + h²
Therefore, diagonal of the box = √ 5² + 5² + 8² = 10.67 in
Hence, The length of the straw fitted in the box is 10.67 inches.
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The animals at a safari park include camels,
kangaroos and meerkats.
There are 12 more kangaroos than there are
camels.
There are 3 times as many meerkats as there
are camels.
There are the same number of kangaroos as
there are meerkats.
How many camels are there at the safari park?
Number of camels are there at the safari park are 6 unit.
The animals at a safari park include camels, kangaroos and meerkats.
Let kangaroos are represented as K and Camels are represented as C and Meerkats are represented as M.
There are 12 more kangaroos than there are camels which means
K = C + 12.
There are 3 times as many meerkats as there are camels which means
M = 3C.
There are the same number of kangaroos as there are meerkats which means
K = M
If K = M
therefore,
3C = C + 12
2C = 12 ,
C = 6 unit.
So, K = 6 + 12 = 18
Or M = 18
Therefore number of camels, kangaroos and meerkats at the safari park are 6 , 18 and 18 respectively.
Number of camels are there at the safari park are 6 unit.
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Version 1 for Game Design Determine the center and radius of the circle with equation x² + y² + 4x − 6y + 12 = 0
Answer:
Step-by-step explanation:
Equation of circle is, (x-h)^2+ (y-k)^2=r .......(eqn1)
where, (h,k) is the center and r is the radius.
therefore, from the question by rearranging the equation,
x² + y² + 4x − 6y + 12=0
viz, (x² +4x+4) + (y²-6y+9)-1=0
(x+2)^2 + (y-3)^2=1
therefore from eqn1, (-2,3) is the center and radius is 1
Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. (Round your answer to four decimal places. Enter your answers as a comma-separated list.)
f(x)= 5[tex]\sqrt{x}[/tex], [4,9]
The value of c by using the mean value theorem is c = 6.25.
What is a mean value theorem?The mean value theorem in mathematics says that for any given planar arc between two endpoints, there exists at least one point where the tangent to the arc is parallel to the secant between its endpoints. It is one of the most significant findings in the real-world analysis.
Given that the function is f(x) = 5√x and the interval is (4,9).
Calculate the value of 'c' as below,
f(x) = 5√x
f(4) = 5√4 = 10
f(9) = 5√9 = 15
Calculate the value of f'(c) as below,
f'(c) = ( f(b) - f(a) ) / (b - a)
f'(c) = f(9) - f(4) / ( 9 - 4 )
f'(c) = (15 - 10 ) / ( 9 - 4)
f'(c) = 1
Again the value of f'(x) is,
f'(x) = 5/2/√x
f'(c) = 5 / 2 / (√c)
5 / 2 / (√c) = 1
√c = 5 / 2
c = 25 / 4
c = 6.25
Therefore, the value of c by using the mean value theorem is c = 6.25.
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In the acute triangle ABC with angle ACB = 60°, M is the midpoint of side AB. Points D and E are the height points on sides BC and AC, respectively. Show: The triangle MDE is equilateral
An equilateral triangle in geometry is a triangle with three equal-length sides. An equilateral triangle has congruent sides, which means that each side is the same length. The triangle MDE is equilateral only because it is midpoint of ACB
Explain about the Acute triangle?If the square of the longest side is smaller than the sum of the squares of the two smaller sides, the triangle is said to have an acute angle according to Pythagoras's theorem. Given a triangle with sides "a," "b," and "c," with side "a" being the longest, the triangle is steeply angled if "a2" exceeds "b2" plus "c2."
By adding the squares of the triangle's two smaller sides and comparing the result to the square of the largest side, you may determine whether the triangle is acute, right, or obtuse. The triangle is sharp because this total is higher.
Isosceles, equilateral, or scalene acute triangles are all possible. An acute triangle's longest side is located across from its biggest angle.
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126=2×3×3×k
Solve for k
[tex]{ \huge{ \boxed{ \red{ \sf{x = 7}}}}}[/tex]
Step-by-step explanation:-
[tex]{ \sf{126 = 2 \times 3 \times 3 \times k}}[/tex]
[tex]{ \sf{126 = 6 \times 3 \times k}}[/tex]
[tex]{ \sf{126 = 18 \times k}}[/tex]
[tex]{ \sf{126 = 18k}}[/tex]
Divide both the sides by 18 in order to find the value of k. Then,
[tex]{ \sf{ \frac{126}{18} = \frac{18}{18} k}}[/tex]
[tex]{ \boxed{ \boxed{ \purple{ \sf{x = 7}}}}}[/tex]
Jim borrows $200 at 18% per annum compounded quarterly for 7 years. Determine the interest due on the loan.
The interest on the borrowed amount after 7 years is $486.
What is compound interest?The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.
Given that,
The amount borrowed is P = $200.
Rate of interest is r = 18% per annum compounded quarterly.
Total time is t = 7 years
Then, the rate of interest for quarterly compounding is given by,
r = 18 / 4%
= 4.5%
And, total time period for compounding is,
n = 7 × 4
= 28
The formula for compound interest is given as,
P[(1 + r / 100)ⁿ - 1]
Substitute the respective values to get,
200 × [(1 + 4.5 / 100)²⁸ - 1]
= 200 × 2.43
= 486
Hence, the interest due on the loan is given as $486.
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Which of the following are less than -0.625
Answer: The answer is A
Step-by-step explanation:
-5/8 is literally equal to -0.625 meaning this asnwer is equal not less
-0.5 is Greater than -0.625 because -0.6 is much larger
-8/5 is -1.6 which is Less than -0.625
Mia is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 15 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 18^{\circ}
∘
, and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 53^{\circ}
∘
. If her eyes are 1.75 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest tenth of a meter if necessary.
Considering the angle of elevations, the distance from point AA to point BB which is the height of the antenna is 5.34 meters
How to find the distance between the pointsinformation given in the question
Mia stands at a horizontal distance of 15 meters from the building
The angle of elevation from her eyes to the roof ((point AA)) is 18
the angle of elevation from her eyes to the top of the antenna ((point BB)) is 53^
her eyes are 1.75 meters from the ground
The direction of movements describes a right angle triangle of
opposite = height of antenna + height of the building
adjacent = 15 meters
The distance from point AA to point BB and the height of the antenna is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The the height of the antenna is calculated using tan, TOA let the angle be x
tan x = Opposite / Adjacent
using 53 gives the height of the antenna + height of the building, while using 18 gives height of the building only
tan 53 = opposite / 15
opposite = 15 * tan 53 = 19.906 meters
opposite = 15 * tan 18 = 14.266 meters
Height of the antenna
= 19.606 - 14.266
= 5.34 meters
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