Applying the properties of operations; it follows that; 3.5n + 4 (5 1/4n - 1.5) is equivalent to -21 (2/7 - 7/6n).
Properties of OperationsThere are four (4) basic properties of real numbers which apply to addition and multiplication: namely; commutative, associative, distributive and identity.
Hence, by the cumutative property of multiplication and associative property of addition, it follows that;
4× -1.5 = -21(2/7)3.5n + 4(5 1/4n) = -21(7/6n)Hence, it follows that the expressions are equivalent.
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What is the gradient of the blue line
Answer:
4
Step-by-step explanation:
gradient = diffrence in y / diffrence in x
= 4-0/5-4
4
A circle with center O(3,3)O(3,3) contains the point A(-1,14)A(−1,14).
Write a subtraction expression for each length OF AB and ABAB:
The equation for the subtraction of length of AB is -3-(-14)
How to calculate the distance between two points:The distance between two points is the measure of the distance covered by an object.
From the given diagram, we are to find the distance between the point A and B. Since the x-coordinate are equal, hence:
AB = y2 - y1
AB= -3 - (-14)
AB = 11 units
Hence the equation for the subtraction of length of AB is -3-(-14)
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The radius of a cylindrical water tank is 6.5ft, and its height is 17ft. What is the volume of the tank?
Use the value 3.14 for [tex]\pi[/tex], and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer
718.25 pi or 2,256.4489
Step-by-step explanation:
The volume formula for cylinders is V=pi * r^2 * h
So plug in your numbers!
r=6.5 h=17
pi times 6.5^2 times 17 = pi*718.25 or 2,256.4
3) You need to paint shutters on a window that is on the second floor of your house. You have a 20 foot ladder that you will use. There is a warning on the ladder that states the angle formed by the ladder and the ground must not be less than 70 degrees, or the ladder may slip and cause serious injury or death. You planned on placing the bottom of the ladder 3 feet from the base of the house. Will the angle formed between the ground and the ladder be safe? What is the furthest possible distance the ladder can be placed to maintain a safe angle? Sketch:
Answer:
See below ↓↓
Step-by-step explanation:
Height of ladder = 20 feetDistance of base of ladder from house = 3 feetAngle must not be < 70°Taking the cos ratio of the angle
Let the angle formed be α cos α = adjacent side / hypotenusecos α = 3 / 20 = 0.15α = cos⁻¹ (0.15)α = 81.37°⇒ The angle formed is safe
Finding furthest possible distance
Take α to be 70°cos 70° = 0.34 = x/20⇒ x = 20 x 0.34 = 6.8 feetAnswer:
Yes, the angle formed between the ground and the ladder is safe
6.84 ft (nearest hundredth)
Step-by-step explanation:
We can use the cos trig ratio to determine the angle made between the 20ft ladder and 3ft from the base of the house (see first attached image for sketch).
[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]
where:
[tex]\theta[/tex] is the angleA is the side adjacent to the angleH is the hypotenuseGiven:
A = 3 ftH = 20 ft[tex]\sf \implies \cos(\theta)=\dfrac{3}{20}[/tex]
[tex]\sf \implies \theta=\cos^{-1}\left(\dfrac{3}{20}\right)[/tex]
[tex]\sf \implies \theta=81.37307344..^{\circ}[/tex]
Therefore, as the ladder is forming an 81.37° angle and 81.37...° > 70° the angle formed between the ground and the ladder is safe.
To find the furthest possible distance the ladder can be placed, set [tex]\theta[/tex] to 70° (max safe angle) and the hypotenuse (ladder length) to 20, then solve for A (see second attache image for sketch):
[tex]\sf \implies \cos(70^{\circ})=\dfrac{A}{20}[/tex]
[tex]\sf \implies A=20\cos(70^{\circ})[/tex]
[tex]\sf \implies A=6.840402867...\: \sf ft[/tex]
So the furthest possible distance the ladder can be placed to maintain a safe angle is 6.84 ft (nearest hundredth).
_ __
0.47 and 0.47 as simplified fractions
Answer:
Here is your answer
Step-by-step explanation:
What is 0.47 as a fraction? 0.47 as a fraction in simplest form is written as 47/100.
A fraction represents a part of a whole, written in the form of p/q where p and q are integers.
Here we will show you how to convert 0.47 decimal number to fraction form and as a mixed number with steps.
0.47 as a simplified fraction
47/100
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE
Answer:
47/100
Step-by-step explanation:
0.47 as a fraction in simplest form is written as 47/100.
Please mark me Brainliest
What is the perimeter of the polygon below?
The perimeter of the polygon will be 30 units. Then the correct option is D.
What is the perimeter of the regular polygon?All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.
P = (Side length) x n
The sides length of the polygon is 10 units, 5 units, 3 units, 2.5 units, 7 units, and 2.5 units.
Then the perimeter of the polygon is given as,
P = 10 + 5 + 3 + 2.5 + 7 + 2.5
P = 30 units
The perimeter of the polygon will be 30 units. Then the correct option is D.
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Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
12, 10, 8,.........
This is______sequence and the _______is equal to _________.
Answer:
Step-by-step explanation:
This is an arithmetic sequence and the common difference = - 2
You might be a little puzzled by the minus sign in front of the two. You can look at the sequence for the answer. It is going down. A plus 2 would make it go up. Minus signs are always a bit tricky and you have to watch out what you do with them. But the rule is simple
a minus common difference produces a sequence that goes down.a plus common difference produces a squence that goes up.You know that this is an arithmetic sequence because the common difference can be found by adding or subtracting a number from the previous term to get to the next term.
A geometrice sequence would use multiplication or division to get from one term to the next.
what is the angle of BTC, Angle TBC,Angle TCB
By geometric and algebraic properties the angles BTC, TBC and TBC from the triangle BTC are 128°, 26° and 26°, respectively.
How to determine the angles of a triangle inscribed in a circle
According to the figure, the triangle BTC is inscribed in the circle by two points (B, C). In this question we must make use of concepts of diameter and triangles to determine all missing angles.
Since AT and BT represent the radii of the circle, then the triangle ABT is an isosceles triangle. By geometry we know that the sum of internal angles of a triangle equals 180°. Hence, the measure of the angles A and B is 64°.
The angles ATB and BTC are supplmentary and therefore the measure of the latter is 128°. The triangle BTC is also an isosceles triangle and the measure of angles TBC and TCB is 26°.
By geometric and algebraic properties the angles BTC, TBC and TBC from the triangle BTC are 128°, 26° and 26°, respectively.
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I dont know how to solve equations by completing the square x^2 −51=14x
Answer:
or, x^2-14x-51=0
or, x^2-(17-3)x-51=0
or, x^2-17x+3x-51=0
or, x(x-17)+3(x-17)=0
or, (x-17)(x+3)=0
Either, x-17=0. Or, x+3=0
x=17. x= -3
Hence,x=17, -3
[tex]x^2-51=14x\\\\\implies x^2-14x = 51\\\\\implies x^2 -2\cdot 7\cdot x+7^2-7^2 =51\\ \\\implies x^2 -2\cdot 7 \cdot x +7^2 = 51 +49\\\\\implies (x-7)^2=100\\\\\implies x-7 = \pm\sqrt{100}\\\\\implies x =\pm10+7\\ \\\text{Hence,}~ x=17, ~x=-3[/tex]
good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
The degree of the polynomial is
options 2,3,5,6
The leading coefficient of the polynomial is
options 2,3,5,6
Is there a constant term in the polynomial?
options: yes, no.
This expression can be called a blank
expression.
options: monomial, binomial, trinomial
Answer:
2
5
YES
trinomial
Step-by-step explanation:
Given expression: [tex]5x^2+3x+6[/tex]
The degree of the polynomial is the highest exponent = 2
The leading coefficient, is the coefficient (value) before the [tex]x^2[/tex] = 5
The constant in the polynomial is the value without a variable, i.e. 6 = YES
This expression can be called a trinomial expression since it is a polynomial with exactly three terms.
Expression given:-
5x^2+3x+6So
Degree=2Leading coefficient=5Constant yes(6)Three variables a,b,c hence trinomial14 g of copper was heated from 50°C to 85°C. How much energy was used to heat Cu? (Specific heat capacity of Cu is 0.385 J/g °C)
HELP PLEASE GIVING OUT BRIANLEST TO THE CORRECT ANSWER THANK YOUU
Q = mcΔt
Q = 14 x 0.385 x (85-50)
Q = 161.7 J
a. Find the mean and the median of this data:9,6,5,3,28,6,4,7.
b. Which better describes the data set, the mean or the median? Explain.
Answer:
a) organized-
3,4,5,6,6,7,9,28
median is 6
68/8=8.5
the mean is 8.5
b) the median, because there is an outlier
If the zeros of a quadratic function, F, are -2 and 4, what is the equation of the axis of symmetry of F
Answer:
x=1
Step-by-step explanation:
if the zeroes are (-2,0) and (4,0), then the axis of symetry is going to be right in the middle of those two, with the graph reflected equally on either side.
so you get:
(4-2)÷2=1
therefore the equation of the axis of symetry is x=1
2(3x+2)=6x+4 linear equations
Answer:
0 or 6x+4=6x+4 (Technically no slope at all!!)
Step-by-step explanation:
You need to do distributive property and then solve for x!!
meaning the 2(3x+2) has to get distributive property process.
6x+4=6x+4
That shall be equal together!!! (You could stop here!!)
If continue:
6x-6x=4-4
0=0
HELP PLS MY SISTER NEEDS HELP A LOT I WILL GIVE BRAINLIEST
Answer:
38 is the correct answer
Step-by-step explanation:
6 x 7 - 16 ÷ 4
BODMAS
Division first
6 x 7 - 4
Then multiplication
42 - 4
Then subtraction
=38
The blueprint for the Moreno's living room has a scale of . The family wants to 2 inches= 3 feet use a scale of 1 inch =4 feet. What is the width of the living room on the new blueprint?
Answer:
If I am understanding the question correctly, every 6 feet in real life will be equivalent to 1 inch "on paper", or in the blueprint. Using dimensional analysis, which is a methodology for converting from one unit to another, we have:
18 feet * 1 inch / 6 feet = 3 inches
On the other axis,
24 feet * 1 inch / 6 feet = 4 inches
Therefore, the blueprint for this 18x24 foot room, with a scale of 6 feet:1inch, should be 3x4 inches.
Write all the names of the quadrilateral shown.
A square, rhombus, parallelogram
B square, rectangle, parallelogram
C square, rectangle
D square, rhombus, rectangle, parallelogram
Answer:
A
Step-by-step explanation:
my brain says so?
Select the correct answer.
What is the range of the function shown on the graph?
у
1
6
2-
4
-8
-6
x
х
-2
2
8
-21
64
8
The range of the function shown on the graph is 20≤y≤60
What is a function?A relation is a function if it has only One y-value for each x-value.
What can go into a function is called the Domain.
What may possibly come out of a function is called the Codomain.
What actually comes out of a function is called the Range.
Range is all the possible values of 'y'.
When we observe the graph, the smallest value of 'y' is 20, where the point is (6, 20), and the largest value of 'y' is 60, where the point is (1, 60).
Therefore, the range of the function shown on the graph is 20≤y≤60
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What is the range of the function in the graph?
. 1≤x≤6
B. 20≤y≤60
C. 20≤x≤60
D. 1≤y≤60
The price of a machine depreciates by 10% every
year. If the machine is bought for $18000 and sold
after 3 years, what price will it fetch?
i need help with this i will give 100 pt
Answer:
1. Where you shop at
2. The tax in the state you live in.
Hope this helps!
Answer:
1. Where you shop at2. The tax in the state you live in.
Step-by-step explanation:
Two friends are biking. Greta starts at mile marker S on a bike trail and is biking at a speed of 12 miles per hour The table shows the mile marker Shayla reaches after biking x hours. What is the difference in the initial values of the functions? Record your answer on the grid. Then fill in the bubbles.
The distance covered by Greta after biking at a speed of 12 miles per hour for x hours is 12x miles.
What is speed?Speed is the ratio of distance travelled to time taken. It is given by:
Speed = distance / time
Greta starts at mile marker S on a bike trail and is biking at a speed of 12 miles per hour. If she biked for x hours:
Distance covered = 12 mph * x = 12x miles
The distance covered by Greta after biking at a speed of 12 miles per hour for x hours is 12x miles.
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SOMEONE PLEASE HELP ME WITH THIS!!
IMAGE DOWN BELOW!!
ILL GIVE YOU BRAINLIST ANSWER!!
Answer:
5.735
pythagorian theorem is a^2 + B^2 = c^2
C is the longest side of the right triangle
You ran 4 1/2 times around a quarter-mile track how far did you run
Answer:
1,809 meters. (1 & 1/8 of a mile)
Step-by-step explanation:
quarter of a mile = 402 meters
402 * 4.5 = 1,809 meters = 1 1/8 mile
Find the length of the third side. If necessary, round to the nearest tenth
Pythagorean Theorem (Rounding)
Answer:
8
Step-by-step explanation:
[tex]a^2+b^2=c^2\\a^2+6^2=10^2\\a^2+36=100\\[/tex]
subtract 36 from each side
[tex]a^2=64\\\sqrt{a^2=64}\\a=8[/tex]
or you could recognize the 3-4-5 Pytagorean triple, as the ratio is doubled.
Find the center and radius of the circle represented by the equation below.
(x − 13)² + (y + 11)² = 361
-
Center:
Radius:
Answer: Center: (13, -11)
Radius: 19
Step-by-step explanation: yeah
A company made 189,909 stuffed animals in 2009 in 2010 the company made 198,909 stuffed animals which statement correctly compares the number of stuffed animals that were there CHOICES : A 189,909 > 198,909 B 198,909 < 189,909 C 189,909 < 198,909 D 198,909 = 189,909 and can you please tell me what to do and the answer PLEASEEEEEE
The comparison of the number of stuffed animals in both years is an illustration of inequalities
The statement that compares the number of stuffed animals is 189909 < 198909
How to compare the stuffed animals?The given parameters are:
Stuffed animals in 2009 = 189,909Stuffed animals in 2010 = 198,909By comparing the number of stuffed animals in both years, we have:
198909 > 189909 or 189909 < 198909
Hence, the statement that compares the number of stuffed animals is 189909 < 198909
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Factor the expressions 7 – 42
Answer:
7 (1-6)
Step-by-step explanation:
you find the greatest common factor of 7 and 42.
7
7x1
42
1x42
2x21
3x14
6x7
Please help me calculate the area of all the grey parts of this shape :)
Answer:
.858 cm^2
Step-by-step explanation:
Area of square - area of circle = grey corner areas
(2 * 2) - ( pi * 1^2 ) =
4 - pi = .858 cm^2
NEED HELP ASAP.PLEASEEEE
Hello, can you help me out with this please i will give brainlist :D
Answer:
2.23
Step-by-step explanation:
