Evaluate using a suitable identity: (997)³
Answer:991026973
Step-by-step explanation:Given:
(997)³
To solve this using an appropriate identity;
i. Rewrite by splitting the value in bracket (997) into a difference of two numbers. i.e
(997)³ = (1000 - 3)³
ii. Use the appropriate identity
Since the split from (i) above gave a cube of the difference of two numbers, we can apply the following identity for finding the cube of the difference of two numbers;
(a - b)³ = a³ - b³ - 3ab(a - b)
In this case;
a = 1000
b = 3
(iii) Substitute the values of a and b into the identity equation and solve;
(1000 - 3)³ = 1000³ - 3³ - 3(1000)(3)(1000 - 3)
(1000 - 3)³ = 1000000000 - 27 - 9000(997)
(1000 - 3)³ = 1000000000 - 27 - 8973000
(1000 - 3)³ = 991026973
Therefore,
(997)³ = 991026973
⚠️TEST QUESTION PLEASE HELP DUE IN 5 MINUTES⚠️
Answer:
Step-by-step explanation:
The letter c
probability please help i will give brainliest
There are (5 C 1) = 5! / (5 - 1)! = 5 ways of drawing a red marble, and (11 C 1) = 11! / (11 - 1)! = 11 ways of drawing any marble, so that the probability of drawing a red marble is 5/11.
After putting back the first marble, the probability of drawing another red is again 5/11.
So the probability of drawing 2 red marbles with replacement is (5/11)² = 25/121.
Determine the solution, if any, to the system of equations below. 8. 2y = 1 - 4x + y = 3 Show your work or explain how you got your answer.
Answer:
y=1/2 , x= -5/8
Step-by-step explanation:
⇒[tex]2y=1. -4x+y=3 : y=\frac{1}{2} \\\left \{ {{2y=1} \atop {-4x+y=3}} \right. \\ where: y=\frac{1}{2} \\-4x+\frac{1}{2}=3\\isolate for -4x+\frac{1}{2} =3: x=-\frac{5}{8} \\y=\frac{1}{2} : x=\frac{-5}{8}[/tex]
The length of the base of an isosceles triangle is x. The length of a leg is 3x-4. The perimeter of the triangle is 97. Find x.
Answer:
x = 15
Step-by-step explanation:
Given that,
The length of the base of an isosceles triangle is x.
The length of a leg is 3x-4.
Perimeter, P = 97
An isosceles triangle has one base. The perimeter of a triangle is given by :
97=x+3x-4+3x-4
97 = 7x-8
97+8=7x
105 = 7x
x = 15
So, the value of x is 15.
Find the missing length of the triangle. 12 in 85 in.
Answer:
From Pythagoras Theorem
The square of the hypotenuse is equal to the sum of the squares of the other two sides
C² = 12² + 35²
C= √12²+35²
C= 37in
Answer:
side c = 37 in.
Step-by-step explanation:
side c is the hypotenuse as it is opposite of right angle (90 degree ).
12 and 35 are the two other smaller sides of the given right angles triangle.
using pythagoras theorem to find side c
a^2 + b^2 = c^2
12^2 + 35^2 = c^2
144 + 1225 = c^2
1369 = c^2
[tex]\sqrt{1369}[/tex] = c
37 = c
On a coordinate plane, a curved line with a minimum value of (0, 1) and a maximum value of (negative 1.3, 2.2), crosses the x-axis at (negative 2.2, 0) and crosses the y-axis at (0, 1).
Which statement correctly identifies a local minimum of the graphed function?
Over the interval [–3, –2], the local minimum is 0.
Over the interval [–2, –1], the local minimum is 2.2.
Over the interval [–1, 0.5], the local minimum is 1.
Over the interval [0.5, 2], the local minimum is 4.
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
cuz i did the test
can someone please help for brainlest
Click an item in the list or group of pictures at the bottom of the problem and holding the button down drag it into the correct position in the answer box release mouse evaluate
Answer:
1/9
Step-by-step explanation:
0.1(repeating)
Thank you if anyone help me
Answer
The answer is y= x-3
- - - - -
5
Explanation
Replace
f(x) with y.
y =5x+3
Swap x and y.
x =5y+3
Solve for y.
x - 3=5y
x-35=y
Estimate the perimeter and the area of the shaded figure to the nearest tenth.
A board 180 cm long is cut into two pieces such that 3 times the length of the larger piece is 85 cm longer than 4 times the length of the smaller piece. How long are the two pieces of board?
Answer:
smaller piece is 65cm
larger piece is 115cm
Step-by-step explanation:
let 's' = smaller piece
let '180-s' = larger piece
3(180-s) = 85 + 4s
540 - 3s = 85 + 4s
540 = 85 + 7s
455 = 7s
s = 455/7 which is 65cm
larger piece = 180-65 or 115cm
CAN SOMEONE HELP ME WITH THIS, PLEASE AND THANK YOU.
1 1/3 × 4
= 4/3 × 4
= 16/3
= 5 1/3
Answer:
5 1/3
Step-by-step explanation:
1 1/3 * 4
Change 1 1/3 to an improper fraction
1 1/3 = (3*1+1)/3 = 4/3
4/3 *4 = 16/3
Change to a mixed number
3 goes into 16 5 times with 1 left over
5 1/3
đa thức p (x) = 2x ^ 3 - 3x ^ 2 + qx +56 có nhân tử là x-2 a) chứng tỏ q = -30? b) thừa số p (x) hoàn toàn và do đó xác định tất cả các nghiệm của p (x) = 0
Please help me with these three questions...
I will be really thankful for help
Answer:
1. Terminating
2. 60
3. I don't know
Step-by-step explanation:
Which ratios are equal to cos(B)? Choose the TWO ratios that apply.
Answer:2 and 5
Step-by-step explanation:
The ratios that are equal to [tex]cos(B)[/tex] : [tex]\bold{\frac{BC}{AB}}[/tex] and [tex]\bold{\frac{EF}{DE}}[/tex]
What are similar triangles?"Two triangles are said to be similar
- if corresponding angles are equal and the sides
- if corresponding sides of the triangles are in proportion."
What is cosine angle?In a right triangle,
cos(Ф) = (adjacent side of angle Ф) ÷ hypotenuse
For given example,
Triangles ABC and DEF are similar triangles.
This means, ∠A = ∠D, ∠B = ∠E, ∠C = ∠F
And, [tex]\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}[/tex] ..............(i)
For a right triangle ABC,
the cosine of angle B is,
[tex]cos(B)=\frac{BC}{AB}[/tex]
From (i),
[tex]\frac{BC}{AB}=\frac{EF}{DE}[/tex]
So, the cosine of angle B is,
[tex]cos(B)=\frac{EF}{DE}[/tex]
Therefore, the ratios that are equal to [tex]cos(B)[/tex] : [tex]\frac{BC}{AB}[/tex] and [tex]\frac{EF}{DE}[/tex]
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It takes for plumbers five days to fit central heating in an office block. How long would it take ten plumbers?
Answer:
2 days
Step-by-step explanation:
It takes four plumbers five days
total labor needed
4 * 5 = 20 days
How long would it take ten plumbers?
20 / 10 = 2 days
calculate (4.8×10⁵)÷(1.2×10³),give your answer in standard form to 3 significant figures
Step-by-step explanation:
pleae mark as brain list please give me some thanks please
if you horizontally shift the square root parent function f(x)=√x left two units what is the equation of the new function
Answer:
[tex] \sqrt{x + 2} [/tex]
If you horizontally shift the square root parent function f(x)=√x left two units the equation of the new function is: g(x) = √(x + 2).
What is horizontal shift?A horizontal shift is a function transformation that shifts a graph to the left or right without changing its shape.
If we want to shift the square root parent function f(x) = √x two units to the left, we must replace the argument x with (x + 2), because a positive value of x + 2 gives us the same x value two units to the left.
So the equation of the new function is:
g(x) = √(x + 2)
This new function is the square root function shifted two units to the left. For any given input value of x, we add 2 to it before taking the square root. This causes the graph to shift horizontally to the left by two units.
Thus, g(x) = √(x + 2) will be the new function.
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harleys house has a value of £160000 correct to 2 significant figures
write down the least possible value of the house
write down the greatest possible value of the house
Answer:
155,000
159,999
Step-by-step explanation:
In order to correct to 2 significant figures, look at the third figure, if the number is greater or equal to 5, add 1 to the ten thousand figure. If this is not the case, add zero. Replace all the figures before the thousand figure with zero. i.e. the hundred ten, unit
e.g. Rounding off 10,999 to the nearest thousand is 11,000
In this example, the least figure, the thousand figure should have to be rounded off to 2 significant figures is 5 and the greatest figure it can have is 9
Question is in photo.
Thanks
Answer: yes
Step-by-step explanation: because if you can draw a line through the graph and hit most of the dots it would be considered linear.
Answer:
Yes
Step-by-step explanation:
The correlation of the dots is very strong although it can't be a straight line.
Hope this helps
A scale model of a sculpture has a scale of 2:53
The height of the model is 20cm.
Find the height of the actual sculpture.
Give your answer in m.
Answer:
ok so we can simpley this is 1:106
so we multiply
20*106=2120 this is cm so we make it meters...
21.2meters!!!
Hope This Helps!!!
find the value of discriminant of the equation X square + 10 x - 7 =02
Answer:
136
Step-by-step explanation:
as you know that discriminant of a quadratic equation is
D= b² - 4ac
here, according to the give equation
x² + 10x -7 -2= 0
x²+ 10x -9 = 0
b= 10 , c= -9 and a= 1
by putting all these values in D.
you can get the value of discriminant which is 136.
I got this explained answer from an app called GAUTHMATH. Which is completely dedicated to maths problem. You can check it out too. It's available on Play Store and App Store.
hope this helps.
y = 4x – 18
y = -5x +9
Answer:
(3, -6)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Coordinates (x, y)Terms/CoefficientsSolving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 4x - 18
y = -5x + 9
Step 2: Solve for x
Substitution
Substitute in y [2nd Equation]: 4x - 18 = -5x + 9[Addition Property of Equality] Add 5x on both sides: 9x - 18 = 9[Addition Property of Equality] Add 18 on both sides: 9x = 27[Division Property of Equality] Divide 9 on both sides: x = 3Step 3: Solve for y
Substitute in x [1st Equation]: y = 4(3) - 18Multiply: y = 12 - 18Subtract: y = -6Answer:
x=3
y = -6
Step-by-step explanation:
y = 4x – 18
y = -5x +9
Set the two equations equal
4x – 18 = -5x +9
Add 5x to each side
4x – 18 +5x= -5x+5x +9
9x -18 = 9
Add 18 to each side
9x -18 +18 = 9+18
9x =27
Divide by 8
9x/9 = 27/9
x = 3
Now find y
y = 4x-18
y = 4*3 -18
y =12-18
y = -6
Sean las proposiciones p : "Cinco es mayor que diez" y q : "Dos más dos son cuatro". Escriba en lenguaje natural la proposición ∼p∧q
Answer:
"cinco es menor o igual que diez, y dos más dos son cuatro"
Step-by-step explanation:
Primero definamos los simbolos utilizados.
∧ significa "y"
∼ es el simbolo de la negación, es decir:
∼p significa "no p"
terminemos de resolver el problema para que el concepto quede claro.
si:
p = cinco es mayor que diez (5 > 10)
entonces:
∼p = cinco es menor o igual que diez (5 ≤ 10)
y
q = dos más dos son cuatro. (2 + 2 = 4)
entonces:
∼p∧q se escribe como:
"cinco es menor o igual que diez, y dos más dos son cuatro"
if the circumfrence of a circl is 18π inches, what is the radius of the circle
Answer:
r≈2.86
Step-by-step explanation:
Using the formula
C=2πr
Solving forr
r=C
2π=18
2·π≈2.86479
Determine the measure of CD from the diagram below.
A
E
809
88
Answer:
88
Step-by-step explanation:
line AC is equal to line DB
pls explaing by tep by step
Answer:
a = 3
Step-by-step explanation:
If (x+3) is a factor of f(x) = x³+ax²+x+3,
From remainder theorem,
When we substitute -3 into the expression, we equate to zero
That is,
F(-3) = 0
(-3)³+a(-3)²+(-3)+3 = 0
-27+9a-3+3 = 0
9a = 27
divide both sides by the coefficient of a
a = 27/9
a = 3
Hence the value of a = 3
I need your help!!!
In which triangle is the value of x to tan^-1(3.1/5.2)??
(Images may not be drawned on the scale)
The angle of x in the right angle triangle is 30.80 degrees
Right angle triangle:
Right angle triangle have one of it angles as 90 degrees. The angles can be found using trigonometric ratios.
Let's find the angle x using trigonometric ratios;
tan x = opposite / adjacent
Therefore,
tan x = 3.1 / 5.2
x = tan⁻¹0.59615384615
x = 30.7991697243
x ≈ 30.80°
Therefore, the angle of x is 30.80 degrees
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the question how old is my mathematics teacher is an example of non statistical question which of the following make it a statistical question?
Include options please
The statistical question is "What is the typical age of the grade 7 Mathematics teacher?"
How to determine the statistical question?The question is given as:
"how old is my mathematics teacher?"
A statistical question is such that requires statistical data to be answered or completed.
A statistical question for "how old is my mathematics teacher?" could be "What is the typical age of the grade 7 Mathematics teacher"
Read more about statistical question at:
https://brainly.com/question/15980493
Help me to do this set question