Answer:
For any integer number n, the inverse additive of n is also an integer K such that:
n + K = 0
solving this for K, we get that:
K = -n
Then the inverse additive of n is -n.
Now that we know this let's complete this.
We know that for any two integers A and B, a minus b is equal to a plus the additive inverse of b.
To check this:
a minus b is written as:
a - b
And a plus the additive inverse of b is:
a + (-b)
because -b is the additive inverse of b.
Remember the rule sign:
(+)*(-) = -
Then we can rewrite:
a + (-b) = a - b
Then the statement is true.
"For any two integers a and b, a minus b is equal to a plus additive inverse of b is equal to a + (-b)"
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
can someone please help for brainlest
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
Estimate the perimeter and the area of the shaded figure to the nearest tenth.
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
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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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.
hELPpppPpPP pLEAaSSEEseE
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]
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
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
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
need help with this asap!
Answer:
Step-by-step explanation:
1 ) 2 + 7t [ there are no like terms , so no further simplifying ]
2) 6r + ( - 16 r )
= 6 r - 16 r [ both are like terms ]
= - 10 r
3) (3x + 2 ) + ( 2x - 4 )
= 3x + 2 + 2x - 4
= 3x + 2x - 4 + 2 [ arranging like terms together ]
= 5x - 2
4) (8 n² - 3 n + 6 ) + ( n - 2 )
= 8n² - 3n + 6 + n - 2
= 8n² - 3n + n + 6 - 2 [ bringing like terms together ]
= 8n² - 2n + 4
Answer:
1.) 2 + 7 t
2.) - 10 r
3.) 5 x - 2
4.) 8 n² - 2 n + 4
Step-by-step explanation:
1.) 2 + 7 t
No like terms, so no further simplifying.
2.) 6 r + ( - 16 r )
6 r - 16 r. ... ( combine like terms)
- 10 r
3.) ( 3 x + 2 ) + ( 2 x - 4 )
= 3 x + 2 + 2 x - 4
combine like terms
= 3 x + 2 x - 4 + 2
= 5 x - 2
4.) ( 8 n ² - 3 n + 6 ) + ( n - 2 )
= 8 n² - 3 n + 6 + n - 2
combine like terms
= 8n² - 3 n + n + 6 - 2
= 8 n² - 2 n + 4.
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
Find the measure of "theta". Round all answers to the nearest tenth.
Answer:
[tex]\displaystyle \theta \approx 36.4[/tex]
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 EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] tanθ = opposite over adjacentInverse TrigStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ
Opposite Leg = 31
Adjacent Leg = 42
Step 2: Find Angle
Substitute in variables [tangent]: [tex]\displaystyle tan(\theta) = \frac{31}{42}[/tex]Inverse Trig: [tex]\displaystyle \theta = tan^{-1}(\frac{31}{42})[/tex]Evaluate: [tex]\displaystyle \theta = 36.4309[/tex]Round: [tex]\displaystyle \theta \approx 36.4[/tex]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"
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Which equation represents a line that passes through the two points in The table
Answer:
y = mx + by= mx+ b
Step-by-step explanation:
since we know the two points on the line. we use the two points formed to find its equation. the final equation.the slope intercept form ,y=mx+by = mx+b
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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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
Find the sine ,cosine and tangent ratios of
Step-by-step explanation:
Given that,
Hypotenuse, H = 13
Base, b = 12
Perpendicular, P = 5
[tex]\sin\theta=\dfrac{P}{H}\\\\\sin\theta=\dfrac{5}{13}[/tex]
[tex]\cos\theta=\dfrac{B}{H}\\\\\sin\theta=\dfrac{12}{13}[/tex]
and
[tex]\tan\theta=\dfrac{P}{B}\\\\=\dfrac{5}{12}[/tex]
Hence, this is the required solution.
Help me to do this set question
52 %of U.S. Adults have very little confidence in newspapers. You randomly select 10 U.S. Adults. Find the probability that the number of U.S. Adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.
Answer:
a. P(x = 5) = 0.24
b. P(x ≥ 6) = 0.43
c. P(x < 4)= 0.14
Step-by-step explanation:
According to the Question,
Given, 52 %of U.S. Adults have very little confidence in newspapers & We have to randomly select 10 U.S. Adults.⇒We use Binomial Probability Formula
[tex]P(X = x ) = \frac{n!}{x!((n-x)! } * p^{x} * (1-p)^{n-x}[/tex]
Where, p=0.52 & n=10
a. The probability that the number of U.S. adults who have very little confidence in newspapers is exactly five . So, (x=5)
Thus, [tex]P(X = 5 ) = \frac{10!}{5!((10-5)! } * 0.52^{5} * (1-0.52)^{10-5}[/tex]
On Solving Above Equation we get,
P(5)=0.2441 ≈ 0.24
b. The probability that the number of U.S. adults who have very little confidence in newspapers is at least 6 . So, (x≥6)
Then,
P(x≥6) = P(6)+P(7)+P(8)+P(9)+P(10)
P(x≥6) = [tex]\frac{10!}{6!((10-6)! } * 0.52^{6} * (1-0.52)^{10-6}[/tex] + [tex]\frac{10!}{7!((10-7)! } * 0.52^{7} * (1-0.52)^{10-7}[/tex] +[tex]\frac{10!}{8!((10-8)! } * 0.52^{8} * (1-0.52)^{10-8}[/tex] + [tex]\frac{10!}{9!((10-9)! } * 0.52^{9} * (1-0.52)^{10-9}[/tex]+[tex]\frac{10!}{10!((10-10)! } * 0.52^{10} * (1-0.52)^{10-10}[/tex]
On solving above equation we get,
P(x≥6) = 0.4270 ≈ 0.43
c. The probability that the number of U.S. adults who have very little confidence in newspapers is less than 4 . So, (x<4)
Then,
P(x < 4)=P(3) + P(2)+P(1)+P(0)
P(x<4) = [tex]\frac{10!}{3!((10-3)! } * 0.52^{3} * (1-0.52)^{10-3}[/tex] + [tex]\frac{10!}{2!((10-2)! } * 0.52^{2} * (1-0.52)^{10-2}[/tex]+ [tex]\frac{10!}{1!((10-1)! } * 0.52^{1} * (1-0.52)^{10-1}[/tex] + [tex]\frac{10!}{0!((10-0)! } * 0.52^{0} * (1-0.52)^{10-0}[/tex]
On solving we get,
P(x < 4)= 0.1410 ≈ 0.14
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:
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
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
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
f(x) = x2. What is g(x)?
5
[ f(x)
g(x)
(3,3)
X
-5
5
x2
O A. g(x)=1
-02-G
B.
X
O c. g(x) = 3²
O D. g(x)=-* x2
Please help :/
The function g(x) = x²/3
Given that graph of the function f(x) = x²,
Since, the graph of f(x) is transformed to form the g(x).
We see that g(x) is passing by (3, 3)
Here, the scale factor is 1/3,
So, we can say that the equation of the function g(x) is g(x) = x²/3
Therefore, the required function is g(x) = x²/3
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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.
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
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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