The restriction on the variable x for the expression 5x+15/10x-10÷x²+6 x+9/3x²-3 is x ≠ -3 .
Restriction in algebraic expression is defined as the value that makes the denominator as 0 or the whole expression as not defined.
For Example: 1/(x+2) , here the restriction is x ≠ -2 as -2 will make the denominator 0.
In the given question
[tex]=\frac{5x+15}{10x-10} \div\frac{x^{2} +6x+9}{3x^{2} -3}[/tex]
rewriting the expression
[tex]=\frac{5x+15}{10x-10} \times\frac{3x^{2} -3}{x^{2} +6x+9}[/tex]
Simplifying the numerator and denominator we get
=5(x+3)/10(x-1) x 3(x² -1)/(x²+3x+3x+9) ...( by splitting the middle term )
=5(x+3)/10(x-1) x 3(x-1)(x+1)/(x+3)(x+3) ...( using identity a²-b²=(a+b)(a-b) )
On further simplifying we get ,
=5*3*(x+1)/10(x+3)
=3(x+1)/2(x+3)
For finding restriction;
denominator, 2(x+3)≠0
means (x+3)≠0 ⇒ x ≠ -3.
Therefore , the restriction on the variable x is x ≠ -3 as -3 will make the expression not defined, and the value after division is 3(x+1)/2(x+3).
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List and explain the 4 listening steps as outlined in the jade wu podcast (4 secrets therapists use to be a great listener). which step did you find the most interesting or useful?
A capable listener have find the most interesting or useful.
Here are 4 therapist secrets to help you hone this important skill -
Reflect back what you hearAsk questions instead of providing answersValidate feelings, even if you don’t agree with the logicRefrain from giving unsolicited adviceHere are 4 therapist insider tips to help you master this crucial ability.This is the first lesson in the therapy training program. It's a straightforward advice, yet it works wonders. Basically, the first action you should take as a listener is to repeat what the speaker stated back to them.Yes. I am aware that this may seem robotic, unnatural, or even unpleasant. But try it out! You won't even be aware that you're doing it, I bet the person you're listening to. Try doing it while nodding in agreement. perhaps a little bit of phrasing Begin by saying, "It sounds like..."
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
(A) x2 + (y – 3)² = 36, is the equation that represents circles with a diameter of 12 units and a center on the y-axis.
What are equations?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.So, the standard form for calculating the equation of a circle is as follows:
(x-a)² + (y-b)² = b = r²
Where;
(a, b) is the circle's center.The radius of the circle is denoted by r.Information:
diameter = 12 unitsradius = 12/2 = 6 unitsIf the center is on the y-axis, it will be at (0, 3).
By substituting into the formula, we get (x-0)² + (y-3)² = 6² is equivalent to
x²+ (y-3)² = 36Therefore, the equation that represents circles with a diameter of 12 units and a center on the y-axis is (A) (A) x2 + (y – 3)² = 36.
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The correct question is given below:
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
a. x2 + (y – 3)2 = 36
b. x2 + (y – 5)2 = 6
c. (x – 4)² + y² = 36
d. (x + 6)² + y² = 144
e. x2 + (y + 8)2 = 36
Which statement is the Law of Detachment? Help asap
Answer:
d
Step-by-step explanation:
is a true statement and p is trueHow many moles of calcium atoms do you have if you have 5.03 × 10²¹ atoms of calcium. (The mass of one mole of calcium is 40.08 g.)
5.03 x 10²¹ atoms of calcium are equivalent to 8.6 × 10⁻³ moles of calcium atoms.
What is the number of moles?To convert atoms to moles we need a conversion factor: Avogadro's number. According to Avogadro's number: there are 6.02 × 10²³ calcium atoms in 1 mole of calcium atoms. The number of moles corresponding to 3.00 × 10²¹ atoms of calcium is:
Number of moles = 5.03 x 10²¹ / 6.02 × 10²³
Number of moles = 8.6 × 10⁻³ moles of calcium
5.03 x 10²¹ atoms of calcium are equivalent to 8.6 × 10⁻³ moles of calcium atoms.
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A medical insurance policy requires Ana to pay the first $100 of her hospital expense. The insurance company will then pay 90% of the remaining expense. Ana is expecting a short surgical stay in the hospital, for which she estimates the total bill to be about $4,700. How much (in $) of the total bill will Ana owe
The total bill that Ana would pay is $560.
What is the total bill Ana would pay?The total bill that Ana owes is the sum of the first $100 and 10% of the remaining bill since the insurance company would pay 90% of the bill.
The mathematical operation that would be used to determine the total bills are addition, multiplication and subtraction. Addition is the process of determining the sum of two or more numbers. Subtraction is the process of calculating the difference between two or more numbers. Multiplication is the process of determining the product of two or more numbers.
Total bill = first $100 + 90%(total bill - $100)
$100 + 10%($4,700 - $100)
$100 + 10% x 4,600
$100 + (0.1 x 4,600)
$100 + $460
$560
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Pick the description of a geometric object that best matches the real-world object:
Box for a deck of cards
O a three-dimensional shape with two similar, parallel rectangular bases and sides that are parallelograms
O a three-dimensional shape with two similar, parallel triangular bases and sides that are parallelograms
a three-dimensional geometric shape with two parallel and circular bases and a curved side
o a three-dimensional figure in which all points on the surface are the same distance from the center
o a three-dimensional box-shaped figure, with six identical square faces
Athree dimensional shape with two similar, parallel rectangular bases and sides that are parallelogram" will be the correct option.
The box for a deck of cards will have a rectangular prism shape.
Two parallel rectangular bases, two sides that run parallel to one another along their width, and two similarly parallel rectangular sides running along their height make up a rectangular prism.
A rectangular prism has two parallel rectangular bases, 2 sides parallel to each other along width and 2 similar parallel rectangular sides along the height.
As a result, choice A, "a three-dimensional shape with two comparable, parallel rectangular bases and sides that are parallelograms," will work.
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ANSWER ASAP WILL MARK AS. BRAINLYST (Only if answer is correct)
Look at the photo and answer broth questions
Answer:
see explanation
Step-by-step explanation:
A drop in temperature is indicated by - ( negative symbol )
A drop of 2° followed by a drop of 3° is
- 2 + (- 3) = - 2 - 3 = - 5°
the sign of the sum is - ( negative add a negative is negative )
the total change in temperature is - 5°
the sum of 2 positive integers is positive , that is
+ 2 + (+ 3) = + 2 + 3 = = + 5
Relocate vertex C so that ABCDE is convex, and all sides remain the same length.
According to the illustration below The figure becomes convex if vertex C is reflected over the BD line.
What exactly is a reflex angle?A reflex angle is any angle larger than 180 degrees but less than 360 degrees. For example, a reflex angle is 270 degrees. There are several sorts of angles in geometry, including acute, obtuse, and right angles that are less than 180 degrees. There is a reflex angle for every acute as well as an obtuse angle.
How do you calculate a reflex angle?The reflex angle can be measured in one of two ways: either measure its inner angle and subtract it from 360° (to get the reflex angle) and measure the reflex angle itself.
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The temperature was -6°F. It rose so that the temperature was 0°F
Answer:
It rose 6 degrees
Step-by-step explanation:
I hope that's what you're asking...
Suppose that three customers are selected randomly, without replacement, for a survey. what is the probability that at least two selected customers use express shipping?
Answer:
3 upon 2. that's the answer ..
Solve the following equation for A. Be sure to take into account whether a letter is capitalized or not.
F = D + A
Answer:
A = f - D
Step-by-step explanation:
f = D + A ( isolate A by subtracting D from both sides )
f - D = A
Answer:
A=F-D
Step-by-step explanation:
fht7ts3yfx yi. 4hu c h 4tyfdrhuezjuf drucdtufdgyt
Select the expressions that are equivalent to 7(-7u - 4) - 5.
(-7u - 4)7 - 5
7(-8u+ u 4) - 5
-33u - 49
-7u - 33
Answer: only the first one
Step-by-step explanation:
The equation the quantity 2x minus 10 divided by 4 = 3x models temperature change, where x represents the difference in degrees in the last 24 hours. Solve for x. x = −10 x = −1 x = 2 x = 11
Answer:
I'm pretty sure it's -1 but correct me if I'm wrong
Answer: x=-1
Step-by-step explanation:
x=-1
because
2x - 10
over = 3x
4
we can put everything in parentheses and multiply by 4
2x - 10
4( over )= (3x) 4
4
The 4's on the left side will cancel out around and leave
2x - 10
on the right we multiply 3x x 4 which equals 12x
rewrite the equation
2x - 10 = 12x
subtract 2x on each side with the variable.
2x - 10 = 12x
-2x -2x
the 2x's on the left will cancel out.
on the right 12x - 2x equals 10x
now the equation is
-10=10x
but we are not done
divide 10 on each side
on the left -10/ 10 equals -1 because one number is negative and that does not give a postive result.
on the right 10x/ 10 the 10's cancel out leaving the varible x
we are left with
x=-1
What is the justification for the first step in proving the formula for factoring the sum of cubes? a3 b3 = (a b)(a2 â€"" ab b2) = a3 â€"" a2b ab2 a2b â€"" ab2 b3 distributive property commutative property definition of additive inverse definition of multiplicative inverse
The justification for the first step in proving the formula for factoring the sum of cubes [tex]a^3+b^3[/tex] is the distributive property.
Given the formula for sum of cubes [tex]a^3+b^3[/tex] = [tex](a+b)(a^2-ab+b^2)[/tex]
= [tex]a^3-a^2b+ab^2+a^2b-ab^2+b^3[/tex]
In this step distributive property is utilized.
Distributive property is used for expanding the factors into the polynomial.
i.e., a(b+ c) = ab +ac
or, (a+ b)c = ac + bc
This is referred as the distributive property.
In the formula for [tex]a^3+b^3[/tex], (a+ b) is distributed over [tex](a^2-ab+b^2)[/tex].
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Answer:
a. Distributive
Step-by-step explanation:
took da test 100%
Jesse has been saving his earnings from his lemonade stand. Jesse has 47 dollars to spend. If He buys a new hat for 19 dollars, how many scarves can He buy with the remaining spending money if they cost 7 dollars each?
Answer: 4 scarves.
Step-by-step explanation: $47-$19= 28. 28 divided by $7 is 4, so Jesse could buy 4 scarves with the remaining money.
can someone help me with this? ive been trying for a while
Answer:
The value of x after simplification is 6, which when substituted in the given expression will make both the sides equal.
Step-by-step explanation:
It is given that the expression given below is to be simplified using the order of operations;
The given expression is;
=> (3×2)² + 8 = ___² + 8
Now, let us assume that the blank space is 'x' in the above-mentioned question;
Firstly,
We will solve the terms within brackets as per BODMAS rules that is multiplication of both the terms;
=> (3×2)² + 8 = x² + 8
=> 6² + 8 = x² + 8
Now, we will solve the squares of the terms given above;
=> 36 + 8 = x² + 8
Now, we will add the terms as per BODMAS rules;
=> 44 = x² + 8
=> 44 - 8 = x²
Now, we will subtract the terms as per BODMAS rules;
=> 36 = x²
Now, we will square-root both the sides given above;
=> x = √36
=> x = 6
Therefore, the value of x after simplification is 6, which when substituted in the given expression will make both the sides equal.
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Read each question. Then write the letter of the correct answer on your paper.
What are the first five terms of the sequence a n =2 n-1 ?
(F) 0,1,2,3,4
(G) 1,3,5,7,9
(H) 2,4,6,8,10
(I) 3,5,7,9,11
The first five terms of a sequence with explicit formula a(n) = 2n - 1 are 1,3,5,7,9 (G)
An arrangement of numbers with particular pattern is called a sequence. In general, there are four types of sequence: arithmetic sequence, geometric sequence, quadratic sequence, and special sequence.
Suppose we are given an explicit formula for the nth term of a sequence, then its terms can be evaluated by substituting n = 1, 2, ...
The explicit formula of the given sequence:
a(n) = 2n - 1
Take n = 1, then
a(1) = 2.(1) - 1 = 1
Take n = 2, then
a(2) = 2.(2) - 1 = 3
Take n = 3, then
a(3) = 2.(3) - 1 = 5
Take n = 4, then
a(4) = 2.(4) - 1 = 7
Take n = 5, then
a(1) = 2.(5) - 1 = 9
Hence, the first five terms are 1,3,5,7,9 (G)
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what is 4/3 y= 16 for math 8
9,369 divided 53 help please
Answer:
the answer is
[tex]176 \times \frac{41}{53} [/tex]
hope this helps
Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer.
4.2,6.4,7.6
Yes, the given set of numbers can be the measures of the sides of a triangle. The triangle is obtuse.
By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.
4.2 + 6.4 > 7.6
6.4 + 7.6 > 4.2
7.6 + 4.2 > 2.6
Hence, these set of numbers can be the measures of the sides of a triangle.
According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:
acute if [tex]a^{2} + b^{2} < c^{2}[/tex]
obtuse if [tex]a^{2} + b^{2} > c^{2}[/tex]
right if [tex]a^{2} + b^{2} = c^{2}[/tex]
∴The longest side is 7.6.
Hence, a = 4.2, b = 6.4 and c = 7.6;
Consider [tex]a^{2} + b^{2}[/tex] :
= [tex]4.2^{2} + 6.4^{2}[/tex]
= 58.6.
Now consider [tex]c^{2}[/tex] :
= [tex]7.6^{2}[/tex]
=57.76.
Thus, [tex]a^{2} + b^{2} > c^{2}[/tex]
Hence, the triangle is obtuse.
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What is the value of x in the equation (4x-1)-3x = -(x + 2)?
1/16
3/16
19/16
3
Answer:
Step-by-step explanation:
x − 1. _. 3. = 3 by 3 gives x − 1 = 9 and then adding 1 to both sides of x − 1 = 9 gives x = 10. Choices A, B ... written as the equation 16 + 4x = 10 + 14, which is equivalent to 16 + 4x = 24. Subtracting
You have three numbers. two of the numbers are 24 and 42. what is the gcf of these two numbers? the third number is grater tan 42 and does not change the gcf. what is one possibility for the third number?
If two of the three numbers are 24 and 42, then the GCF of these two numbers is 6 and the third number is possibly 48.
Factor is a number which when a number is divided will result to another number(whole). For two or more numbers, the largest common factor that they have is called the Greatest Common Factor (GCF).
To find the GCF of 24 and 42, list all the factors of both numbers.
24 : 1, 2, 3, 4, 6, 8, 12, 24
42: 1, 2, 3, 6, 7, 14, 21, 42
Common Factors: 1, 2, 3, 6
Greatest Common Factor: 6
If the third number is grater than 42 and does not change the GCF, then the third number is possibly 48.
24 : 1, 2, 3, 4, 6, 8, 12, 24
42: 1, 2, 3, 6, 7, 14, 21, 42
48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Common Factors: 1, 2, 3, 6
Greatest Common Factor: 6
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Write and solve a system of equations for each situation. Check your answers.A store sells small notebooks for 8 and large notebooks for 10 . If you buy 6 notebooks and spend 56 , how many of each size notebook did you buy?
I bought 2 small notebooks and 4 large notebooks.
Let us represent the number of small notebooks with x and number of large notebooks with y.
Forming equation according to bought number of books -
x + y = 6 - equation 1
Rewriting the equation according to x
x = 6 - y - equation 2
Now, forming equation according to cost of notebooks -
8x + 10y = 56 - equation 3
Keep the value x from equation 2 in equation 3
8 (6 - y) + 10y = 56
Performing multiplication
48 - 8y + 10y = 56
Performing subtraction and shifting values to other side of equation
2y = 56 - 48
2y = 8
Shifting 2 to other side of equation and performing division
y = 8 ÷ 2
y = 4
Keep the value of y in equation 2
x = 6 - 4
x = 2
Hence, I bought 2 small notebooks and 4 large notebooks.
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ALGEBRA In ∠ X Y Z, m ∠ X=157, mV Y=y , and m∠Z=z . Write an inequality to describe the possible measures of V Z . Explain your reasoning.
According to the statement an inequality to describe the possible measures of ∠Z = 23.
In algebra, what is inequality?An inequality is a relationship that makes a non-equal comparison of two integers or any other mathematical expressions. It is most commonly used to compare two digits upon that number line based on their size. a statement of an order relationship—greater than, larger than the other or equal thereto, less than, or lesser than or equal to—between two integers or algebraic expressions
According to the given data:the sum of the angles' measurements
triangle is 180 and ∠ X=157.
∠ X + ∠ Y +∠ Z = 180
∠ Y +∠ Z = 23
If ∠Y was 0, then ∠Z would equal 23. But since an angle must have
a measure greater than 0, ∠Z must be less than
23, so z < 23.
an inequality to describe the possible measures of ∠Z = 23.
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What are the new coordinates of a point (x, y) that is rotated 270°C ?
90° rotation in clockwise direction.
What is coordinates ?
Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical).The formulae for finding the new coordinates are given by
x' = x cosθ - y sinθ
y' = x sinθ + y cosθ
Substituting θ = 270
x' = x cos270° - ysin270° = x(0) - y( -1) = y
y' = x sin270° + y cos270° = x(-1) + y( 0) = x
New coordinates are ( y , -x)
270° rotation in anti-clockwise direction is same as 360 -270 = 90° rotation in clockwise direction.
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Write the function rule for each function reflected in the given axis.
f(x)=2 x-4 ; x - axis
The given function is f(x) = 2x-4,
We have to find the equation where the reflection of this function is over the x-axis.
There are two types of reflections in general when we talk about functions;
One reflection is over the x-axisThe other is over the y-axis.Now we take an example that we are provided with a point with coordinates (x, y). If we want to reflect it over the x-axis, then the coordinates of this point will become (x, -y). This is because the values of y are negative when we move above the x-axis and positive when we move below the x-axis and vice versa.
The equation to show this is: y = -f(x).
We multiply the entire function, f(x), to find it by a negative. Since f(x) = 2x-4, the transformed function is f(x) = -2x+4.
Therefore, the function rule for the function shown is -f(x).
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What is the sine for the figure below?
The sine for the right triangle A is 3/5.
The ratio between the side opposite the angle and the triangle's hypotenuse is known as the sine (sin) of an acute angle in a right-angled triangle. A right angle in geometry and trigonometry is an angle that is exactly 90 degrees, or 2 radians, which is equivalent to a quarter turn. If a ray is positioned so that its terminal is on a line and they are equal, the neighbouring angles are right angles.
Sin(A) = opposite/hypotenuse
=BC/AB
=3/AB
Given,
BC = 3
AC = 4
Now solve for AB using Pythagorean theorem:
BC2 + AC2 = AB2
32 + 42 = AB2
9 + 16 = AB2
25 = AB2
AB = 5
Hence,
The value of AB is 5.
BC/AB = 3/5
Therefore, The sin of triangle A is 3/5.
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1 Dɔntrez had 1/2 lb of trail mix. Each day, he took 1/8 lb of trail mix to
=chool for a snack. If he had 1/4 lb of trail mix left over, how many days did
Dontrez take trail mix to school?
For your answer, ONLY type the number and your word label.
Your answer
Dontrez took 1/8 lb fraction of trial mix to school for only 2 days.
What is a fraction?
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction consists of a numerator, displayed above a line, and a non-zero denominator, displayed below that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.
Dontrez took 1/8 lb fraction of trial mix to school for only 2 days.
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Give an example of a number that is not a rational number. Explain why it is not rational.
Give an example of a number that is not a rational number. [tex]\pi =3.14[/tex]
Why it is not rational?
[tex]\pi[/tex] is a real number that cannot be represented by a simple fraction since it is an irrational number. [tex]\pi[/tex] is what mathematicians refer to as a infinite decimal since the digits continue indefinitely after the decimal point.What is an irrational number?
A real number that cannot be expressed as a straightforward fraction is referred to as an irrational number. It cannot be described using a ratio. When p and q are integers and q is not equal to 0, N is not equal to p/q if N is irrational.To learn more about irrational numbers, refer:
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Kerim jogged 3 miles on Thursday: On Friday, he jogged of a mile
farther. How far did he jog on Friday
Answer:
4 miles
Step-by-step explanation:
3 miles plus 1 additional mile is 4 miles.
