Which statement is true when comparing how a student would complete the solution for the linear equation -2x + 3 = 6 to how the student would complete the solution for the linear inequality -2x + 3 < 6?
Completing the solution for the equation is the same as completing the solution for the inequality. The student would divide both sides by -2 in either case.
Completing the solution for the equation is the same as completing the solution for the inequality. The student would divide both sides by -2 in either case.
Completing the solution for the equation is the same as completing the solution for the inequality. The student would multiply both sides by -2 in either case.
Completing the solution for the equation is the same as completing the solution for the inequality. The student would multiply both sides by -2 in either case.
Completing the solution for the equation is not the same as completing the solution for the inequality. The student would divide by -2 to complete the solution for the equation and would divide by -2 and change the less than sign for the inequality to greater than.
Completing the solution for the equation is not the same as completing the solution for the inequality. The student would divide by -2 to complete the solution for the equation and would divide by -2 and change the less than sign for the inequality to greater than.
Completing the solution for the equation is not the same as completing the solution for the inequality. The student would multiply by -2 to complete the solution for the equation and would multiply by -2 and change the less than sign for the inequality to greater than.
The statement that is true is completing the solution for the equation is the same as completing the solution for the inequality. The student would divide both sides by -2 in either case. Option A
How to determine the statementFrom the information given, we have that;
The linear equation is ;
-2x + 3 = 6
Let's solve for x
First, collect like terms
-2x = 6 - 3
-2x = 3
Divide both sides by - 2
x = 3/ -2
The linear inequality is;
-2x + 3 < 6
collect like terms
-2x < 6 - 3
Make 'x' the subject by dividing both sides by -2
-2x/ -2 = 3/ -2
x = 3/ -2
We can see that the linear equation and the linear inequality have the same solution and steps.
Thus, the statement that is true is completing the solution for the equation is the same as completing the solution for the inequality. The student would divide both sides by -2 in either case. Option A
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Explain the properties used to solve inequalities and how they are different from properties of equality
The major difference between inequality and equality is that equality represents a particular value(s) while inequality represents a range of values that are in a specific direction.
What are the properties that are used to solve inequalities?This must be noted when solving questions on equality and inequality.
For example:
x = a means that the value of x is a. It represents a particular value which is a
x < a represents all the values that are less than a.
x ≤ a represents values from a and below.
x > a represents all the values that are greater than a
x ≥ a means that the values of x are greater than or equal to a.
From the examples given above, it is obvious that a change in the direction of the inequality sign changes the values of the data represented by the inequality.
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In any circle the ratio of circumference to diameter is constant and is approximately equal to 22:7. what is the circumference of a circle if its diameter is 60 in?
Answer:
188.57 in
Step-by-step explanation:
Circumference = 2πr = 2πd/2 = πd
[tex] = \frac{22}{7} \times 60 \: in[/tex]
= 188.57 in ( approx.)
A cereal box manufacturer changes the size of the box to increase the amount of cereal it contains. The expressions 16 + 6.6n and 14 + 7.1n, where n is the number of
box? smaller boxes, are both representative of the amount of cereal that the new larger box contains. How many smaller boxes equal the same amount of cereal in the larger
The larger box of cereal has as
(Type a whole number.)
boxes
Answer:
The answer should be 10.5 from what i have seen in the past
Step-by-step explanation:
TR= 3x + 5, and RA = x + 17. Find the value of x.
Greetings from Brasil...
The small green lines on the line segments indicate that TR = RA, as well as the small red lines indicate that MR = RH, then
TR = RA
3X + 5 = X + 17
X = 6
Need the answer asap
Pls answer it correctly
Answer:
I will be your human calculator! top to bottom!
1. (+1) 5. (+28) 9. (+8)
2. (+4) 6. (+3) 10. (-5)
3. (+14) 7. (+24) 11. (+6)
4. (-3) 8. (-3) 12. (+1)! Good Luck!
Use the distance formula to find the area of the square:
Answer:
10
Step-by-step explanation:
Distance formula:
d = √(x₂-x₁)²+(y₂-y₁)²
A (1,2) D (4,3)
d = √(4-1)²+(3-2)² = 3.16227766
All 4 sides of a square are equal lengths.
The equation for the area of a square:
A = a²
A = (3.16227766)² = 10
Question in photo. Too lazy to solve lol (I might mark u as brainliest if u answer)
Answer:
The first, third, and fourth.
Step-by-step explanation:
Those answers involve scaling the measurement up, which requires a positive power of 10. For scaling down, you'll need a negative power of 10, e.g., 2x10^-2=0.02.
a unicorn is tethered by a 20-foot silver rope to the base of a magician's cylindrical tower whose radius is 8 feet. the rope is attached to the tower at ground level and to the unicorn at a height of 4 feet. the unicorn has pulled the rope taut, the end of the rope is 4 feet from the nearest point on the tower, and the length of the rope that is touching the tower is $\frac{a - \sqrt{b}}{c}$ feet, where $a$, $b$, and $c$ are positive integers, and $c$ is prime. find $a b c$.
The values of a=60, b=750, c=3, a+b+c= 813 as determined by Pythagorean Theorem..
What is Pythagorean Theorem?
A geometric theorem states that the square of a right triangle's hypotenuse equals the sum of the squares of its other two sides.
Call the circle's center O, the unicorn's tether point A, and the final spot where the rope reaches tower B. Triangle OAB is a right triangle since BA is a tangent line at point B and OB is a radius. We determine the horizontal component of AB has length [tex]4\sqrt{5}[/tex] using the Pythagorean Theorem.
The cylinder is "unrolled" to become a flat surface. Let C be the rope's bottom tether, D the point below A on the ground, and E the point directly beneath B. Triangles CDA and CEB share characteristics of right triangles. The Pythagorean Theorem states that CD=8cdotsqrt6.
Let x represent the size of CB.[tex]CD=8\cdot\sqrt{6}[/tex]
[tex]\[\frac{CA}{CD}=\frac{CB}{CE}\implies \frac{20}{8\sqrt{6}}=\frac{x}{8\sqrt{6}-4\sqrt{5}}\implies x=\frac{60-\sqrt{750}}{3}\][/tex]
Therefore,
a=60, b=750, c=3,a+b+c= 813 as determined by Pythagorean Theorem.
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D - 8 over -2 = 12 solve for D
Answer: D = -6
Step-by-step explanation:
[tex]\frac{D-8}{-2} =12[/tex]
1) Divide both sides by -2
[tex]D - 8=-6[/tex]
2) Add 8 to both sides
[tex]D=-6[/tex]
What is the quotient of 204 decided by 34
Answer:
204 ÷ 34 = 6
Step-by-step explanation:
204 ÷ 34 = 6
Check:
34
x 6
------
204
hope this helps :)
Answer : 6
Explanation :
34 + 34
68
68 + 34
102
102 + 34
136
136 + 34
170
170 + 34
204
OR just simply use Multiplication
34 x 6
please help with this question, thank you!!
Answer:
[tex]-\sqrt{2}[/tex]
Step-by-step explanation:
Note that:
[tex]a^2-2ab+b^2=(a-b)^2 = 4ab \\ \\ a^2 + 2ab+b^2 = (a+b)^2 = 8ab \\ \\ \implies \frac{a+b}{a-b}=\frac{\sqrt{8ab}}{-\sqrt{4ab}}=-\sqrt{2}[/tex]
Answer:
[tex]\sf \dfrac{a+b}{a-b}= -\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sf a^2 + b^2 = 6ab \qquad where\:\:0 < a < b[/tex]
Basic formula:
[tex]\sf (a + b)^2 = a^2 +b^2 +2ab[/tex]
[tex]\sf (a - b)^2 = a^2 + b^2 -2ab[/tex]
solve for a + b
[tex]\sf \rightarrow a^2 + b^2 = 6ab[/tex]
[tex]\sf \rightarrow (a+b)^2-2ab = 6ab[/tex]
[tex]\sf \rightarrow (a+b)^2 = 6ab+2ab[/tex]
[tex]\sf \rightarrow (a+b)^2 = 8ab[/tex]
[tex]\sf \rightarrow a+b = \pm \sqrt{8ab}[/tex]
solve for a - b
[tex]\sf \rightarrow a^2 + b^2 = 6ab[/tex]
[tex]\sf \rightarrow (a-b)^2 + 2ab = 6ab[/tex]
[tex]\sf \rightarrow (a-b)^2 = 6ab-2ab[/tex]
[tex]\sf \rightarrow (a-b)^2 = 4ab[/tex]
[tex]\sf \rightarrow a-b = \pm \sqrt{4ab}[/tex]
Now solve for (a + b)/(a - b)
[tex]\sf \rightarrow \dfrac{a+b}{a-b}= \dfrac{\pm\sqrt{8ab} }{\pm\sqrt{4ab} }[/tex]
[tex]\sf \rightarrow \dfrac{a+b}{a-b}= \pm \sqrt\dfrac{8ab }{4ab}[/tex]
[tex]\sf \rightarrow \dfrac{a+b}{a-b}= \pm \sqrt{2}[/tex]
As, the value of b is greater than the value of a and both the values a and b are greater than 0. It turns the value of expression negative as the denominator will be always evaluated to negative integer and the numerator value always > 0. So, the answer will be negative, -√2.
[tex]\sf \rightarrow \dfrac{a+b}{a-b}= - \sqrt{2}[/tex]
pls help u with these to
Answer:
5 acute
6 acute
3 obtuse
4 obtuse
Step-by-step explanation:
Hope this helps
use the space provided to create a list of important talent, skills and competencies a person will need to fill the position on (business functions on ) purchasing
There is space to identify the important talents, abilities, and competencies a person will need because every company aims to attain financial stability by streamlining its operations using resources.
A stable economy is what?Every firm strives to achieve financial stability by streamlining its operations with resources, thus there is room available to identify the critical talents, abilities, and competencies a person will require.
What is financial stability?"A state in which the financial system is not unstable" is the definition of financial stability. It may also refer to a state of stability among the three elements of the financial system, namely the infrastructure, markets, and institutions.The phrase "stability of financial institutions" refers to the degree to which each financial institution is sound enough to effectively perform the function of financial intermediation.Due to the advancement of financial deregulation, many nations around the world have experienced the benefits of rapid financial industry growth since the 1980s.
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PUNTOS Write the equation of the line parallel to y = -1/3x + 4 and passing through the point (-6, -9). Be sure to write your answer in slope-intercept form(y=mx+b)
The slope intercept of the line is y = -1/3x -11
Slope-intercept is one of the special forms of line equation
The slope intercept of a line can be found by solving the slope-intercept equation of a line which is parallel to that line.
Slope-intercept equation is
y = mx + b
where m is the slope and b is the intercept.
The slope-intercept equation of the parallel line is
y = -1/3x + 4
The slope will be the same for both lines as they were parallel to each other.
Thus m = -1/3
The point in which the line passes is given as (-6,-9)
So with these data, We can find the intercept of the line
y = mx + b
where m = -1/3 and (x,y) is (-6,-9),Thus
-9 = -1/3(-6) +b
-9 = 6/3 +b
-9 = 2 + b
b = -9-2
b = -11
Thus the intercept of the line passing through the point (-6,-9) is -11
Thus, the slope-intercept equation of the line we need to find is
y = -1/3x -11
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How do I solve x for 2x+8=3x+10
To solve for x in: [tex]2x + 8 = 3x + 10[/tex]
Collect like terms
[tex]→8 - 10 = 3x - 2x \\ - 2 = x[/tex]
Therefore:
[tex]x = - 2[/tex]
Ana compra en la tienda 15/20 gramos de jamon y 15/20 gramos de queso y quiere saber a cuanto equivale en decimales
15/20 gramos equivalen a 0 . 75 en forma decimal. Si se supone que las cantidades decimales deben sumarse, entonces 1 . 5
-------------------------------
Espero que esto te ayude.
Que tengas un buen día y que Dios te bendiga. :)
If h(x)= -5/6x + 7/8 find the following values. Simplify your answer.
H(3)=
H(4)=
H(-1/2)=
If [tex]h(x)=\frac{-5}{6} x+\frac{7}{8}[/tex] then the value of h(3) = -13/8 , h(4) = -59/24 , h(-1/2) = 31/24 .
In the question , the equation is given as
[tex]h(x)=\frac{-5}{6} x+\frac{7}{8}[/tex] ....(i)
Part(a)
To find the value of h(3)
we substitute the value of x=3 .
On substituting the value of x=3 in equation (i),
we get ,
h(3) = (-5/6)3+7/8
= -15/6+7/8
taking LCM of 6 and 8 as 24, we get
= -60/24 + 21/24
= (-60+21)/24
= -39/24
Writing in the simplest form we get
= -13/8
so, the value of h(3)= -13/8 .
Part(b)
for h(4) ,we substitute the value of x=4 .
On substituting the value of x=4 in equation (i) ,
we get ,
h(4) = (-5/6)4+7/8
= -20/6+7/8
taking LCM of 6 and 8 as 24, we get
= -80/24 + 21/24
= (-80+21)/24
= -59/24
so , the value of h(4)= -59/24 .
Part(c)
for h(-1/2) ,we substitute the value of x as -1/2 .
On substituting the value of x = -1/2 in equation (i) ,
we get ,
[tex]h(\frac{-1}{2} )=\frac{-5}{6} *\frac{-1}{2} +\frac{7}{8}[/tex]
= 5/12 +7/8
taking LCM of 12 and 8 as 24, we get
= 10/24 + 21/24
= (10+21)/24
= 31/24
so , the value of h(-1/2)= 31/24 .
Therefore , if h(x) = (-5/6)x+7/8 the the value of h(3)= -13/8 , h(4)= -59/24 and h(-1/2)= 31/24 .
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la tarifa de un recorrido de taxi es de 7.25 de cargo fijo y de 7 por cada km recorrido determina la ecuación si p corresponde al valor del pago por x km recorridos
The equation that illustrates the amount to be paid for the number of kilometers will be 7.25 + 7x.
How to illustrate the information?Fixed rate for taxi = 7.25
Additional charges per kilometers = 7
Number of kilometers = x
Therefore, the equation that illustrates the amount to be paid for the number of kilometers will be:
= 7.25 + (7 × x)
= 7.25 + 7x
Therefore, the equation is 7.25 + 7x.
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Write the terminology for the power of a factored expression of a polynomial
function.
Answer:
a power function is a function with a single term that is the prudoct of a real number
What is the equation of the line that passes through the point (-3, 1) and has a slope
of -1/3?
Answer:
y=-1/3x+1
Step-by-step explanation:
Slope-Intercept Form: y=mx+b
m is the slope
b is the y-intercept
In the given statement it tells us the point is (-3,1).
-3 is the x-intercept while 1 is the y-intercept
In the given statement it tells us the slope is -1/3
Plug in the m for -1/3 and the b for 1
y=-1/3x+1
Hope this helps.
Please help quickly!!!!
-3/5 - (-2/5) =
Write the answer as a fraction
Answer:
-1/5
Step-by-step explanation:
Minus a negative is plus.
-3/5 - (-2/5) =
= -3/5 + 2/5
= -1/5
Simplify this expression.
9y + 3 - 4y + x +9
Answer: 5y + x + 12
Step-by-step explanation:
9y + 3 - 4y + x + 9
Group together 9y and -4y
5y + 3 + x +9
Group together 3 + 9
5y + 12 + x
Reorder the expression.
5y + x + 12
dark city had a population of 350,000 in 1990, and has increased exponentially since then, to 475,000 in 2008. project the population in 2015.
The population of the dark city in 2015 will be 449,245.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
The dark city had a population of 350,000 in 1990 and has increased exponentially since then, to 475,000 in 2008. Then the equation will be
350,000 = a(b) ...1
475,000 = a(b)¹⁸ ...2
From equations 1 and 2, then we have
475,000 / 350,000 = b¹⁷
b = 1.018
Then the value of the variable a will be
350,000 = 1.018a
a = 343768.87
Then the equation will be
y = 343,768.87 (1.018)ˣ
The population in 2015 will be
y = 343,768.87 (1.018)¹⁵
y = 343,768.87 x 1.3068
y = 449,245
The population of the dark city in 2015 will be 449,245.
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What is the solution set of the equation
3X=-6/1-X
for x # 1?
The solution set of the equation 3X=-6/1-X for x # 1 is {-2,1)
3x = -6/(1-x)
3x(1-x) = -6
3x – 3x2 = -6
Taking 3 as common from both sides
x –x2 = -2
x2 – x +2 =0
Using factorisation method we will get two factors
Factoring quadratics is a method of expressing the quadratic equation ax2 + bx + c = 0 as a product of its linear factors as (x - k)(x - h), where h, k are the roots of the quadratic equation ax2 + bx + c = 0. This method is also is called the method of factorization of quadratic equations. Factorization of quadratic equations can be done using different methods such as splitting the middle term, using the quadratic formula, completing the squares, etc.
( x – 2)(x+1)=0
So, x = 2 , -1
Now, when x ≠ 1
The solution of the equation will vary from {-2,1) .
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Round off 28.964 to the nearest tenths
Answer:
Its 29.000Step-by-step explanation:Since we need to Round the Nearest Tenths, First we need to find what is the thenths.
So the order of numbers are
Hundreds - Tens - Ones - . - Tenths - hundreths
So tenths is the digit after the decimal Dot
When we convert .964 to the nearest tens
since there is .064, the number will be greater than .964
so the rounded number will be 1.000
we did this with only .964m but when we add 28.964 then the answer will be
28.000 = 1.000 - 29.000
Hope U will be clear
Pls Mark Brainliest−5(−x−1)+4x−1= 49 solve for x
Find the area of the triangle
Answer:
Step-by-step explanation: lengthxwidth
The number line represents −412+314.
What is the sum?
Answer:
-98
Step-by-step explanation:
-412 + 314 = 314 -412
= -98
Tip:
Write the opposite symbol in the equation, then in the answer, write the opposite symbol
Just do 412 - 314
which is 98
opposite of 98 is -98
Answer is -98
not even an actual assignment question, just wanted to ask, how are you?
Answer:
Im sleepy. How are you?
Answer:
oh thx im good how are you
Step-by-step explanation: