|x-5| + 7 = 13 is equal to x= -11 and x = 1.
[tex]|x-5|+7=13[/tex]
Subtract 7 from both sides
[tex]|x-5|+7-7=13-7[/tex]
Simplify
[tex]|x-5|=6[/tex]
Apply absolute rule: If [tex]$|u|=a, a > 0$[/tex] then [tex]$u=a$[/tex] or [tex]$u=-a$[/tex] [tex]$x-5=-6$[/tex] or [tex]$x-5=6$[/tex]
[tex]$$x-5=-6 \text { or } x-5=6$$[/tex]
[tex]$$x=-1 \text { or } x=11$$[/tex]
Making something simpler is making it less intricate or crowded. When you describe a complex mathematical idea to a youngster in words they can easily comprehend, you are simplifying. When you eliminate many of the tasks that were keeping you occupied and stressed out, you have simplified.
Making something simpler refers to making it simpler to accomplish or comprehend. Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. In order to do this, we divide both the numerator and the denominator by the biggest integer that can be divided precisely into both numbers.
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The formula for calculating the volume of a cone is V=-rh. Solve this formula for h.
that is the solution above
help Finding the initial amount and rate of change given a table for a linear function
(a) The table clearly shows distance gets smallers as time passes, so the first choice is correct.
Since we know the rate at which the escalator moves is constant, we know that the average rate of change of the escalator's distance from the first floor is the same across any time interval we choose. Take for instance the average rate of change from [tex]t=6[/tex] to [tex]t=9[/tex]. If [tex]d(t)[/tex] denotes distance at time [tex]t[/tex], then the average rate of change over these 3 seconds, and at every point in time for that matter, is
[tex]\dfrac{d(9) - d(6)}{9 - 6} \dfrac{\rm cm}{\rm s} = \dfrac{890 - 980}{9 - 6} \dfrac{\rm cm}{\rm s} = -30 \dfrac{\rm cm}{\rm s}[/tex]
In other words, the distance from the first floor is decreasing at a rate of 30 cm/s. (negative sign = decreasing)
(b) At the start, when [tex]t=0[/tex], suppose Alan's distance from the first floor was [tex]x[/tex]. For every second that passes, we know the distance from the first floor decreases by 30 cm. This would mean that after [tex]t[/tex] seconds have passed, the distance would have decreased by a total [tex]30t[/tex] cm.
This tells us that Alan's distance from the first floor at any time [tex]t\ge0[/tex] is
[tex]d(t) = x - 30t[/tex]
Using any of the values from the table, we can solve for [tex]x[/tex].
[tex]t=6 \implies d(6) = x - 30\cdot6 \implies 980 = x - 180 \implies x = 1160[/tex]
which places Alan 1160 cm = 11.6 m from the first floor at the start.
the diagram shows a rectangle 0.5cm length, 7cm width. four of these rectangles are put together?
Area of Rectangle :42 [tex]cm^{2}[/tex]
To calculate the shaded area, first calculate the overall area and then deduct the areas of the four little rectangles.
The following are the dimensions of the large rectangle:
The length is merely one of the little rectangles' length: 7
The width is equal to the length of one of the tiny rectangles plus the width of two of the small rectangles, thus 7 + 0.5 + 0.5 = 8.
As a result, the area of the largest rectangle is 7 × 8 = 56 cm^2.
We must now calculate the areas of the four smaller rectangles. It's simply length multiplied by width:
7 ×0.5 = 3.5
Because there are four rectangles, multiply by four:
14 cm squared = 3.5 ×4
Finally, the shaded area is calculated as 56 - 14 = 42 cm squared.
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Suppose x and y vary together such that y = 2 x 8 . suppose x varies from x = 3 to x = 9.5 . over this interval, how much does x change by?
A function assigns the values. The value of x changes by 6.5, and the value of y changes by 13.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that x and y vary together such that y = 2x+8. Also, the of x varies from x = 3 to x = 9.5. Therefore, we can write,
x change by = Maximum value of x - Minimum value of x
= 9.5 - 3
= 6.5
Further, the minimum and the maximum value of y will be when the value of x is minimum and maximum, this is because the function is linear. Therefore, we can write,
Minimum value of y, y = 2(3) - 8 = -2
Maximum value of y, y = 2(9.5) - 8 = 11
y change by = Maximum value of y - Minimum value of y
= 11 - (-2)
= 11 + 2
= 13
Hence, the value of x changes by 6.5, and the value of y changes by 13.
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(-1.5) to the 5th power * (3.2) to the 5th power
Answer:
-2548.03968
Step-by-step explanation:
(-1.5)^5*(3.2)^5
Answer:
Step-by-step explanation:
Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms. f(x)=-2(3+x)²+2 x²
The given function f(x)=-2(3+x)²+2x² , is a linear function.
Where:
Its quadratic term is 0x².Its linear term is -12xConstant is -18What is a function?A function is a mathematical expression or equation that allows us to visualize graphically the behavior of a function. A function is not real when it cuts the vertical axis at the same point of x.
A function can be linear or quadratic, this is evidenced by the higher exponential degree, in our case we have the following function:
f(x) = -2(3+x)²+2x² we solve the function that seems to be quadratic because it has the highest degree the number "2" in the variable, however we will solve its reduction.
We solve the trinomial and substitute
(3+x)² = (9 + 6x + x²)
-2(9 + 6x + x²) + 2x²
-18 - 12x - 2x² + 2x² + 2x²
0x² - 12x - 18 is a linear function
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If 8 + 13 = 21, then 21 = 8 +
The complete equation is 8 + 13 = 21, then 21 = 8 + 13
What is commutative property of additionThe commutative property of addition states that a change in the arrangement or order of a number being added does not affect the sum of the numbers.
Example;
5 + 4 is equivalent to 4 + 5
2 + 3 is equivalent to 3 + 2
Given the expression;
8 + 13 = 21
Using the commutative property of addition, it can also be expressed as;
21 = 8 + 13
In this case, there's no net change in the equation.
Thus, the complete equation is 8 + 13 = 21, then 21 = 8 + 13
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Assume that x is an int variable. what value is assigned to x after the following assignment statement is executed? x = -3 4 / 5;
The value of x as an int variable is 0
What is a int variable?An int(integer) variable is a variable containing only whole numbers.
Given the expression;
x = - 3 + 4 % 6/ 5
Let's make into proper fraction, we have
x = - 3 + {}4/ 100 × 6/ 5
Multiply through
x = -3 + 6/ 5/ 4/ 100
x = -3 + {6/ 5 ÷ 0. 4}
x = -3 + {3}
expand the bracket
x = -3 + 3
Add like terms
x = 0
Thus, the value of x as an int variable is 0
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Complete question;
Assume that x is an int variable. what value is assigned to x after the following assignment statement is executed? x = -3 + 4 % 6/ 5;
Solve each system by elimination. 2x + 3y = 7 , -2x + 5y = 1
By elimination, the solution of the system of equations, 2x + 3y = 7 and -2x + 5y = 1, is (2 , 1).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
Adding the two equations will eliminate the variable x.
2x + 3y = 7 (equation 1)
-2x + 5y = 1 (equation 2)
0x + 8y = 8
y = 1
Substitute the value of y to any of the two equation and solve for x.
2x + 3y = 7 (equation 1)
2x + 3(1) = 7
2x = 7 - 3
2x = 4
x = 2
Hence, the solution of the system of equations is (2 , 1).
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i need help on
4-9x=14
Answer:The answer is x=-10/9 or -1 1/9
Step-by-step explanation:
Multiple the question bellow
[tex]y+\frac{4}{5} =1\frac{2}{5}[/tex]
Given LM- MP and L, M, and P are collinear, which of the following is false about the relationship of L, M. and P?
(1) LM = MP (2) M is the midpoint of LP (3) LM +MP=180 (4) M bisects LP
The statement that is false about the relationship of L, M, and P that are collinear is: 3. LM + MP = 180.
What are Collinear Points?When two or more points are on a straight line, they are classified as collinear points.
What is the Midpoint of a Segment?The point on a line segment that bisects the segment into two equal parts is referred to as the midpoint of the line segment.
We are given that:
LM = MP, since, points L, M. and P are collinear points, therefore, it implies that point M is the midpoint of segment LP.
It also means that M bisects segment LP since LM = MP, where M is the midpoint of segment LP.
Thus, the statement that is false about the relationship of L, M, and P that are collinear is: 3. LM + MP = 180.
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2t² +t-3 = 0 ….???………????????
what is 49/200 equal to explain
Answer: It can not be simplified
Step-by-step explanation:
49 is divisible by 1 and 7
200 is not divisible by 7
Let g be a translation 4 units down and a horizontal shrink by a factor of 1/4 of the graph of f(x)=x
Answer:
X is the value of cordinatinate so X is 1
Maria has a square brick patio. She wants to reduce the width by 3 feet and
increase the length by 3 feet.
T
3 ft
3 ft
3 ft
O A. Iw= x(x-3); 40 square feet
3 ft
Let x represent the length of one side of the square patio. Write expressions
for the length and width of the new patio. Then find the area of the new patio
if the original patio measures 8 feet by 8 feet.
Answer:
Length = x + 3 ft
Width = x - 3 ft
Area of new patio = x² - 9 sq ft
If original side length = 8, new area = 55 sq ft
Step-by-step explanation:
The original patio has side length of x
If one side is reduced by 3 we get (x - 3) as the new side
If the side is increased by 3' we get (x + 3) as the new side
Area of new Patio = (x - 3)(x+3) = x² - 9
Original patio is 8 x 8
New patio width = 8 - 3 = 5
New patio length = 8 + 3 = 11
Area = 5 x 11 =55 sq ft
Razonar ¿Cuál es el primer paso para resolver la
ecuación 3(3x - 5x) + 2 = -8?
Evaluate each expression for x=0 . 5 x+2
After evaluation each expression for x = 0 then the equation 5 x+2
⇒ 5(0)+2
⇒ 0 + 2
⇒ 2
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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The population of Georgia is growing at a yearly rate of about 1.3%. The current population is
about 9,815,210 people. The population of North Carolina is growing at a yearly rate of about
1.25%. North Carolina's current population is about 9,656,401 people.
a. What is the equation that models Georgia's population growth?
b. What is the equation that models North Carolina's population growth?
c. What do the graphs of the equations look like? Graph the equations on the provided grid.
The equation for population growth in Georgia is P = 8,815,210 ( 1.013 )ⁿ ( red line on the graph) and the equation for population growth in North Carolina is P = 9,656,401 ( 1.0125)ⁿ ( blue line on the graph).
We are given that:
For Georgia:
Growth rate of population = 1.3 %
Population = 8,815,210
For North Carolina:
Growth rate of population = 1.25 %
Population = 9,656,401
a) The equation that models Georgia's population growth can be found out by using the concept of compound interest as the population will increase in a compounded way.
So, the equation will be:
P = 8,815,210 ( 1 + 1.3 % )ⁿ
P = 8,815,210 ( 1.013 )ⁿ
where P is the population after n years.
b) the equation that models North Carolina's population growth:
P = 9,656,401 ( 1.0125)ⁿ
where P is the population after n years
Therefore, we get that, the equation for population growth in Georgia is P = 8,815,210 ( 1.013 )ⁿ ( red line on the graph) and the equation for population growth in North Carolina is P = 9,656,401 ( 1.0125)ⁿ ( blue line on the graph)
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Formula; f(x)=x
1. x+1=
Step-by-step explanation:
1.x+1
1+1 is 2
1.x+1 and is 22+X and is 2xWhich statements have an inverse that is false?
1.If two angles are congruent, then they are vertical angles.
2.If two angles are a linear pair, then they are supplementary.
3.If two angles are acute, then their sum is less than 90.
4.If two angles are complementary, then both angles are acute.
Statement 1 is a false statement.
What are supplementary angle?
Supplementary angles are two angles whose measures add up to 180° . ex 150° and 30°
What are complementary angles?
When the sum of two angles is equal to 90° degrees, they are called complementary angles. For example, 30° and 60° are complementary angles.
What are vertical angles?
Vertical angles are formed when two lines meet each other at a point. A vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180°What are congruent angles?
Two or more angles that are identical to each other.
False - All vertical angles are considered congruent but not all congruent angles are considered vertical angles. Any acute or obtuse angle may also be considered congruent. True - If 2 angles whose measures add to 180°, it means they are supplementary. They form a linear pair.True - Let one angle be 30° and the other angle is 40° , both of which are acute angles, then their sum is 70°, which is less than 90° True - Both angles in a complementary pair will always be acute. For ex: 30° and 60° are complementary angles , but are less than 90°, so they both are acuteThus we can conclude that all vertical angles are congruent but not all congruent angles are considered vertical angles
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Can anyone help me solve this math problem, I don’t understand these at all
The relative frequency of the data is being found.
We have the data:
Ages Number of students
15 - 18 5
19 - 22 5
23 - 26 5
27 - 30 10
31 - 34 3
35 - 38 10
We need to find the relative frequency of the data:
Total students = 5 + 5 + 5 + 10 + 3 + 10 = 38
Relative frequency = Number / Total × 100
So, we get that:
Ages Number of students Relative frequency
15 - 18 5 13.16 %
19 - 22 5 13.16 %
23 - 26 5 13.16 %
27 - 30 10 26.32 %
31 - 34 3 7.89 %
35 - 38 10 26.32 %
Therefore, we get that, the relative frequency of the data is being found.
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i don’t know how to do it pls help
Answer:
[tex] - 1 \geqslant x \geqslant 2[/tex]
Humpback whales are known to weigh as much as 80,000 pounds. The tiny krill they eat weigh only
2
.
1875
×
10
−
3
pound. About how many times greater is the weight of a humpback whale?
Select Choice
The weight of the Humpback whale is 3.6571 x [tex]10^{7}[/tex] times greater than the weight of the tiny krill.
What are factors of a number?A factor is a number that divides the given number without any remainder.
We have,
Weight of a Humpback whale = 80,000 pounds
Weight of tiny krill = 2.1875 x [tex]10^{-3}[/tex] pounds
We need to find what value multiplied with 2.1875 x [tex]10^{-3}[/tex] would give 80,000.
Let the value be M.
M x 2.1875 x [tex]10^{-3}[/tex] = 80,000
M = 80,000 / 2.1875 x [tex]10^{-3}[/tex]
M = 80,000 x / 2.1875 x [tex]10^{-3}[/tex]
M = 3.6571 x [tex]10^{7}[/tex]
Thus the weight of the Humpback whale is 3.6571 x [tex]10^{7}[/tex] times greater than the weight of the tiny krill.
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Find the magnitude and direction of the following vector.
-AB : A<-1,10> and B(1,-12)
AB has a magnitude of 9√6 according to estimates.
AB's vector direction is given as Ф = 84.80° (angle which lies in the 4th quadrant with clockwise direction).
What basically does a distance formula mean?In complex numbers, the distance formula is employed to demonstrate the plane as well as its magnitude. Furthermore, distance formulas can be used to calculate the distance between two planes in three-dimensional and n-dimensional planes.
Now, in response to the given question;
J and K have (-1,10) and (1,-12) coordinates, respectively.
The distance formula for the points A and B is as follows:
AB² = (x₂ - x₁)² + (y₂ - y₁)²
AB = √[(x₂ - x₁)² + (y₂ - y₁)²]
The coordinates for the points A and B's are-
(x₁,y₁) = (-1,10) and (x₂,y₂) = (1,-12).
Substituting the given values in the distance formula;
AB = √[(1 + 1)² + (-12 - 10)²]
AB = √[(2)² + (-22)²]
AB = √[4 + 484] = √486
AB = 9√6 (magnitude of the vector AB)
Estimate this same vector AB's direction now. The direction of a vector is defined by the angle formed by it with a horizontal line.
To determine the direction of a vector, utilize one of the formula given.
tan Ф = Δy/Δx
Where, x = horizontal change
and, y = vertical change
tan Ф = (y₂ - y₁)/(x₂ - x₁)
= (-12 - 10)/(1 + 1)
tan Ф = -22/(2) = -11
Ф = 84.80° (angle which lies in the 4th quadrant with clockwise direction).
As a result, this same distance between A and B is discovered to be 9√6 (the same as the magnitude of a given vector AB).
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Joseph is mixing 5 1/2 gallons of orange drink for his class picnic. Every 1/2 gallon requires 1 packet of orange drink mix. How many packets of orange drink mix does Joseph need?
Joseph needs 22.4 packets of orange drink mix which requires one packet of orange drink mix for every half gallon.
What is Ratio?A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other
We have been given that Joseph is mixing 5 1/2 gallons of orange drink for his class picnic.
And every 1/2 gallon requires 1 packet of orange drink mix.
We have to determine the number of packets of orange drink mix Joseph needs.
Let the number of packets of orange would be x
We can write this as a ratio as
1/2 gallon : 1 packet = 5 1/2 gallons : x packets
0.5 gallon : 1 packet = 11.2 gallons : x packets
⇒ x = 11.2/0.5
⇒ x = 22.4
Therefore, he needs 22.4 packets of orange drink mix.
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what is the correct answer to the following solution 5−3y≤−y−15.
Identify a pattern and find the next three numbers in the pattern.
4,20,100,500, . ..
The pattern exists described as a sequence of repeating objects, shapes, or numbers. Patterns can also occasionally be referred to as a series.
The pattern follows the rule tn = t(n-1) × 5
The next three numbers in the pattern be 4, 20, 100, 500, 2500, 12500, 62500.
What is meant by pattern?A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
Let the numbers in the pattern be 4, 20, 100, 500, . . .
t2 = 4 × 5 = 20
t3 = 20 × 5 = 100
t4 = 100 × 5 = 500
t5 = 500 × 5 = 2500
t6 = 2500 × 5 = 12500
t7 = 12500 × 5 = 62500
Thus, the pattern follows the rule tn = t(n-1) × 5
The next three numbers be 2500,12500,62500
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Moving to
estion 1
Identify the inequality or equality that describes the following situation. Juan has over 77 marbles.
The inequality or equality that describes the following situation is; m ≤ 77 marbles.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
Also set of values of the variable involved in the inequality for which the considered inequality holds true is called the solution set for that inequality.
We need to find the inequality or equality that describes the following situation; Juan has over 77 marbles.
Let the marbles juan has m then
The inequality or equality that describes the following situation is;
m ≤ 77 marbles.
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