When the inequality expression 1 > |b - 5| is evaluated, the value of the expression is 4 < b < 6
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to determine the solution to the inequality?The absolute value inequality is given as
1 > |b - 5|
Remove the absolute value inequality symbol
So, we have the following expression
-1 < b - 5 < 1
Add 5 to all sides of the inequality expression
So, we have the following expression
5 -1 < b - 5 + 5 < 1 + 5
Evaluate the sum and the difference in the above inequality expression
So, we have the following expression
4 < b < 6
Hence, the solution to the inequality expression 1 > |b - 5| is 4 < b < 6
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what is 130x1000 well I've been on this app and it has answered this question for me and and can for u to and can I know how this app has helped you with mathematics??
the answer to 130x1000 is
130,000
hello please help me i dk
The value of x is 67°.
What are the properties of angles made by the transversal?Properties of the angles created by a transverse line and two parallel lines are:Corresponding angles as well as Alternate angles (Interiors & Exterior ) are both congruent. Co-Interior angles are supplementary. ( adds up to 180°)To determine the value of x,
Draw a line parallel to lines l and m passing through the vertex at angle x dividing it into two angles a and b.
∠a = 35° (Interior Alternate angles are congruent)
∠b + 148° = 180° (Co-Interior angles are supplementary)
⇒ ∠b = 32°
∠x = ∠a + ∠b
⇒ ∠x = 35° + 32°
⇒ ∠x = 67°
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Follow all the rules, please .
Helppppp
By solving a simple linear equation, we will get that:
36° = m∠AOB
How to find m∠AOB?
We can write a simple linear equation here, we know that:
m∠AOC = 108°
And we also know that:
m∠AOC = 3*m∠AOB
If we replace the first equation into the second one, then we will have the linear equation:
108° = 3*m∠AOB
And we want to solve this for m∠AOB, to do so, we just need to divid both sides by 3, we will get:
108°/3 = m∠AOB
36° = m∠AOB
We conclude that the measure of angle ∠AOB is 36°
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f(x) = 4x²-3x, what is the value of f (2) ?
Answer:
Step-by-step explanation: : f(x) = 4x² + 3x – 7f(-2) = 4(-2)²+3(2)-7f(-2) =16+6-7 =32-7 = 25.
Work out the difference between the highest value and the lowest value in
the list below.
-55, 45, -30, 25, -90
Answer:
105
Step-by-step explanation:
Work out the difference between the highest value and the lowest value in
the list: -55, 45, -30, 25, -90
The lowest value will be the largest negative number in the list: -90
The highest value will be the largest positive number in the list: 45
the difference between -90 and 45:
-90 - 45 = 105
Cristina goes to the market with 50 pesos. she buys one bag of papayas for 20 pesos and spends the rest of her money on clusters of bananas. each cluster of bananas cost 6 pesos. how many clusters of bananas can cristina buy
Answer:
5 clusters
Step-by-step explanation:
This is because she went to the market with 50 pesos and buys one bag of papayas for 20 pesos.
That means that her the remaining money she would have would be 50-20=30.
she would have 30 pesos.
Each banana cost 6 pesos so, she would buy 5 clusters because 30÷6=5
Find the slope and write an equation of the line which passes through the points.
A
(5,6) and (3,4)
The slope and equation of line with the coordinates (5,6) and (3,4) are 1 and y = x + 1 respectively.
How determine the slope of a line segment line?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point A(5,6)
x₁ = 5y₁ = 6Point B(3,4)
x₂ = 3y₂ = 4Slope m = ?
To determine the slope, plug the given coordinates into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 4 - 6 )/( 3 - 5 )
Slope m = ( -2 )/( -2 )
Slope m = ( -1 )/( -1 )
Slope m = 1/1
Slope m = 1
Next, use the the formula for the equation of line to determine the y-intercept 'b'.
y = mx + b
Plug in slope m = 1 and point (5,6)
6 = 1(5) + b
6 = 5 + b
b = 6 - 5
b = 1
Now that we have both the slope m ( 1 ) and y-intercept b ( 1 ), plug these values into y = mx + b to find the linear equation.
y = mx + b
y = 1x + 1
y = x + 1
Therefore, the slope is 1 and equation of line is y = x + 1.
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Select all ratios equivalent to 4:16
5:8 3:12. 15:32
Answer:
3:12 is equivalent 4:16
Step-by-step explanation:
5:8 = 0.625
3:12 = 0.25
15:32 = 0.48...
and 4:16 is 0.25, equal to 3:12
:]
(Brainliest would help a lot) Tell me if this is incorrect!
Sarah has three sisters. lea is 4 less than 3 times the age of sarah. rachel is 3 years less than one-half sarah’s age. amanda is 1 year older than twice the age of sarah. if the sum of the ages of the four sisters is 46 years, how old is each sister?
Answer:
Sarah=x
Lea=3x-4
Rachel=1/2x-3
Amanda=2x+1
Sum=46
x+3x-4+1/2x-3+2x+1=46
6.5x-6=46
6.5x=52
x=52/6.5x
x=8
input x in each sister's age:
Sarah= 8 years
Lea = 3(8)-4=20 years
Rachel = 1/2(8)-3=1 year
Amanda = 2(8)+1=17years
Step-by-step explanation:
Aldo spent $17.49 at the store. How much change will he receive if he pays with a $20 bill?
Answer:
he will receive $2.51
Step-by-step explanation:
Find the distance between each pair of points
Based on the given graph and line, the distance between the pair of points is 5
How to find the distance between a pair of points?To find the distance between two points on a line or a pair of points, first find the coordinates of the points:
(-1, -2) and (-1, 3)
The distance then be found by applying the formula:
=√((x2 – x1)² + (y2 – y1)²)
Solving for the distance gives:
=√((-1 – (-1))² + (3 – (-2))²)
= 5
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The difference of two and a number is 7.
2 + n = 7
2 - n = 7
n - 2 = 7
n + 2 = 7
Answer:
the answer for n is 5
Step-by-step explanation:
2 + n = 7
n = 7-2
n = 5
heloo! i need help with this;)
if a box is 216 cm3, what is the edge length?
The length of the edge of the box is 6 cm.
Here, we are given that the volume of a box is 216 cm cube.
Here, we assume that the box is a cube and not a cuboid since only then we will be able to find the edge of the box.
The volume of a cube is given by the formula-
Volume = side × side × side
Let the side of the given cube be x.
Then we can form the following equation-
[tex]x^{3}[/tex] = 216
x = (216)^1/3
we can find the 216 is the cube of 6. Thus,
x = 6
Hence, the length of the edge of the box comes out to be 6 cm.
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The equation 270 = f + 6.50(30) represents the cost of printing the shirts at a second printing company. Find the solution to the equation and state what it represents in this situation
The solution to the equation is f = 75.
The initial charge or setup cost is represented by the intercept or f.
What is the slope-intercept function?The linear function is expressed using the slope of the line and the y-intercept in the slope-intercept form. Its form is y = mx+ b where the slope is m and the y-intercept is b.Given equation: 270 = f + 6.50(30)
We must identify the equation's solution and explain what it represents in this situation.
The equation above is written in the form of a slope-intercept function where 6.50 is the gradient or slope of the function and 30 equals the number of shirts. The total cost of printing is 270.
The equation 270 = f + 6.50(30) can be solved as follows:
270 = f + 6.50(30)
⇒ f = 270 - 195 = 75
Therefore, the initial charge or setup cost is represented by the intercept or f. As a result, the setup fee is 65.
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Question: 4 + 2x - 7(2)³
1. What is the variable?
2. What is the coefficient of the variable?
3. What is the term with the variable?
Answer:
1: x
A variable is a letter in an equation that represents an unknown value or a value that can change.
2: 2
A coefficient for a variable is the leading number in front of the variable. It tells you how many times the variable happens
3: 2x
A term is a multiplication or division statement separated by a +/- sign.
Hope that helps
please help with 13 14 15 16
The domain and the range for the relations are given as follows:
13. Domain x ∈ R, range y ∈ R.14. Domain {x ∈ Z| -4 ≤ x ≤ 4 and x is even} , range y ∈ {y ∈ Z| -1 ≤ y ≤ 4}.15. Domain {x ∈ Z| -4 ≤ x ≤ 1} , range y ∈ {y ∈ Z| -4 ≤ y ≤ 1}.16. Domain x ∈ R, range y ∈ R.What are the domain and range of a function?The domain of a function is the set that contains all possible input values. Hence, in a graph, the domain is given by the values of x. The range of a function is the set that contains all possible output values. Hence, in a graph, the domain is given by the values of y.For items 13 and 16, the functions are continuous, hence it is over the real numbers, and both the domain and range are all real values.
For items 14 and 15, the functions are discrete, hence it is over the integer numbers, and the domain is composed by the values assumed by x and the range is composed by the values assumed by y.
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Identify the following parts
The following results of the quadratic equation are summarized below:
Vertex: (h, k) = (3, 1)
Axis of symmetry: x = 3
Min/Max value: f(3) = 1 (Maximum)
y-Intercept: - 8
x-Intercepts: (2, 0), (4, 0)
Domain: All real numbers.
Range: y ≤ 1.
Sketch of the graph: Please see image.
Standard form: f(x) = x² - 6 · x + 8
Rigid transformations: Horizontal translation / Reflection about x-axis / Vertical translation
How to determine all the features of a quadratic equation
In this problem we have a quadratic equation in standard form, whose definition is shown below:
f(x) - h = C · (x - h)² (1)
Where:
(h, k) - Coordinates of the vertex.C - Vertex constant.Now we proceed to determine each of the required features:
Vertex
The quadratic equation has a vertex at point (3, 1).
Axis of symmetry
The axis of symmetry of the parabola is x = 3.
Min/Max value
For as the vertex constant is a negative number, then the vertex represents a maximum. Then, we evaluate the function at x = 3:
f(3) = 1
y-Intercept
The y-intercept is the value of the quadratic equation evaluated at x = 0.
f(0) = - (0 - 3)² + 1
f(0) = - 9 + 1
f(0) = - 8
x-Intercepts
The x-intercepts are the values of x such that f(x) = 0, all these can be found by using algebra properties:
- (x - 3)² + 1 = 0
- (x² - 6 · x + 9) + 1 = 0
- x² + 6 · x - 9 + 1 = 0
x² - 6 · x + 8 = 0
(x - 2) · (x - 4) = 0
Then, the x-intercepts of the parabola are (2, 0) and (4, 0).
Domain
The domain of all quadratic equations are all real numbers.
Range
Since the vertex constant is negative, the range of the quadratic equation is the subset of all real numbers equal or less than the y-value of the vertex.
Sketch of the graph
Please check the image attached below to see the graph.
Standard form
The standard form of the quadratic equation is:
f(x) = x² - 6 · x + 8
Rigid transformations done
Let be g(x) = x², it is transformed into f(x) = - (x - 3)² + 1 by using the following rigid transformations:
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Determine which integer(s) from the set S:{−18, 2, 15, 20} will make the inequality five sixths m minus four is less than one third m plus 5 false.
The integer in the solution set of 5/6m - 4 < 1/3m + 5 that would make it false is 20
How to determine the integers in the set?The set is given as
S:{−18, 2, 15, 20}
The inequality expression is given as
five sixths m minus four is less than one third m plus 5
Rewrite the inequality expression properly
So, we have
5/6m - 4 < 1/3m + 5
Subtract 1/3m from both sides of the inequality expression
So, we have
1/2m - 4 < 5
Add 4 to both sides of the inequality expression
So, we have
1/2m < 9
Divide both sides of the inequality expression hy 1/2
So, we have
m < 18
This means that the integers in the solution set are integers that are less than 18
These integers are −18, 2, 15
All other integers would make the inequality false
Hence, the solution is 20
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Find the approximate circumference of a circle with a radius of 75 yards.
O 942 yards
O 24 yards
O236 yards
O 471 yards
Any line segment that starts at the circle's center and ends at one of the circle's edges is known as a radius. The circumference is 471 yards
Do you need to know how to calculate a circle's circumference? Having trouble recalling the circumference formula?Do not worry; we have you covered. Simply enter the diameter into this formula, C=[tex]\pi[/tex]d, if you know it. Instead, did you receive the radius? No issue, just use the equation C=2[tex]\pi[/tex]r. For all the information you need on calculating a circle's circumference using its diameter or radius, keep reading. To make things simple, we even provide a circumference calculator.
To determine the circumference using the radius, use the formula C = 2[tex]\pi[/tex]r. The radius of the circle is denoted by "r" in this expression. Again, you can enter the number value of, which is a closer approximation of 3.14, into your calculator.
Any line segment that starts at the circle's center and ends at one of the circle's edges is known as a radius.
You might have noticed that this resembles the formula C = [tex]\pi[/tex]d. This is due to the fact that the diameter can be thought of as 2[tex]\pi[/tex]r because the radius is only half as long as the diameter.
Circumference= 2[tex]\pi[/tex]r
= 2*3.14*75 yards
= 471 yards
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the 66th term of the arithmetic sequence - 10, 7, 24, ...
Answer:
the 66th term is 1095
What is the value of x (3x-10)° 152°
PLSSS HELP 20 POINTS I NEED IT BEFORE 12 PM SATURDAY
Graph each parabola and identify the axis of symmetry, focus, and directrix.
2x^2 − 8y=0
For given parabola 2x² - 8y = 0,
the axis of symmetry : y-axis
focus : (0, 1)
directrix : y = -1
In this question, we have been given an equation of parabola 2x² − 8y = 0
We need to graph the parabola and identify the axis of symmetry, focus, and directrix.
2x² - 8y = 0
2x² = 8y
x² = 8y/2
x² = 4y
The graph of the parabola x² = 4y is as shown below.
From this graph, the vertex is (0, 0)
We know that, for a parabola of the form x² = 4ay, the focus is (0, a) and directrix is y = -a
For the parabola x² = 4y, a = 1
So, the focus is (0, 1) and the directrix is y = -1
And the axis of symmetry for the parabola x² = 4y is the y-axis.
Therefore, for given parabola 2x² - 8y = 0,
the axis of symmetry : y-axis
focus : (0, 1)
directrix : y = -1
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Jacob had $180 in his savings account at the beginning of summer vacation. over the next 12 weeks, he mowed lawns in his neighborhood earning $145 and spending $55 each week. he deposited all of his weekly profits to his savings account each week. when summer vacation is over, he plans to spend $180 per month. for how many months can he make withdrawals from his saving account until his balance is $0?
Jacob will need 7 months to spend all the money.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jacob had $180 in his savings account at the beginning of summer vacation. over the next 12 weeks, he mowed lawns in his neighborhood earning $145 and spending $55 each week. he deposited all of his weekly profits into his savings account each week. when summer vacation is over, he plans to spend $180 per month.
The number of months will be calculated as:-
Total money in the account = 180 + 12(145-55)
Total money in the account = $1260
Total months = 1260 / 180
Total months = 7 months
Therefore, Jacob will need 7 months to spend all the money.
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The ratio of the weight of max to that of his friend artur is 5:9. artur goes on a diet and lose 4kg and now the ratio of their weights is 5:7. how much does artur weigh now?
After losing 4 Kg ,the weight of Artur is 14 Kg .
In the question ,
it is given that ,
the ratio of weight of Max : Artur is 5 : 9 .
So the weights of Max and Artur before dieting is 5x and 9x .
Now Artur goes on dieting and lose 4 Kg weight and
the ratio of weight of Max and Artur becomes 5:7 .
and the weights of Max and Artur after dieting is 5x and 7x .
Present weight of Artur = 7x .
As we can see that the change in Artur weight is 9x - 7x = 2x
According to the question
2x = 4
x = 2
hence Artur now weighs 7*(2) = 14 Kg
Therefore , after losing, 4 Kg the weight of Artur is 14 Kg .
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Find the coordinates of point P along the directed line segment AB, from A(-2,-4) to B(6, 1), so that
to PB is 3 to 2
Answer:
the coordinate of point P is (14/5, -1)
Step-by-step explanation:
Identify the zeros of the functions.
1. y = 5(x - 3)(x + 5)
2. y = (x - 7)^2
Help with these problems above would be greatly appreciated, thanks!
Answer:
1. 3 and -5
2. 7
Step-by-step explanation:
The zeros of functions are the x-values when y = 0, i.e the point(s) at which the line crosses the x-axis.
To find the zeros of the given functions, set the function to zero and solve for x.
Question 1Given function:
[tex]y=5(x-3)(x+5)[/tex]
Set the function to zero:
[tex]\implies 5(x-3)(x+5)=0[/tex]
[tex]\implies \dfrac{5(x-3)(x+5)}{5}=\dfrac{0}{5}\\[/tex]
[tex]\implies (x-3)(x+5)=0[/tex]
Using the Zero Product Property, set each factor equal to zero and solve for x:
[tex]\implies (x-3)=0 \implies x=3[/tex]
[tex]\implies (x+5)=0 \implies x=-5[/tex]
Therefore, the zeros of the function are 3 and -5.
Question 2Given function:
[tex]y=(x-7)^2[/tex]
Set the function to zero and solve for x
[tex]\implies (x-7)^2=0[/tex]
[tex]\implies \sqrt{(x-7)^2}=\sqrt{0}[/tex]
[tex]\implies x-7=0[/tex]
[tex]\implies x=7[/tex]
Therefore, the zero of the function is 7 (with multiplicity 2).
Which of the following are possible side lengths for a
right triangle?
2, 4, 6
3,4,5
6,7,9.
6, 8, 10
5, 12, 13
Answer:
3, 4, 5
6, 8, 10
5, 12, 13
Step-by-step explanation:
If you are given side lengths and must determine if it is a right angle, you will use the Pythagorean Theorem. Which states that the square length of the hypotenuse (longest side of a triangle) must equal to the sum of the square length of the two shortest.
Formula: a² + b² = c²
2, 4, 6
a² + b² = c²
(2)² + (4)² ≟ (6)²
4 + 16 ≟ 36
20 ≠ 36
3, 4, 5
a² + b² = c²
(3)² + (4)² ≟ (5)²
9 + 16 ≟ 25
25 = 25
6, 7, 9
a² + b² = c²
(6)² + (7)² ≟ (9)²
36 + 49 ≟ 81
85 ≠ 81
6, 8, 10
a² + b² = c²
(6)² + (8)² ≟ (10)²
36 + 64 ≟ 100
100 = 100
5, 12, 13
a² + b² = c²
(5)² + (12)² ≟ (13)²
25 + 144 ≟ 169
169 = 169
find the measure of each interior angle and each exterior angle of a regular 12 -gon (a twelve-sided polygon).
Answer:
interior = 150° , exterior = 30°
Step-by-step explanation:
the sum of the exterior angles of a polygon = 360°
since the polygon is regular then each exterior angle is
360° ÷ 12 = 30°
the sum of the exterior angle and interior angle = 180° then
interior angle = 180° - 30° = 150°
Divide using either synthetic division or long division.
(3x^3 + 4x^2 - x + 7) / (x + 2)
Answer:
Quotient = 3x² - 2x + 3
Remainder = 1
Step-by-step explanation:
We have to solve: [tex]\dfrac{3 x^{3} + 4 x^{2} - x + 7}{x + 2}[/tex]
We will use synthetic division to calculate this divisor
First, take the constant term of the divisor with the opposite sign and write it to the left. Write the coefficients of the dividend expression to the right Where there is no coefficient for a specific x term, use 0
Step 1: Write down the first coefficient asis
| x³ x² x¹ x⁰
2 | 3 4 -1 7 ← Coefficient row
|
---------------------------------
3 ← Result Row
Step 2: Multiply the entry in the left part of the table by the last entry in the result row and add he obtained result to the next coefficient of the dividend, and write down the sum.
| x³ x² x¹ x⁰
-2 | 3 4 -1 7
| -6 -6 = -2 x 3
---------------------------------
3 -2 -2 = 4 + (-6)
Repeat step 2 until we have finished with all the entries. These are the snapshots of each computation. Current operands are in bold
| x³ x² x¹ x⁰
-2 | 3 4 -1 7
| -6 4
---------------------------------
3 -2 3
| x³ x² x¹ x⁰
-2 | 3 4 -1 7
| -6 4 -6
---------------------------------
3 -2 3 1
The last entry in the result table shows the remainder of the division
The resultant coefficients are 3, -2, 3, 1
Therefore the answer is
Quotient = 3x² - 2x + 3
Remainder = 1
In the diagram below, the numbers in each box is the sum of two numbers below it. Work out the missing numbers for boxes A and B.
The value of the missing number in box A is [tex]1\frac{1}{2}[/tex]
The value of the missing number in box B is [tex]7\frac{1}{4}[/tex]
What are the missing numbers?In order to determine the value of A, subtract [tex]1\frac{1}{4}[/tex] from [tex]2\frac{3}{4}[/tex]. Subtraction is the mathematical operation that is sued to determine the difference between two or more numbers
A = [tex]2\frac{3}{4}[/tex] - [tex]1\frac{1}{4}[/tex]
[tex]1\frac{3 - 1}{4}[/tex] = 1 [tex]\frac{2}{4}[/tex] = [tex]1\frac{1}{2}[/tex]
In order to determine the value of B, add [tex]4\frac{1}{2}[/tex] and [tex]2\frac{3}{4}[/tex] together. Addition is the process used to determine the sum of two or more numbers.
B = [tex]4\frac{1}{2}[/tex] + [tex]2\frac{3}{4}[/tex]
[tex]6\frac{2 + 3}{4}[/tex] = [tex]6\frac{5}{4}[/tex] = [tex]7\frac{1}{4}[/tex]
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