The inequality which represents the situation is; |x - 7| < 20 and the solution is; 27 > x > -13.
What is the inequality that represents the situation?Since the number is less than 20 units away from.the number 7 on the number line, it follows.from interpretation that the inequality is;
|x - 7| < 20
Hence; x-7 < 20; x < 27
Or
-x + 7 < 20
-x < 13
x > -13
Hence, the solution of the inequality is; 27 > x > -13.
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The sum of the angle 5 and angle 6 is 180 degrees. Then the correct option is C.
What is Supplementary angle?When two angles are said to be supplementary angles if their sum is 180 degrees.
A triangle is shown with its exterior angles.
The interior angles of the triangle are angles 2, 3, 5.
The exterior angle at angle 2 is angle 1.
The exterior angle at angle 3 is angle 4.
The exterior angle at angle 5 is angle 6.
We know that the sum of interior and exterior angle of the triangle is 180 degrees.
∠1 + ∠2 = 180°
∠3 + ∠4 = 180°
∠5 + ∠6 = 180°
Then the correct option is C.
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You are walking directly away from your house.
You are 5 miles away from your house when
you start walking, so you can determine your
distance from your house by adding 5 to the
number of miles you have walked. In the
equation below, a represents the number of
miles you have walked, and y represents your
distance from home in miles.
The relationship between these two variables
can be expressed by the following equation:
y = x + 5
Identify the dependent and independent
variables.
Your distance
from home
Number of
miles you
walk
Dependent
variable
Independent
variable
Answer:
dependent: your distance from home
independent: number of miles you walk
Step-by-step explanation:
lmk if you want an explanation
The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square bas-
is x units.
Which expression represents the volume of the prism, in cubic units?
x³ +9
x³ + 3x²
x³ + 3x + 3
x³ + 6x² + 9x
Answer:
College dropout is the greatest album of all-time
Under her cell phone plan, Aubree pays a flat cost of $58.50 per month and $3 per gigabyte. She wants to keep her bill at $72.30 per month. How many gigabytes of data can she use while staying within her budget?
Answer:
Aubree can use 4.6 gigabytes of data while staying within her budget.
If the answer choices only use whole numbers, use 4 gigabytes, because it is the number of full gigabytes she can use.
Step-by-step explanation:
x= gigabyte
58.50 + 3x = 72.30
3x = 72.30-58.50
3x= 13.8
x= 4.6
The graph of g(x), shown below in red, has the same shape as the graph of
f(x) = 2x, shown in blue. Which of the following is the equation for g(x)?
A. g(x) = 2(x-1) - 3
B. g(x) = 2(x+3) - 1
C. g(x) = 2(x-3) -1
D. g(x) = 2(x+1) - 3
Which function is graphed below?
-
Answer:
y=3 (1/3)x
Step-by-step explanation:
On a graph, the closest graph you pictured is this answer
Answer:
y = [tex]3 (\frac{1}{3} )^{x}[/tex]
Step-by-step explanation:
Step 1:
Check the y-intercept; in the graph, when x = 0, y = 3. Which equation satisfies this?
y = [tex]\frac{1}{3}[/tex] [tex](3)^{x}[/tex] = [tex]\frac{1}{3}[/tex] [tex](3)^{0}[/tex] = [tex]\frac{1}{3}[/tex] ❌
y = [tex]3 (\frac{1}{3} )^{x}[/tex] = [tex]3 (\frac{1}{3} )^{0}[/tex] = 3 ✅
y = [tex](\frac{1}{2} )^{x}[/tex] + 2 = [tex](\frac{1}{2} )^{0}[/tex] + 2 = 3 ✅
So the last two equations are possible.
Step 2:
Now check the y-value on the graph for any other x-value, whose corresponding y-value can be easily estimated from the graph.
For example, when x = 2, the y-value is between 0 and 1.
• 2nd equation: y = [tex]3 (\frac{1}{3} )^{x}[/tex] = [tex]3 (\frac{1}{3} )^{2}[/tex] = 0.333 ✅
• 3rd equation: y = [tex](\frac{1}{2} )^{x}[/tex] + 2 = y = [tex](\frac{1}{2} )^{2}[/tex] + 2 = 2. 25 ❌
∴ 2nd equation (y = [tex]3 (\frac{1}{3} )^{x}[/tex] ) is the one being represented by the graph.
How do I solve this?
Answer:
x = 4
Step-by-step explanation:
The figure in the picture is a parallelogram. In parallelograms diagonals bisect each other. That means that they divide each other in half. That means that 6x + 1 is the same as 4x + 9.
6x + 1 = 4x + 9
2x + 1 = 9
2x = 8
x = 4
What are the domain and range of f(x) = 2x - 41?
O domain: x < 2; range: (-∞0,00)
O domain: (-∞,00); range: f(x) > 0
O domain: (-∞0,00); range: f(x) < 0
O domain: x ≥ 2; range: (-∞,00)
The domain of the function is a (-∞, 0) and the range of the function will be f(x) < 0. Then the correct option is C.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
f(x) = 2x – 41
Then the domain of the function is a (-∞, 0) and the range of the function will be f(x) < 0.
Then the correct option is C.
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Hey I need help on this question. Could I have a simple explaination as I find it difficult to understand things
Answer:
9
Step-by-step explanation:
The surface, in this case, describes the number of squares that are painted. On the left hand side, we have a cube, so we know we're going to have 6 faces. And each face on the cube has 9 little squares, they can be counted on the diagram. So, the total number of squares that are painted on the left cube = [tex]9 * 6 = 54[/tex]
The star means multiplication.
We are told in the question that it takes 9 litres of paint to cover the surface of the left hand cube, meaning it takes 9 litres of paint to cover 54 squares.
This can be written in the ratio = [tex]9:54[/tex]
If we divide both sides of the ratio by 9, we can figure out the amount of squares that 1 litre of paint covers, [tex]1:6[/tex].
The ratio tells us that 1 litre of paint covers 6 squares.
Let's look at the shape on the right. It is still a cube, however, some segments have been removed. Some faces still remain the same as in the shape on the left, such as the bottom face, the back face and the face to the left. Those faces may not be so apparent on the diagram, however, they exist. So we have to count them.
The number of small squares on these faces = [tex]9 * 3=27[/tex]
If you look on the inside of the cube, which can be seen on the diagram, we can see three faces, each having four squares. So, the total number of squares here = [tex]3*4=12[/tex]
Also, we have some squares on the top, and if you count these, there are 5.
This also applies for the front and the right hand side if you count, so we add 10 squares to the total as there are another two lots of five.
So, the total number of squares on the right cube = [tex]27 + 12 + 5 + 5 + 5 = 54[/tex]
Let's bring back the ratio of litres of paint to the number of squares covered: [tex]1:6[/tex]
In the ratio, there are 6 squares per litre. We know that 6 × 9 = 54 (our total). So, we multiply left hand side of the ratio by 9 as well, bringing the total amount of paint required to 9 litres.
I hope this helps.
The surface area of cuboid = [tex]$400 \mathrm{~cm}^{2}$[/tex].
How to estimate the surface area of cuboid?
If the left cube takes 9 liters of paint to cover the surface. Then, also right cube takes 9 liters of paint to cover the surface.
Cuboid dimension [tex]$\frac{10 \mathrm{~cm}}{(l)} \times \frac{10 \mathrm{~cm}}{(b)} \times\frac{5 \mathrm{~cm}}{(h)}$[/tex]
Surface area = 2(lb + lh + bh)
= 2((10 [tex]\times[/tex] 10)+(10 [tex]\times[/tex] 5)+(10 [tex]\times[/tex] 5))
= 2(100+50+50)
= [tex]400 \mathrm{~cm}^{2}[/tex]
Therefore, surface area of cuboid = [tex]$400 \mathrm{~cm}^{2}$[/tex].
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The total pages a person reads in x days, if the person reads 6 pages a day
the cost of x boxes of mangoes, if 1 box costs $6 and the shipping charge is $6 per order (for any number of boxes)
the total cost of x notebooks, if one notebook costs $6 and students receive a discount of $1 off their total bill
the total cost of x novels and a pocket dictionary if you buy x novels each at $6 and get a pocket dictionary at $1
what are the corresponding functions for each situation?
The given expression will be written as follows:-
y = 6x
y = 6x + 6
y = 6x - 1
y = 6x +1
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
A) The total pages a person reads in x days, if the person reads 6 pages a day
y = 6x
B) The cost of x boxes of mangoes, if 1 box costs $6 and the shipping charge is $6 per order (for any number of boxes)
y = 6x + 6
C) The total cost of x notebooks if one notebook costs $6 and students receive a discount of $1 off their total bill
y = 6x - 1
D) The total cost of x novels and a pocket dictionary if you buy x novels each at $6 and get a pocket dictionary at $1
y = 6x + 1
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What is the value of the blue dot?
Answer:
17
Step-by-step explanation:
Solution
The distance between each marker is 2. So going upwards 9+2 = 11
11 + 2 = 13
13 + 2 = 15 But we still have 1 more space to go.
15 + 2 = 17
Please help me!!!!!!
Answer:
It is an obtuse triangle I think because
Write g(f(x)) as an expression in terms of x
An expression is defined as a set of numbers, variables, and mathematical operations. The value of g(f(x)) is (x²-10x+13) / (x²-10+29).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The complete questions is,
Write g(f(x)) as an expression in terms of x
f(x) = x-5
[tex]g(x) = \dfrac{x^2-12}{x^2+4}[/tex]
The value of g(f(x)) as an expression in terms of x can be written as,
[tex]g(f(x)) = \dfrac{(x-5)^2-12}{(x-5)^2+4}\\\\\\g(f(x)) = \dfrac{x^2+25-10x-12}{x^2+25-10x+4}\\\\\\g(f(x)) = \dfrac{x^2-10x+13}{x^2-10+29}[/tex]
Hence, the value of g(f(x)) is (x²-10x+13) / (x²-10+29).
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For any positive numbers a, b, and d, with b 1,
A.
logb a logb d
B.
logb a + logb d
C.
d logb a
done
D.
logb a - logb d
Answer:
D
Step-by-step explanation:
using the rule of logarithms
log x - log y ⇔ log ( [tex]\frac{x}{y}[/tex] )
then
[tex]log_{b}[/tex] ( [tex]\frac{a}{d}[/tex] ) = [tex]log_{b}[/tex] a - [tex]log_{b}[/tex] d
Suppose that g(x) = f(x) + 6. Which statement best compares the graph of g(x) with the graph of f(x)?
A) The graph of g(x) is the graph of f(x) shifted 6 units down.
B) The graph of g(x) is the graph of f(x) shifted 6 units to the left.
C) The graph of g(x) is the graph of f(x) shifted 6 units up.
help please D:
From the graph attached below, we can see that the graph of g(x) is the graph of f(x) shifted 6 units up. the correct option is C.
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
Given;
Suppose that g(x) = f(x) + 6.
From the graph attached below, we can see that the graph of g(x) is the graph of f(x) shifted 6 units up.
Hence, the correct option is C.
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The complete question is
"Suppose that g(x) = f(x) + 6. Which statement best compares the graph of g(x) with the graph of f(x)?
A) The graph of g(x) is the graph of f(x) shifted 6 units down.
B) The graph of g(x) is the graph of f(x) shifted 6 units to the left.
C) The graph of g(x) is the graph of f(x) shifted 6 units up.
D. The graph of g(x) is the graph of f(x) shifted 6 units to the right."
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does y - x = 2 show direct variation
Answer:
no
Step-by-step explanation:
if I use any numbers too .the numbers can not be constant numbers so this equation is not a direct variation
7 - 5 = 2
6- 4 = 2
not contstant
For what values of x does 25× - 5ײ-3?
O x = -3, x = 1
O x = -1, x = 3
3
0 X=-²2/₁X-2
Ox
3
O x= -2, x=-2/
Answer:
X = 3, -1; B
Step-by-step explanation:
Use log properties, log 5 on both sides, log 5 of 25 is 2 that times the exponent, so 2*x = 2x, and on the other side, log 5 and base of 5 cancels. So 2x = x^2 -3, which can be solved using factoring:
x^2 -2x -3 = (x-3)(x+1) = 0, x=3,-1
The value of x in 25ˣ = 5ˣ²⁻³ is x =3 or x = -1.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
Given that the equation is 25ˣ = 5ˣ²⁻³.
To solve the equation, take logs on both sides, we get,
x log(25) = (x²- 3)log5
2x log 5 = (x²- 3) log5
2x = x²-3
x²- 2x -3 = 0
Now, factorize the quadratic equation,
we get,
x² - 3x + x - 3 = 0
x(x- 3) + 1(x - 3) = 0
x = 3 or -1.
Therefore, x = 3 or x = -1.
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Ten years ago Victors age WAs half of the age he will be in 10 years how old is he now?
By solving a linear equation, we will see that Victor is 30 years old.
How old is Victor now?
Let's say that Victor is x years old.
We know that 10 years ago, (x - 10), his age was half of what it will be in 10 years (x + 10).
Then we can write the linear equation:
(x - 10) = (x + 10)/2
Now we can solve that equation for x:
2*(x - 10) = x + 10
2x - 20 = x + 10
2x - x = 10 + 20
x = 30
So we conclude that Victor is 30 years old.
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factorise the expression as fully as possible 10xsquared -5x
Answer:
5x(2x - 1)
Step-by-step explanation:
Factor 10x^2 - 5x:
Then: 10x^2 - 5x = 5x(2x - 1), since 5x is common to the two given terms
Answer:
[tex]10x^{2} -5x[/tex] in factored form would be [tex]5x(2x-1)[/tex]
Step-by-step explanation:
If we look at all of the terms in this binomial, we can see that they both have 5x in common. We can now factor 5x out of the equation to get our answer.
To do this, we must divide both terms by 5x.
[tex]10x^2[/tex] divided by [tex]5x[/tex] is [tex]2x[/tex], and [tex]-5x[/tex] divided by [tex]5x[/tex] is [tex]-1[/tex].
So, our final answer is [tex]5x(2x-1)[/tex].
is this correct ?-?
I need to get this done lol
Answer:
6
Explanation:
[tex]\textsf {The range of a data representation refers to difference of the smallest and }\\\textsf {greatest possible values. }[/tex]
[tex]\textsf {Here :}[/tex]
[tex]\textsf {smallest value = 5}\\\textsf {greatest value = 11}[/tex]
[tex]\textsf {Then the range will be :}\\\implies \textsf {greatest value - smallest value}\\\implies \mathsf {11 - 5}\\\implies \mathsf {6}[/tex]
Write an equation for a graph that is the set of all points in the plane that are equidistant from the point F(4, 0) and the line x = –4.
The equation of the graph is y ² = 16x.
What is a Parabola ?A parabola is a U shaped curve ,all the point of which is equidistant from a point called as focus and a line called as Directrix .
In the given question , the graph is a horizontal parabola as the directrix is x = -4 , and as the focus lies on the right side , it is opening towards the right.
The equation for the horizontal parabola is given b y
(y-k)² = 4p(x-h)
h , k is the mid point of focus and the directrix , i.e. the vertex and is given by
h = ([tex]\rm x_f[/tex] +a )/2 , k = [tex]\rm y_f[/tex]
h = (4 -4)/2 , k = 0
h=0 , k = 0
The vertex is 0 , 0
p = (|[tex]\rm x_f[/tex] - a|)/2 = 8/2 = 4
Therefore the equation of the graph is
y ² = 4 * 4 *x
y ² = 16x
The equation of the graph is y ² = 16x.
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The two-way frequency table below shows the preferred communication method of employees at a company
The percentage of employees with 8 or more years at the company reported that email is their preferred method of communication is 20.48%
Complete questionThe two-way frequency table below shows the preferred communication method of employees at a company, based on years of employment with the company.
See attachment
What percentage of employees with 8 or more years at the company reported that email is their preferred method of communication?
A. 44.79% B. 20.48% C. 48.84% D. 67.19%
How to determine the percentage of employee that prefers email?From the attached image, we have:
Email 8 or more = 43
The total number of employees in the company is
Total = 210
So, the percentage that prefers email is
Percentage = 43/210 * 100%
Evaluate
Percentage = 20.48%
Hence, the percentage of employees is 20.48%
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Solve the inequality W> Y+H /P
Answer: C
Step-by-step explanation:
Given the following inequality:
[tex]W& > \dfrac{Y + H}{P}[/tex]
Solve for H.
To solve for H we will start by multiplying both sides of the equation by P
[tex]PW& > \dfrac{Y + H}{P}\times P\\[0.3cm] PW& > Y + H\\[0.3cm][/tex]
Next, we will subtract Y from both sides of the inequality
[tex]\boxed{{WP - Y > H}}[/tex]
Therefore, the correct answer is C
HELPPPPPPPPP IMMEDIATELY
Answer:
4/8 = y/14
Step-by-step explanation:
These triangles are similar (see 1 sign of similarity of triangles)
Let's rotate the 2nd triangle, we'll see that the ratio of y to 14 is 4/8
The French club is sponsoring a bake sale to raise at least $305. How many pastries must they sell at $2.05 each in order to reach their goal?
Answer:
148.7804878
Step-by-step explanation:
All you have to do is divide!
Use the graphing calculator to graph the function f(x)=√x Which list contains three points that lie on the graph of
the function?
0(83) (42) (-11)
O (11 (42) (9. 3)
Answer:
The last option that starts with (1,-1)
Difference between 13.40 and 17.15
Answer:
3.75
Step-by-step explanation:
17.15-13.40=3.75
Answer:
3.75
Step-by-step explanation:
17.15- 13.40=3.75
William can pack 60 toys in 4 hours. Find the unit rate with which he packs toys.
O14 toys/hour
O13 toys/hour
15 toys/hour
16 toys/hour
Please help
(a) Write an equation for the volume V of the box in terms of x.
(b) Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process.
Answer:
V = 4*8
V= 32
(x+x) * (x+x) = 2x * 2x = 4x^2
In January, Bangkok is hotter than Cape Town while Cape Town is hotter than Moscow. Which inequality correctly compares the temperatures of the three cities?
Which Answer-
A.Bangkok's temperature < Cape Town's temperature < Moscow's temperature
B.
Bangkok's temperature < Moscow's temperature < Cape Town's temperature
C.
Bangkok's temperature > Moscow's temperature > Cape Town's temperature
D.
Bangkok's temperature > Cape Town's temperature > Moscow's temperature
The correct answer is option A which is A.Bangkok's temperature < Cape Town's temperature < Moscow's temperature.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
Given that:-
In January, Bangkok is hotter than Cape Town while Cape Town is hotter than Moscow.We have the data from the question that the temperature of Bangkok is hotter than cape town.
Bangkok > Cape town
And the temperature of Cape town is hotter than Moscow.
Cape town > Moscow
Now for both the statements, the inequality will be given as:-
Bangkok's temperature < Cape Town's temperature < Moscow's temperature.
Therefore the correct answer is option A which is A.Bangkok's temperature < Cape Town's temperature < Moscow's temperature.
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