Question:
Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26.
What is the solution set of this problem?
Answer:
[tex]x \leq -21[/tex]
Step-by-step explanation:
Given
Represent the number with x
So:
[tex]5 * (x + 27) \geq 6 * (x + 26)[/tex]
Required
Determine the solution set
[tex]5 * (x + 27) \geq 6 * (x + 26)[/tex]
Open Both Brackets
[tex]5 * x + 5 * 27 \geq 6 *x + 6 * 26[/tex]
[tex]5x + 135 \geq 6x + 156[/tex]
Collect Like Terms
[tex]5x - 6x \geq 156-135[/tex]
[tex]- x \geq 21[/tex]
Multiply both sides by -1
[tex]x \leq -21[/tex]
Hence, the solution set is [tex]x \leq -21[/tex]
Answer:
[tex]x\leq -21[/tex]
Step-by-step explanation:
Jeremy is painting his room over the
summer. Here are 4 different wall
colors and 3 different trim colors.
How many different ways can he
paint his room?
Answer:
Jeremy has 12 ways of painting his room.
He has 4 different wall colors and 3 different trim colors, so, if we want to know how many ways does he have to paint his room, we only need to multiply:
4 * 3 = 12
That's why he has 12 ways of painting his room. That's because for each of the 4 different wall colors, there are 3 trim colors he can use.
Answer: 12 different ways
Step-by-step explanation:
The question is asking for a combination of a wall color and a trim color because his room required one wall color and one trim color.
In this case, combination will be the number of first kind multiplies with the second kind. This is similar to sketching a tree diagram but instead, we will be using numerical method which will be quicker.
If you are still confused, I will provide some examples.
You have 5 kind of bread and 4 kind of toppings, there will be 20 different ways to buy a pair (5×4=20)You have 5 different shoes, 3 different laces, and 2 different tops, there will be 30 different ways to match (5×3×2=60)This also applies to your question. You have 4 different wall colors and 3 different trim colors.
4×3=12
You have 12 different ways to paint the room
Hope this helps!! :)
Please let me know if you have any question
Using the slope formula, find the slope of the line through the given points (3,3) and (1,1)
Answer:
1
Step-by-step explanation:
The slope formula is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] so when you plug in all of the numbers to where they are supposed to be you would get [tex]\frac{1-3}{1-3}[/tex] which is [tex]\frac{-2}{-2}[/tex] which can be simplified to [tex]\frac{1}{1}[/tex] which is just 1 and that would be our answer
A plant is 8 cm tall, and grows 3 cm taller each week. How tall will the plant be after 25
weeks?
Answer:
83 cm
Step-by-step explanation:
let's make an equation for this situation. The plant starts at 8 cm and grows 3 cm every week. If x represents time in weeks and y represents height in cm, then:
y = 8+3x
filling in 25 for x, we find that:
y = 8+75
y = 83 cm
Answer:83
Step-by-step explanation:
25 x 3 = 75
75 + 8 = 83
What is the DOMAIN of the following relation? {(-5,4), (-4,2), (0,2), (1,3), (2,4)}
Answer:
{-5, -4, 0, 1, 2}
Step-by-step explanation:
The domain is the inputs or the x values
{-5, -4, 0, 1, 2}
Answer:
See below.
Step-by-step explanation:
The domain of a relation is all of the x-coordinates.
So we have the relation:
{(-5,4), (-4,2), (0,2), (1,3), (2,4)}
This means that the domain will be the following values:
{(-5,4), (-4,2), (0,2), (1,3), (2,4)}
So, our domain is:
[tex]\{-5, -4, 0, 1, 2\}[/tex]
Note that the domain is in ascending order.
What is the distance traveled by a train moving at a rate of 45mph in t hours?
Answer:
45t = distance
Step-by-step explanation:
Distance = speed * time
Distance= 45 mph * t hours = 45t
Which of the statements about the following quadratic equation is true?
6x² – 8 = 4x2 + 7×
Answer:
Its a quadratic eqn with complex roots
Answer:
The answer is A on edunuity.
Step-by-step explanation:
PLEASE HELP ME ON THIS IT IS URGENT IT IS GEOMETRY ILL MARK U THE BRAINLIEST DONT WASTE ANSWERS
El operador de un elevador registro el numero de pisos que este subio y bajo en varias ocaciones para llegar a la planta baja hasta el piso 9 si en total se hicieron 5 movimientos 2 de bajada y 3 de subida que operacion podria indicar la cantidad de pisos que el elevador subio bajo en cada movimiento
Answer:
Supongo que en realidad dice
"... Para llegar de la planta baja hasta el piso 9..."
Ok, el elevador comienza en el piso 0, y llega hasta el piso 9 después de 5 movimientos.
De estos 5 movimientos, 3 suben (los podemos definir como positivos)
y 2 bajan (los escribimos como negativos).
Entonces, comienzo en 0.
0 + A + B + C - D - E = 9.
ahí dice que:
"desde el piso 0, tengo 3 subidas y dos bajadas de tal forma que el resultado final es el piso 9"
Una expresión algebraica matemática consta de variables y constantes junto con operaciones algebraicas. Al resolver problemas de palabras algebraicas, es necesario que los problemas se traduzcan con precisión en ecuaciones y se resuelvan correctamente.
Dado que:
Un operador quiere llegar al noveno piso superior desde la planta bajaEl número total de sus movimientos = 5 movimientosNúmero de movimientos hacia arriba = 3Número de movimientos hacia abajo = 2Para configurar una operación que indique el número de pisos que recorrió el ascensor con cada movimiento;
Vamos a considerar
el número de movimientos hacia arriba (es decir, elevado) será = (a)el número de movimientos hacia abajo (es decir, hacia abajo) para ser = (b)∴
Número de movimientos hacia arriba = 3 × a = 3aNúmero de movimientos hacia abajo = 2 × b = 2bAsí, la puesta a punto de la operación que indica el número de pisos que recorrió el ascensor con cada movimiento se puede deducir de la diferencia entre el movimiento de subida y bajada será igual a 9.
Por lo tanto, podemos concluir que la configuración de la operación es:
3a - 2b = 9
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Exponential functions help please
Answer:
8400/2 then simplify
Step-by-step explanation:
b) If a, b, c are three rational numbers where a =
a = 3
3,6 = and c =
olů
Verify: a + (b + c) = (a + b) + C
Step-by-step explanation:
a =
a = 3
3,6 = and c =
olů
what is this please write this clearly
plz, help ASAP!!! WILL MARK YOU BRAINLIEST IF UR ANSWER IS CORRECT QUESTION #5
Answer:
D.
Step-by-step explanation:
The domain remains the same [a, b) and the range is [mc + n,md + n).
Explain the difference between f(2) and f(x) = 2. Use a verbal explanation and create examples to make it very clear. Please help me out
Let x be a variable, and f(x) a function of that variable.
f(2) is a number ; it's the value of the function f(x) when x = 2, assuming that value exists.
f(x) = 2 is a statement ; it says there is some value of x for which the function returns a value of 2. Because it's a statement, it can be true or false.
Here's an example:
Define f(x) = sin(x). Then f(2) = sin(2) ≈ 0.909297.
If x is a real number, then the statement sin(x) = 2 is false, because -1 ≤ sin(x) ≤ 1 for all real x.
If we replace 2 with 1, on the other hand, we get
f(1) = sin(1) ≈ 0.84147
and
sin(x) = 1 ==> x = π/2 + 2nπ
where n is any integer. (So we're talking about numbers like π/2, -3π/2, 5π/2, -7π/2, and so on.) We're saying here that any real number x of the above form satisfies the equation and makes the statement true.
Please help!!!
A pairs of fair die is tossed. What is the probability of not setting a sum 13?
A. 0
B. 1
C. 2
D. 0.5
Answer:
Answer is A the highest number we can get is 12 so its potion A
The both highest numbers are 6 and, 6 6 +6 is 12 so its 0
What is the slope? Look at the chart listed ✨
Answer:
m = -8/3
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Step 1: Find 2 coordinates
(-70, 70)
(-10, -90)
Step 2: Find slope m
m = (-90 - 70)/(-10 + 70)
m = -160/60
m = -8/3
What subset of real numbers does 18.5 inches belong to?
Answer:
The correct answer is rational.
Step-by-step explanation:
The diameter of the tree belongs to the subset of rational numbers.
Natural numbers are the numbers 1, 2, 3 4, etc. Since 18.5 has a fractional/decimal component, it is not considered a natural number. Whole numbers include all of the natural numbers, as well as 0; therefore, 18.5 is not a whole number either.
Integers include all whole numbers as well as negative numbers, but the integer category still does not encompass numbers with a decimal component. For this reason, 18.5 is not an integer either.
Therefore, the only subset of numbers that 18.5 can fall under is rational numbers. A rational number is a number that can be represented as a fraction. 18.5 can be represented as 37/2 and is thus a rational number.
You can also refer to the infographic given in the question for further clarity on which subsets of numbers are more inclusive than others.
Hope this helps!
1. A man is paid $ 600 per week after a pay rise of 20 %. What was he paid before?
Answer:
y. 100
------ = -------
600. 120
120y= 60000
y = 60000÷ 120
= $500
What is the distance between the points (5, 1) and (-3, -5)?
2
2
10
4
Step-by-step explanation:
Hey, there!!
The given points are A(5,1) and B(-3,-5)
We have, distance formulae for AB is,
[tex]ab = \sqrt{ {(x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]
[tex]ab = \sqrt{( { - 3 - 5)}^{2} + ( { - 5 - 1)}^{2} } [/tex]
[tex]ab = \sqrt{( { - 8)}^{2} + ( { - 6)}^{2} } [/tex]
[tex]ab = \sqrt{64 + 36} [/tex]
[tex]ab = \sqrt{100} [/tex]
Therefore, the distance between AB points is 10 units.
Hope it helps...
The irrigation system for a farm sprays water in circular patterns. Each sprinkler is connected to a pipe in the center of a circle and rotates around that pipe. The largest sprinkler sprays water 20 feet. What is the circumference of the circle irrigated by this sprinkler?
Answer:
40 π ft or 125.6ft
Step-by-step explanation:
If the sprinkler can spray water 20 ft, that means the radius is 20 ft and to get the circumference we do 2 r π
or 2r*3.14
The answer is either 40 π ft
or 125.6ft
please help (20 points + brainlest)
Answer:
PT = 24
Step-by-step explanation:
PT = TQ
3x + 6 = 5x - 6
12 = 2x
x = 6
PT = 3(6) + 6
PT = 18 + 6
PT = 24
Answer:
24
Step-by-step explanation:
From the pic,PT=TQ
therefore,
3x+6=5x-6
5x-3x=6+6
2x=12
therefore, x=12/2
=6
therefore, PT=3×6+6
=24
Find the number of ways of arranging the letters of the word MOSHOESHOE, if the letter M must always begin a word
Answer:
7560.
Step-by-step explanation:
There are 9 letters after the M consisting of 3 O's, 2 H's, 2 H's and 2 E's.
So the number of ways is 9! / (3!*2!*2!*2!)
= 362880 / (6*2*2*2)
= 362880 / 48
= 7560.
The number of ways the word MOSHOESHOE can be rearranged, if the letter M must always begin a word is 75,600 ways
Given:
MOSHOESHOE
n = total number of letters = 10
a = number of times O appears = 3
b = number of times S appears = 2
c = number of times E appears = 2
d = number of times H appears = 2
number of ways the word can be rearranged if M must always begin a word
= n! / (a! b! c! d!)
= 10! / (3!, 2!, 2!, 2!)
= (10 × 9 × 8 × 7 × 6 × 5 × 4× 3 × 2 × 1) / (3 × 2 × 1, 2 × 1, 2 × 1, 2 × 1)
= 3,628,800 / (6 × 2 × 2 × 2)
= 3,628,800 / 48
= 75,600 ways
Therefore, the number of ways the word can be rearranged if M must always begin a word is 75,600 ways
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What is the common ratio of the geometric sequence below?
18, -6, 2. - ...
Answer:
C
Step-by-step explanation:
The solution is Option C
The common ratio of the geometric sequence is -1/3
What is Geometric Progression?
A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the geometric sequence be represented by A
Now , the value of A is
A = 18 , -6 , 2 , -2/3
Let the first term of the geometric sequence be = a₁
The value of a₁ = 18
Let the second term of the geometric sequence be = a₂
The value of a₂ = -6
And , the common ratio r is given by the formula
Common ratio r = second term / first term
Substituting the values in the equation , we get
Common ratio r = -6/18
On simplifying the equation , we get
Common ratio r = -1/3
Therefore , the ratio is -1/3
Hence , The common ratio of the geometric sequence is -1/3
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PLEASE HELP!! Stuart invested $800 in a computer and now makes $5 a page typing research
papers. Let x represent the number of pages Stuart has typed, and let y
represent his profit.
a. Write an equation for y in terms of x.
Answer:
y = 5x - 800
Step-by-step explanation:
If x represents the number of pages typed, 5x will represent how much money he earns from typing them, since he gets $5 per page.
Then, 800 needs to be subtracted from this because he spent $800 on the computer.
So, the equation will be y = 5x - 800 to represent his profit.
.
Given g(x)=-x-4, find g(5)
The required g(5) is -9.
Function g(x) = -x-4. g(5) to determine.
The function is a type of mathematical sting that contains an algebraic link.
Here. g(x) = -x-4
Put 5 in place of x.
g(5) = -5-4
g(5) = -9
Thus, g(5) is -9
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A map has a scale of 1:100,000 what is the map distance between two cities if the real distance was 20km
Step-by-step explanation:
I guess you mean 1cm:100000cm
Hence, for every 1 cm on the map 100000 cm is covered on the land.
Take the distance on the map for 20 km be x
Hence, 1:100000:: x: 2000000 cm
In order to solve this ratio, you must multiply the extremes and the moderates (nears).
Hence, 2000000×1=100000×x [1km=100000 cm]
Hence, 2000000= 100000x
Hence, x=2000000/100000 cm
Hence, x=20 cm
Hence, 20 cm on the map
NEED HELP ASAP
given m||n find the value of x
Answer:
x=15
Step-by-step explanation:
These are alternate exterior angles and alternate exterior angles are equal when the lines are parallel
6x+8 = 7x-7
Subtract 6x from each side
6x+8-6x = 7x-7-6x
8 = x-7
Add 7 to each side
8+7 =x
15=x
[tex]\huge\underline{\underline{\mathfrak{\red{A}\green{n}\pink{s}\orange{w}\blue{e}{r}}}}[/tex]
[tex]\boxed{x \:= \:15}[/tex]
Given that \tan\theta =\frac{12}{35}tanθ= 35 12 and that angle \thetaθ terminates in quadrant \text{III}III, then what is the value of \cos\thetacosθ?
Answer:
[tex]cos\theta = -\frac{12}{37}[/tex]
Step-by-step explanation:
Given
[tex]tan\theta = \frac{35}{12}[/tex]
Quadrant: 3rd
Required
Determine [tex]cos\theta[/tex]
This question will be solved using the Pythagoras theorem
[tex]Hyp^2 = Adj^2 + Opp^2[/tex]
The tangent of an angle is calculated as thus;
[tex]tan\theta = \frac{Opp}{Adj}[/tex]
Comparing
[tex]tan\theta = \frac{35}{12}[/tex] to [tex]tan\theta = \frac{Opp}{Adj}[/tex]
We can conclude that
[tex]Opp = 35[/tex] [tex]Adj = 12[/tex]
Substitute these values in the Pythagoras formula
[tex]Hyp^2 = 35^2 + 12^2[/tex]
[tex]Hyp^2 = 1225 + 144[/tex]
[tex]Hyp^2 = 1369[/tex]
Square root of both sides
[tex]Hyp = \sqrt{1369}[/tex]
[tex]Hyp = 37[/tex]
SInce [tex]\theta[/tex] is in the 3rd quadrant, then
[tex]cos\theta = -\frac{Adj}{Hyp}[/tex]
Where [tex]Adj = 12[/tex] and [tex]Hyp = 37[/tex]
[tex]cos\theta = -\frac{12}{37}[/tex]
please answer question with explanation
Answer:
Domain: [tex]\{x|x\in\mathbb{R}\}[/tex]
Range: [tex]\{y|y\in\mathbb{R},y\leq -2\}[/tex]
Step-by-step explanation:
The domain is the span of x-values the graph covers.
The range is the span of y-values the graph covers.
The given graph is a quadratic. We can see that the x-values will extend infinitely in both directions.
Thus, the domain is all real numbers.
In set notation, this is:
[tex]\{x|x\in\mathbb{R}\}[/tex]
From the graph, we can see that the maximum value is y=-2. The graph won't ever go above this.
So, the range is all real numbers less than or equal to -2.
In interval notation, this is:
[tex]\{y|y\in\mathbb{R},y\leq -2\}[/tex]
And we are done :)
Mr. Molesky observes a group of monkeys for 24 hours to learn about their behavior. He records how long they slept (in hours), how many bananas they ate, key
Answer:
Explained below.
Step-by-step explanation:
The complete question is:
Mr. Molesky observes a group of monkeys for 24 hours to learn about their behavior. He records how long they slept (in hours), how many bananas they ate, gender, age (in years), and the specific breed of monkey.
(a) What are the individuals in this data set?
(b) Identify the variables that were recorded, and indicate whether each one is categorical or quantitative?
Solution:
(a)
The term "individuals", in statistics, implies or denotes the objects or people included in a statistical study.
In this case it is provided that Mr. Molesky observes a group of monkeys for 24 hours to learn about their behavior.
So, the "individuals" in this data set are the monkeys.
(b)
Categorical variables belong to a certain category or label values. Such as gender of a person, state from which a person is from, color of the marble and so on.
Quantitative variables are those variables that assume numerical values and represent some sort of measurement. Such as height, weight, annual income of the people working at the same place and so on.
In this case the variables are:
Number of bananas the monkeys ate - Quantitative variable
Gender - Categorical variable
Age (in years) - Quantitative variable
Specific breed of monkey - Categorical variable
The individuals in the data set refers to each monkey used in the experiment.
The variables in the experiment include :
Number of bananas = QUANTITATIVE (DISCRETE) gender = QUALITATIVE (MALE OR FEMALE) Age (in years) = QUANTITATIVE (discrete) and the specific breed of monkey = QUALITATIVE.Individuals used in a research refers to each species or subject used in the research finding.
QUALITATIVE or categorical variables are used as labels rather than numerical values. They include gender, colors , and so on. QUANTITATIVE variables involves numerical variables upon which basic mathematical operations may be performed.DISCRETE variables involves variables whose values or numbers can be obtained by counting.while
CONTINUOUS variables include variable measure are obtained by measurement such as height and weight.
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Complete question :
Mr. Molesky observes a group of monkeys for 24 hours to learn about
their behavior. He records how long they slept (in hours), how many bananas they ate, gender, age (in years), and the specific breed of monkey.
(a) What are the individuals in this data set?
(b) Identify the variables that were recorded, and indicate whether each one is categorical or quantitative(continuous), or quantitative(discrete), make sure tell me which one is continuous and which one is discrete
let's f (x)= 3x - 7 find F (a + 2)
Answer:
3a-1
Step-by-step explanation:
Substitute
3(a+2)-7
Distribute
3a+6-7
Simplify
3a-1
Answer:
Hope it can help you and please mark me as a brainlist...
round three significant figures 12.3456
Answer:
12.3
Step-by-step explanation:
Round it where you have 3 numbers that are not 0.
12.3456
round to the hundredths place
12.34 (round to 4)
12.3 (3 sigfigs)
Answer:
12.4
Step-by-step explanation:
12.3456
first you would round the 5 to a 6, the round the 4 to a 5, because the six is greater than five, than you would change the 3 to a 4, because the four that was changed to a five now is big enough to change the number.