So if you let x and y be the two numbers...
the sum of the two means you add them together... so you get:
x+y=56: the difference means you subtract them.. so
x-y = 16
now you have two equations and two unknowns... which you can solve with various methods... you can use elimination, substitution, or trial and error.
x+y=56
x-y = 16
I will use the elimination method: Because there is a plus y and a negative you cancel that out and add the 2x's. Therefore:
2x=72
x=36
Now, you can plug 36 into one of your original equations:
36+y=56
y=20
Those are your two numbers!
Cada año escolar, los estudiantes de 7º grado que estudian Ciencias de la Vida participan en una excursión especial al zoológico de la ciudad. En 2010, la escuela pagó $1260 para que 84 estudiantes ingresaran al zoológico. En 2011, la escuela pagó $1,050 para que 70 estudiantes ingresaran al zoológico. En 2012, la escuela pagó $1,395 para que 93 estudiantes ingresaran al zoológico. ¿El precio que paga la escuela cada año en derechos de ingreso es proporcional al número de estudiantes que ingresan a la escuela? una. ¿Zoo? b. Explica por qué o por qué no. C. Identifique la constante de proporcionalidad y explique lo que significa en el contexto de esta situación. d. ¿Cuánto pagaría la escuela si 120 estudiantes entraran al zoológico? ¿Cuántos estudiantes entrarían al zoológico si la escuela pagara $1,425? mi‘Doy una corona y 5 corazones de branly
a) El coste total es directamente proporcional al número de estudiantes.
b) Existe una relación directa entre el coste total y el número de estudiantes al existir una constante de proporcionalidad.
c) La constante de proporcionalidad tiene un valor de 15 y representa el precio de ingreso de cada estudiante al zoológico.
d) El coste total por 120 estudiantes es $ 1,800. 95 estudiantes cuestan $ 1,425.
Cómo analizar relaciones de proporcionalidad directa entre dos variables
a) Sea y el coste total pagado para una excursión en el zoológico de la ciudad, en pesos, y x el número de estudiantes que visita el zoológico. Existe una relación directa entre las dos variables si la siguiente expresión es satisfecha:
y = k · x
Donde k es la constante de proporcionalidad, en pesos por estudiante.
A continuación, comprobamos si la relación de proporcionalidad directa existe:
Año 2.010
k₁ = 1260 / 84
k₁ = 15
Año 2.011
k₂ = 1050 / 70
k₂ = 15
Año 2.012
k₃ = 1395 / 93
k₃ = 15
Puesto que k₁ = k₂ = k₃, el coste total es directamente proporcional al número de estudiantes.
b) Existe un relación de proporcionalidad directa debido a la existencia una única constante de proporcionalidad.
c) La constante de proporcionalidad es igual a 15 y representa el costo por estudiante.
d) Si sabemos que y = 15 · x y x = 120, entonces el coste total es:
y = 15 · 120
y = 1800
El coste total es de $ 1,800.
Ahora, si sabemos que y = 15 · x, y = 1,425, entonces el número de estudiantes que ingresan es:
1,425 = 15 · x
x = 1,425 / 15
x = 95
95 estudiantes tienen un coste total de $ 1,425.
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The tape diagram represents the ratio of your monthly allowance to your friend's monthly allowance. The monthly allowances total $63. How much is each allowance?
The difference between your monthly allowance and your friend's monthly allowance. The monthly allowance for you and your friends is $35 and $28.
Given that,
The tape diagram illustrates the difference between your monthly allowance and your friend's monthly allowance. The entire monthly allowance is $63.
We have to find what does each allowance cost.
The 9 parts represent $63 so each part represent
$63/9
7
Then,
The monthly allowance is
$7×5=$35
The monthly allowance for your friends is
$7×4=$28
Therefore, The monthly allowance for you and your friends is $35 and $28.
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write the new coordinates after the triangle is rotated 180 degrees counterclockwise about the origin.
For the new coordinates of point A, that is A' = (x', y'), we have:
x' = 2 . cos (180º) = 2 . (-1) = -2
y' = 10 . cos (180º) = -10
The same happens to the other points. So, for B we have :
x' = 3 . (-1) = -3
y' = -4 . (-1) = 4
And for C:
x' = -3 . (-1) = 3
y' = 1 . (-1) = -1
Therefore, the new coordinates will be:
A'(-2, -10)
B'(-3, 4)
C'(3, -1)
A 25,000 swimming pool is being filled.Two hundred and fifty gallons are in it after 30 minutes. How many hours will it take to fill the pool?
Answer:
100????
Step-by-step explanation:
A bumble bee flutters its wings 7,800 times in one minute. A hummingbird flutters its wings 80 times in 1 second which animal flutters its wing more times 1 minute explain
Answer:
Step-by-step explanation:
the bumble bee flutters it’s wings 3000 times faster
Knowing that the bumble be can do 7800 in one minute and the humming bird can do 80 in a second 1 minute is 80 seconds so if we do 80 times 60 we get 4800 which is less then the amount of flutters the bumble bee does by 3000 flutters
The area of the Mojave desert is 25000 square miles.
A scale drawing of the Mojave desert has an area of 10 square inches.
What is the scale of the map?
I need someone to explain me how to get the answer of this problem. Btw I am in seventh grade
Based on the area of the Mojave desert and the area of the scale drawing, the scale of the map is 1 square inches : 2,500 square miles.
How to find the scale of a map?The scale of a map is used to find out how the distance on the map relates to the distance on the ground. It is usually shown as a ratio.
The fact that the area of the Mojave desert is 25,000 square miles but only 10 square inches on the scale drawing means that every 10 square inches on the map is equal to 25,000 actual square miles.
The scale is:
10 square inches : 25,000 square miles
In its simplest form, this is:
10 / 10 square inches : 25,000 / 10 square miles
1 square inch : 2,500 square miles
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This is urgent I’ll brainlist u !!!!
Answer:
Q9:D
Q10:B
Step-by-step explanation:
Q9:for two graphs to be perpendicular, the product of their gradients has to be -1
multiplying the gradients of the equation in the question and the equation in option "D", we get -1 hence D is correct
I need this solved with work shown.
Base = 17 inches
Height = 12 inches
In the given figure, the shaded region is a triangle,
So, Area of a Triangle = 1/2 x base x Height
⇒ Area of a Triangle = 1/2 x 17 x 12
⇒ Area of a Triangle = 17 x 6
⇒ Area of a Triangle = 102 square inches.
What is a Triangle?Having three straight sides and three angles, a triangle is a flat figure.In Euclidean space, the total of a triangle's internal angles is always 180 degrees. The parallel postulate of Euclid is comparable to this fact. By using the measurements of the first two angles, it is possible to calculate the size of the third angle in any triangle. An angle that is a linear pair (and thus supplementary) to an interior angle is the outside angle of a triangle. The exterior angle theorem states that the measures of two inner angles that are not contiguous to each other add up to the measure of an exterior angle of a triangle. Any triangle's three outside angles, one for each vertex, add up to a total of 360 degrees.To learn more about Triangles, refer to:
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6x + 1 = -6(1-x)
Solve for x
The value of x is 5 / 12.
How to solve for the value of x ?The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.
Thus to solve for x you simply have to keep the like terms one side and the others on the other side .
The given equation is : 6x + 1 = -6 ( 1 - x)
6x + 1 = -6x + 6
12x = 5
x = 5 / 12
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Kim needs 10 cups of apple juice for a recipe. How many quarts does she need? 2 cups (c) =1 pint (pt) 2 pt =1 quart (qt) 4 qt =1 gallon (gal)
Answer: 2 quarts 1 pint
Step-by-step explanation: Kim needs 10 cups of apple juice 2 cups are 1 pint so that makes it already 5 pints so now we need to turn the 5 pints into quarts so 2 quarts is what we have but we have some left over we have 1 pint left so we have 2 quarts and 1 pint, we could always convert the pint into a fraction depends on how or what way your teacher wants it wrote
According to a study by nielsen mobile, "teenagers ages 13 to 17 are by far the most prolific texters, sending 1742 messages a month." mr. williams, a high school statistics teacher , was skeptical about the claims in the article. so he col lected data from his first-period statistics class on the number of text messages they had sent in the past 24 hours. here are the data:
The box-and-whisker plot that correctly summarizes the data is given at the end of the answer.
What does a box-and-whisker plot shows?A box and whisker plot shows five things of a data-set:
The minimum value of the data-set.The 25th percentile, which is the median of the bottom 50% of the data-set.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50% of the data-set.The 75th percentile, which is the median of the upper 50% of the data-set.The maximum value of the data-set.The ordered data-set in this problem is as follows:
0, 0, 0, 1, 1, 3, 3, 5, 5, 7, 8, 8, 9, 14, 25, 25, 26, 29, 42, 44, 52, 72, 92, 98, 118.
The data-set has 25 elements, in which:
The minimum element is of 0.The first quartile is the median of the first 12 elements, which is of Q1 = 3.The median is the 13th element, which is of 9.The third quartile is the median of the last 12 elements, which is of Q3 = 3.The maximum element that is not an outlier is of 98.What is the missing information?The data is missing, and is given as follows:
0, 0, 0, 1, 1, 3, 3, 5, 5, 7, 8, 8, 9, 14, 25, 25, 26, 29, 42, 44, 52, 72, 92, 98, 118.
The problem asks for the box plot that represents the situation.
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What is the answer to this question
-1=5+x/6
Answer: x = -24
#middleschool
Please answer as soon as you can.
Answer:
x > -4
Step-by-step explanation:
Please heart!
The relative growth rate r of a function f measures the change in the function compared to its value at a particular point. It is computed as r(t)=
f′(t)
f(t). A logistic growth model for a certain population with a base population of 6 individuals, carrying capacity of 15 individuals, and a base growth rate of 0.025 is shown below. Complete parts (a) through (c).
P(t)=
90
6+9e−0.025t
Question content area bottom
Part 1
a. Is the relative growth in 1999 (t=0) for the logistic model of the above population equal to r(0)=
P′(0)
P(0)=0.013 (rounding to three decimal places)? This would mean that the population was growing at 1.3% per year.
Yes
Yes
No
No
Your answer is correct.
Part 2
b. Compute the relative growth rate of the population in 2005 and 2020. What appears to be happening to the relative growth rates as time increases?
r(6)=enter your response here
r(21)=enter your response here
(Round to four decimal places as needed.)
Answer: 2
Step-by-step explanation: If you add the chetes value of 6 x6 x88 v6
Choose the equation that represents a line that passes through points (-1,2) and (3,1) . How do I solve?!
The required equation is x+4y-9 = 0.
What is an equation?
Algebra is concerned with two types of equations: polynomial equations and the particular case of linear equations. Polynomial equations have the form P(x) = 0, where P is a polynomial, while linear equations have the form ax + b = 0, where a and b are parameters, when there is only one variable. To solve equations from either family, algorithmic or geometric approaches derived from linear algebra or mathematical analysis are used. Algebra also investigates Diophantine equations with integer coefficients and solutions. The approaches employed are unique and derive from number theory. In general, these equations are complex; one frequently searches just for the existence or lack of a solution, and, if they exist, the number of solutions.
The equation is formed below
(y-2) = {(1-2)/(3+1)} (x+1)
or, y-2 = - 1/4 (x+1)
or, 4(y-2) = -1(x+1)
or, 4y - 8 = 1 - x
or, x+4y-9 = 0
Hence, the required equation is x+4y-9 = 0.
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To make a smoothie you use 12 cup of yogurt for every 34 cup of fruit. what is the constant of proportionality that relates y, the number of cups of fruit needed to x, the number of cups of yogurt needed to make a smoothie?
The constant of proportionality for the smoothie is 0.353.
What is constant of proportionality?It should be noted that the constant of proportionality shows the proportional relationship between the variables that are given.
In this case, to make a smoothie you use 12 cup of yogurt for every 34 cup of fruit, the constant of proportionality will be:
y = kx
where y = number of cups of fruit needed
x= number of cups of yogurt needed to make a smoothie.
This will be:
y = kx
12 = 34k
Divide through by 34
k = 12/34
k = 0.353
The constant is 0.353
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graph the line through (1,0) with m=0
The equation of the line passing through the point (1,0) with slope 0 is
y = 0
The line passing through the point (1,0)
The slope of the given line is m = 0
So, let us write the equation of the line using slope-point form
y = mx + b
where m is the slope
(x,y) is the point passing by the line
b is the intercept
So , now let us substitute the known values in the above equation
0 = 0(1) + b
b = 0
Therefore , the intercept of the given line is b = 0.
Thus , the equation of the line can be written as
y = mx + b
where m = 0 and b = 0
y = 0x + 0
y = 0
Therefore , the equation of the given is y = 0 which is a origin
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8-If-5(2x - 5) = 6x + 3, what is the value
of x?
Answer:
x=7
Step-by-step explanation:
5(2x-5) = 10x-25
1) add 25 to both sides
10x+25=10x 6x+3+25=6x+28
10x=6x+28
2) subtract 6x from both sides
10x-6x=4x 6x+28-6x=28
4x=28
3) divide by 4 from both sides
4x/4=x 28/4=7
x=7
Hope this helps, have a great day!!
The value of y in the expression -5(2x - 5) = 6x + 3 is 22/16
According to the given question
We have an equation in one variable
⇒ -5(2x - 5) = 6x + 3
For finding the value of x solve the above equation by adding and subtracting the like terms.
So, -5(2x - 5) = 6x + 3
⇒ -5 x 2x + 5 x 5 = 6x + 3
⇒ -10x + 25 = 6x + 3
⇒ 25 - 3 = 6x + 10x
⇒ 22 = 16x
⇒ x = 22/16
Hence, the value of y in the expression -5(2x - 5) = 6x + 3 is 22/16
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EASY + URGENT !! WILL REWARD WITH THANKS + BRAINLIEST
(a) The area of triangle F is 4 times the area of triangle G.
(b) The area of triangle B is 1/4 times the area of triangle G.
(c) The area of triangle F is 16 times the area of triangle B.
(d) The area of triangle H is 1/9 times the area of triangle F.
(e) The area of triangle H is 4/9 times the area of triangle G.
(f) The area of triangle B is 9/16 times the area of triangle H.
(a) Triangle G and Triangle F
Consider triangle F,
The height of the triangle is 8.
The base of the triangle is 6.
The hypotenuse of the triangle is 10.
Area of ΔF = ( 1/2 ) × b × h = ( 1/2 ) × 6 × 8 = 24 square units.
Consider triangle G,
The height of the triangle is 4.
The base of the triangle is 3.
The hypotenuse of the triangle is 5.
Area of ΔG = ( 1/2 ) × b × h = ( 1/2 ) × 3 × 4 = 6 square units.
Therefore,
Area of ΔF = 4 × Area of ΔG
(b) Triangle G and Triangle B
Consider triangle G,
The area of the triangle is:
Area of ΔG = ( 1/2 ) × b × h = ( 1/2 ) × 3 × 4 = 6 square units.
Consider triangle B,
The height of the triangle is 2.
The base of the triangle is 3/2.
The hypotenuse of the triangle is 5/2.
Area of ΔB = ( 1/2 ) × b × h = ( 1/2 ) × 3/2 × 2 = 3/2 square units.
Now, 4 × 3/2 = 6
Therefore,
Area of ΔG = 4 × Area of ΔB
Area of ΔB = 1/4 × Area of ΔG
(c) Triangle B and Triangle F
Consider triangle B,
Area of ΔB = ( 1/2 ) × b × h = ( 1/2 ) × 3/2 × 2 = 3/2 square units.
Consider triangle F,
Area of ΔF = ( 1/2 ) × b × h = ( 1/2 ) × 6 × 8 = 24 square units.
Now, 16 × 3/2 = 24
Therefore,
Area of ΔF = 16 × Area of ΔB
(d) Triangle F and Triangle H
Consider triangle F,
Area of ΔF = ( 1/2 ) × b × h = ( 1/2 ) × 6 × 8 = 24 square units.
Consider triangle H,
The height of the triangle is 8/3.
The base of the triangle is 2.
The hypotenuse of the triangle is 10/3.
Area of ΔH = ( 1/2 ) × b × h = ( 1/2 ) × 2 × 8/3 = 8/3 square units.
Now, 9 × 8/3 = 24
Therefore,
Area of ΔF = 9 × Area of ΔH
Area of ΔH = 1/9 × Area of ΔF
(e) Triangle G and Triangle H
Consider triangle G,
Area of ΔG = ( 1/2 ) × b × h = ( 1/2 ) × 3 × 4 = 6 square units
Consider triangle H,
Area of ΔH = ( 1/2 ) × b × h = ( 1/2 ) × 2 × 8/3 = 8/3 square units.
Now,
9/4 × 8/3 = 6
Therefore,
Area of ΔG = 9/4 × Area of ΔH
Area of ΔH = 4/9 × Area of ΔG
(f) Triangle H and Triangle B
Consider triangle H,
Area of ΔH = ( 1/2 ) × b × h = ( 1/2 ) × 2 × 8/3 = 8/3 square units
Consider triangle B,
Area of ΔB = ( 1/2 ) × b × h = ( 1/2 ) × 3/2 × 2 = 3/2 square units
Now,
16/9 × 3/2 = 8/3
Therefore,
Area of ΔH = 16/9 × Area of ΔB
Area of ΔB = 9/16 × Area of ΔH
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Simplify the radical expression.
-2√250
-10√10
3√10
-2√25
-2√125
Answer:
Step-by-step explanation:
Factorise x^2 + 5x + 6
For the given equation, the values of x are -3 and -2.
What does a math factorization mean?The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.
N = Xa Yb Zc is how the general factorization formula is written. The exponential powers of the factors of a factorized number are shown here by the letters a, b, and c.
Given,
x^2 + 5x + 6
⇒ x^2 + 3x + 2x + 6
⇒ x (x + 3) + 2 (x + 3)
⇒ (x + 3) (x + 2)
⇒ x = -3, x = -2
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The average male burns about 100 calories per mile walked and 140
calories per mile jogged. Using x to represent the miles walked and
to represent the miles jogged, write a linear inequality modeling the
number of miles a man should walk and jog in order to burn at least 500
calories.
The required linear equation is 100x + 140 y = 500.
What is a linear equation?If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.
Therefore, a linear equation in two variables is any equation that can be written in the form ax + by + c = 0, where a, b, and c are real values, and a and b are not equal to zero. This implies that you can come up with a ton of these equations. Solution: It is possible to write 2x + 3y = 4.37 as 2x + 3y - 4.37 = 0.
Let the miles walked be represented by x
and the y would represent miles jogged
Thus the equation would become :
100 x + 140 y = 500
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Find the area and perimeter of each polygon. Show your work
Given
To find: The area and the perimeter of the given polygon.
Explanation:
It is given that,
The perimeter of the polygon (rectangle) is,
[tex]\begin{gathered} P=2(l+b) \\ =2(14+5) \\ =2\times19 \\ =38mm \end{gathered}[/tex]The area of the polygon is,
[tex]\begin{gathered} A=l\times b \\ =14\times5 \\ =70mm^2 \end{gathered}[/tex]Hence, the area of the polygon is 70mm² and the perimeter of the polygon is 38mm.
What does the constant 0.15 reveal about the rate of change of the quantity?
The function is decaying exponentially at a rate of 85% every year
Explanation:0.15 is less than 1. This represents decay
Decay rate is 1 - 0.15 = 0.85 = 0.85*100 = 85%
t is given in years
Exponent is t, so it is every year.
The function is decaying exponentially at a rate of 85% every year
question 4 (10 points)
The slope of the table is 3.
In this question, we have been given a table.
We need to find the slope of the table.
For aby two points (x1, y1) and (x2, y2), we use the formula of slope,
m = (y2 - y1) / (x2 - x1)
m1 = (15 - 30) / (-5 - 0)
m1 = (-15) / (-5)
m1 = 3
For a pair of points (-5, 15) and (10, 60)
m2 = (60 - 15) / (10 + 5)
m2 = 45 / 15
m2 = 3
For a pair of points (10, 60) and (5, 45)
m3 = (45 - 60) / (5 - 10)
m3 = -15 / -5
m3 = 3
Therefore, the slope of the table is 3.
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Estimate the sum to the nearest tenth:
(-2.678) + 4.5 + (-0.68)
A. -1.1
B. 1.1
C. 1.9
D. 2.1
What is the actual sum?
A. -3.354
B. -2.502
C. 1.142
D. 6.498
The nearest tenth is option(B.) and actual sum is option(C.)
Define BODMAS
BODMAS is an acronym to remember the order of mathematical operations – the correct order in which to solve maths problems. Bodmas stands for
B-Brackets,
O-Orders (powers/indices or roots),
D-Division,
M-Multiplication,
A-Addition,
S-Subtraction.
Solve the given expression,
(-2.678) + 4.5 + (-0.68)
Follow the Bodmas rule, to solve the given expression.
First, open the brackets,
-2.678 + 4.5 - 0.68
Now, put together -ve terms
-2.678 - 0.68 + 4.5
Add the -ve terms, we get
-3.358 + 4.5
Now subtract this, we get
1.142 or 1.1 (round to nearest tenth)
Hence, the nearest tenth is option(B.) i.e, 1.1 and actual sum is option(C.) i.e, 1.142
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It's an rsm problem I really need help
The simplified expression in the question is x^4y^4
Simplification of ExpressionSimplification of an algebraic expression can be defined as the process of writing an expression in the most efficient and compact form without affecting the value of the original expression. The process entails collecting like terms, which implies adding or subtracting terms in an expression.
In the given expression, x^2y * (-xy) * (-xy^2)
Let's solve this algebraic expression and determine the value;
[tex]x^2y*(-xy)*(-xy^2) = [x^2*(-x)*(-x)] * [y * y * y^2] = x^4y^4[/tex]
The expression is x^4y^4
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The diagram shows a right-angled triangle.
x +4
x-2
All the measurements are in centimetres.
The area of the triangle is 27.5 cm²
Work out the length of the shortest side of the triangle.
You must show all your working.
Shortest side of a triangle is x - 2 = 7 - 2 = 5cm.
Given,
Triangle is a Right - angled triangle
Base of triangle is = x + 4
Height of triangle is = x -2
The area of the triangle is 27.5 cm²
To find the length of the shortest side of the triangle.
Now, According to the question:
We know that
Area of triangle is = 1/2 x base x height
Put the values of base and height in above formula
27.5 = 1/2 × (x + 4) × (x - 2)
27.5 × 2 = x (x - 2) + 4(x -2 )
55 = [tex]x^{2} + 4x - 2x - 8[/tex]
[tex]x^{2}[/tex] + 2x - 63 = 0
[tex]x^{2}[/tex] + 9x - 7x - 63 =0
x (x + 9) -7 (x + 9) =0
x = -9 or x = 7
Hence, Shortest side of a triangle is x - 2 = 7 - 2 = 5cm.
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if 12 people are called for jury duty, what is the probability that all 12 will be available to serve on the jury? (round your answer to three decimal places.)
Label the four quadrants on this graph
Answer:
Top Left - 2
Top Right - 1
Bottom Left - 3
Botton Right - 4
Step-by-step explanation:
