Realice los siguientes ejercicios de lenguaje algebraico
Considerando que Soraya tiene x naranjas
Considerando que y es la edad de José.
Las expresiones algebraicas que completan la tabla son 200+x, 2(200+x), 650+ 2(200+x), y -5, y+ 10, y+8, 75- y
¿Qué es el lenguage algebraico?El lenguaje algebraico es simbólico es decir se expresa mediante consonantes o vocales, el lenguaje algebraico nos permite expresar de manera sencilla y practica el valor desconocido de una determinada cantidad.
¿Cómo se expresan los enunciados dados?A partir de la información dada es decir "x" naranjas y "Y" que es la edad de José vamos a expresar las respuestas en lenguaje algebraico. Para esto se debe relacionar la x o y con el valor dado y el signo matemático correspondiente:
Luis tiene 200 naranjas mas que Soraya = 200+x
Susana tiene el doble de Luis = 2(200+x)
Juan tiene 650 naranjas mas que susana = 650+ 2(200+x)
Considerando que Y es la edad de José
Los años que tenia hace 5 años = y -5
Los años que tendrá en 10 años = y+ 10
Los años que tendrá dentro de 8 años = y+8
Los años que faltan para que cumpla 75 años = 75- y
Podemos concluir que el lenguaje algebraico nos permite representar de manera practica un valor desconocido y de igual manera obtener respuestas practicas y sencillas a partir de variables.
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Three out of nine students passed the SHSAT test. What is the decimal equivalent of students who passed the test?
Ans :
Hence, the decimal equivalent of students who passed the test is [tex]0.33[/tex].
What is the decimal values?
Decimals are a set of numbers lying between integers on a number line.
Here given that,
Three out of nine students passed the SHSAT test.
So,
[tex]\frac{3}{9}=0.33[/tex]
Hence, the decimal equivalent of students who passed the test is [tex]0.33[/tex].
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The selling price for a classic speedboat is $12,000, which is $2500 less than two times its original price. What was the original price of the speedboat?
Answer: 29000
Step-by-step explanation:
12000 + 2500 = 14500
14500 * 2 = 29000
At a local gas station there are two different plans for car washes. Customers can either pay $12 per wash or pay $16 for a discount card that lowers the cost to $8 per wash. Write and solve an equation to find the number of car washes for which the cost of each plan is the same.
1. An equation that finds the number of car washes for which the costs of Plan A and Plan B are the same is 12n = 16 + 8n.
2. The solution of the equation shows that the number of car washes for which the cost of each plan is the same is 4.
What are equations?Equations are mathematical statements claiming that two or more mathematical expressions are equal or equivalent when solved.
Equations use numbers, constants, variables, and the equation symbol (=) to depict the equality of the mathematical expressions.
Plan A Plan B
Cost per cash wash $12 $8
Fixed cost $0 $16
Mathematical Expressions for the Carwash Plans:
Let Plan A = 0 + 12n
Let Plan B = 16 + 8n
The number of car washes when the two plans' costs are equal can be derived by equating the two mathematical expressions above:
12n = 16 + 8n
12n - 8n = 16
4n = 16
n = 4
= 4 car washes
Check:
Plan A = 0 + 12n
= 12(4)
= 48
= $48
Plan B = 16 + 8n
= 16 + 8(4)
= 16 + 32
= 48
= $48
Thus, solving the equation, we can conclude that choosing Plan B will take 4 car washes to equal the cost of Plan A.
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Lianne has some dimes and nickels with a total value of $4.60. The number of dimes she has is 4 more than 3 times the number of nickels. How many nickels does she have?
I need the equation to solve this problem thanks
If Lianne has some dimes and nickels with a total value of $4.60. The number of dimes she has is 4 more than 3 times the number of nickels then 0.15 Nickels does Lianne has.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Lianne has some dimes and nickels with a total value of $4.60.
The number of dimes she has is 4 more than 3 times the number of nickels.
We need to find number of nickels
From the given information
N+D=4.60
D=3N+4
N+3N+4=4.60
4N=4.60-4
4N=0.6
Divide both sides by 4
N=0.15
Hence, 0.15 Nickels does Lianne has.
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The radius of a cone is 2.5 units. The volume of the cone is 19 cubic units
The formula for the volume of a cone is given by the following equation:
V = 1/3 * π * r2 * h
where V is the volume of the cone, r is the radius of the cone, and h is the height of the cone.
In this case, we are given that the radius of the cone is 2.5 units and the volume of the cone is 19 cubic units. We can use this information to complete the expression that represents the height of the cone as follows:
V = 1/3 * π * r2 * h
19 cubic units = 1/3 * π * 2.5 units2 * h
19 cubic units = 1/3 * π * 6.25 units2 * h
19 cubic units = 1/3 * 19.63 units2 * h
19 cubic units = 6.54 units2 * h
h = 19 cubic units / 6.54 units2
h = 2.9 cubic units / 6.54 units
Therefore, the expression that represents the height of the cone is 2.9 cubic units / 6.54 units.
Owen went to Best Buy to purchase a new laptop. He put a down payment of $200 and will pay $75 each month until he pays it off. Use the
formula p= 200 + 75c to identify which statement below is false.
The ‘p’ is represented as the dependent variable
The ‘c’ represents the number of months
The independent variable is 75
The ‘c’ is represented as the independent variable
Owen went to Best Buy to purchase a new laptop. He put a down payment of $200 and will pay $75 each month until he pays it off. Use the
formula p= 200 + 75c to identify which statement below is false.
The ‘p’ is represented as the dependent variable [true]
The ‘c’ represents the number of months [true]
The independent variable is 75 [FALSE]
The ‘c’ is represented as the independent variable [true]
Evaluate
15 ÷ (3+1/3) ²
Answer:
[tex]\dfrac{27}{20}[/tex]
Step-by-step explanation:
First, convert both numbers into fractions:
[tex]\dfrac{15}{1} \div \left(\dfrac{10}{3}\right)^2[/tex]
Then, apply the exponent of the second fraction in parentheses to its numerator and denominator.
[tex]\dfrac{15}{1} \div \left(\dfrac{10^2}{3^2}\right)[/tex]
[tex]\dfrac{15}{1} \div \dfrac{100}{9}[/tex]
Finally, multiply the first fraction by the reciprocal of the second fraction.
(Skip, Flip, Multiply)
[tex]\dfrac{15}{1} \times \dfrac{9}{100}[/tex]
[tex]\dfrac{135}{100}[/tex]
And simplify.
[tex]\dfrac{135 \div 5}{100 \div 5}[/tex]
[tex]\dfrac{27}{20}[/tex]
Rewrite in simplest terms:
−
6
(
6
p
−
9
)
−
10
p
−6(6p−9)−10p
Answer:
Step-by-step explanation:
6(6p-9)-10p-6(6p-9)-10p
36p-54-10p-36p+54-10p
36p-36p-54+54-10p= -10p
f(x)=1/2x+8 reflect x axis
The function of reflect x-axis is g(x) = -(1/2)*x - 8, according to the question.
What do you mean by function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
According to the given question,
First, let's define a reflection over the x-axis.
If we have a point (x, y) and we reflect it over the x-axis, our new point will be (x, -y).
Now, when we have a function
f(x) = y, the points can be written as:
(x, y = f(x) ) = (x, f(x))
Then, after the reflection over the x-axis, we have:
(x, y = g(x)) = (x, -f(x))
So now we have g(x) = -f(x)
and we know that f(x) = (1/2)*x + 8
then our new function is g(x) = y = -f(x) = -( (1/2)*x + 8) = -(1/2)*x - 8.
g(x) = -(1/2)*x - 8.
Therefore, the required answer is g(x) = -(1/2)*x - 8.
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what is [tex]\sqrt{49}[/tex]
Answer:7
Step-by-step explanation:
What it is asking you is what multiplied by it self gets you to 49. the answer would be 7 because 7*7=49
Sebastian and zoey had 3068 buttons in all. Sebastian and Valeria had 2103 button in all. Valeria has half as many buttons as zoey.how many buttons do they have in all.
The total number of buttons they have is 4033.
What is a system of equations?A system having more than two equations is known as a system of equations.
Given that, Sebastian and Zoey had 3068 buttons, Sebastian and Valeria had 2103 buttons, and Valeria has half as many buttons as Zoey.
The equations corresponding to the statements are:
S + Z = 3068 (1)
S + V = 2103 (2)
V = Z/2 (3)
Subtract equation (2) from equation (1):
Z - V = 965
Substitute V = Z/2 into the above equation:
Z - Z/2 = 965
Z/2 = 965
Z = 1930
Substitute Z = 1930 into equation (3):
V = 1930/2
V = 965
Substitute V = 965 into equation (2):
S + 965 = 2103
S = 1138
The total number of buttons is:
S + V + Z
= 1138 + 965 + 1930
= 4033
Hence, the total number of buttons they have is 4033.
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help meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeee
Answer:
t = 11.7
Step-by-step explanation:
r
A = P (1 + -------)^(nt)
n
A = 5000 = (2500 × 2)
P = 2500
n = 2
t = ?
0.06
5000 = 2500 (1 + ----------)^(2)(t)
2
0.06
5000 = 2500 (1 + ----------)^(2)(t)
÷2500 ÷2500 2
0.06
2 = (1 + ----------)^(2)(t)
2
0.06
log₁₀ 2 = log₁₀ (1 + ----------)^(2)(t)
2
0.06
log₁₀ 2 = 2t × log₁₀ (1 + ----------)
2
0.06 0.06
÷ log₁₀ (1 + ----------) ÷ log₁₀ (1 + ----------)
2 2
log₁₀ 2
----------------------------- = 2t
0.06
log₁₀ (1 + -------- )
2
log₁₀ 2
(1/2) ----------------------------- = 2t (1/2)
0.06
log₁₀ (1 + -------- )
2
(1/2) 23.44977225 = 2t (1/2)
11.72488613 = t
11.7 ≈ t
I hope this helps!
The area of the smaller regular pentagon is about 27.5 cm².
What is the best approximation for the area of the larger regular pentagon?
11cm²
172 cm²
70 cm²
275 cm²
Answer:172 cm²
Step-by-step explanation:
when we use the formula, and we can solve out is like 172.05 and round to tenth and will have the answer
Formula is 1/2 × p × a
Please ANSWER ASAP
Dorothy is trying to prove that △PQR is a right triangle.
The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).
Which TWO slope calculations can she use to correctly show that △PQR is a right triangle?
Select TWO of the answers below.
in the picture
The slope of C and D in the picture shows that ΔPQR is a Right Triangle.
What is slope of line?
Slope of line is defined as the angle of line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂).
If the product of slopes of any two sides is equal to -1, then those two sides are perpendicular
Given,
The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).
Slope of PQ = (y₂ - y₁)/(x₂ -x₁ )
= (1 - 5)/(- 1 - (-2)
= -4/1
= - 4
Slope of QR = (y₂ - y₁)/(x₂ -x₁ )
= 3 - 1/7 - ( -1)
= - 1 / 4
The product of Slope of PQ and QR is - 1. It means lines PQ and QR is perpendicular to each other consequently △PQR is a right triangle.
Therefore,The slope of C and D in the picture shows that ΔPQR is a Right Triangle.
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PLEASE ANSWER ASAP
Beverly is trying to prove that △PQR is a right triangle.
The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).
Which TWO slope calculations can she use to correctly show that △PQR is a right triangle?
Select TWO of the answers below.
The slope calculations she can use to correctly show that △PQR is a right triangle are
(a) Slope of PQ = (y₂ - y₁)/(x₂ - x₁) = (1 - 5)/(-1 - (-2)) = -4(d) Slope of QR = (y₂ - y₁)/(x₂ - x₁) = (3 - 1)/(7 - (-1)) = 2/8 = 1/4How to determine the slope calculations she can use correctly?From the question, we have the following ordered pairs that can be used in our computation:
The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).
This means that
P = (-2,5),
Q = (-1,1)
R = (7,3).
The slope of the points are calculated using
slope = (y₂ - y₁)/(x₂ - x₁)
So, we have
Slope of PQ = (y₂ - y₁)/(x₂ - x₁) = (1 - 5)/(-1 - (-2)) = -4
Also, we have
Slope of QR = (y₂ - y₁)/(x₂ - x₁) = (3 - 1)/(7 - (-1)) = 2/8 = 1/4
Hence, the equations are (a) and (d)
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2x-5y=0 a direct variation function, if so identify the constant of variation
Constant of variation for the direct function is y = [tex]\frac{2 x}5}[/tex]
What is Direct Variation?Direct variation in mathematics is the general form of formula y = k x where x and y are variables (numbers that change) and k is a constant
Convert to slope intercept form
2x -5y =0
Add 5y to both sides
2x-5y +5y =5y
2x=5y
divide both sides by 5
[tex]\frac{2x}{5}[/tex] =[tex]\frac{5y}{5}[/tex]
Cross multiply to solve for y
5(2x) =5(5y)
y = [tex]\frac{2 x}5}[/tex]
Therefore, the constant of variation y = [tex]\frac{2 x}5}[/tex]
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I need help please help me
Answer:
GM = 18
Step-by-step explanation:
JK = KL = 2
GJ = LM =7
GM = 7+2+2+7 = 18!
So the answer it is 18.
What are the steps to answer this question 5x60=5xtens
Answer: 12
Step-by-step explanation:
1 2
5 ⟌ 6 0
- 5
1 0
- 1 0
0
If a certain electromagnetic wave has a wavelength of 100m, what type of electromagnetic wave is it?
Answer: Radio
Step-by-step explanation:
An electromagnet wave with a wavelength of 100m is a Radio. These signals are invisible to the human eye, humans are only able to detect visible light.
Solve 4x - 3 = 17
x = ?…
Answer: x=5
Step-by-step explanation:
4x-3=17 Add three to both sides
4x=20 Divide both side by 4 to isolate x
x=5
Alang is going to invest in an account paying an interest rate of 5.7% compounded
continuously. How much would Alang need to invest, to the nearest dollar, for the
value of the account to reach $113,000 in 5 years?
The investment amount is $37263.09.
What is continuous compound interest?Interest that compounded continuously to the principal amount. This interest rate provides exponential growth to period of time.
Formula of continuous compound interest rate;
P(t) = P₀ [tex]e^{rt}[/tex] , where P₀ is the principal amount, r is the interest rate and t is the time period.
Given that the Alang is going to invest with the continuous compound interest rate 5.7%.
Using the formula of continuous compound interest rate,
P(t) = P₀ [tex]e^{rt}[/tex]
P(t) = $113000 x [tex]e^{(5.7)(5)}[/tex]
P(t) = $37263.09
Therefore, the investment amount is $37263.09.
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A scientist polls 40 people, asking if they would participate in a study. 55% say yes. How many people said yes
Answer:
22 people
Step-by-step explanation:
First, let's convert the percentage into a decimal so we can multiply the two.
55% = 0.55
Next, we'll multiply 40 times 0.55. This is so we can find the amount of people who said yes. (55% of people said yes.)
0.55*40 = 22
22 people said yes.
The equation of line u is y–3=7(x–5). Parallel to line u is line v, which passes through the point (1,9). What is the equation of line v?
Answer:
y - 9 = 7(x - 1)
Step-by-step explanation:
The given equation is in Point Slope Form: y - y₁ = m(x - x₁)
m is the slope, and parallel lines have the same slope (7)
x₁ and y₁ are the coordinates of a point on the line
I need help in this 8th grade only part B and D
a) The first term of the sequence is; ³¹/₆
b) The term to term rule is; aₙ = ³¹/₆ + (n - 1)²/₆
c) The next three terms are; ³⁷/₆, ³⁹/₆, ⁴¹/₆
d) The 10th term in the sequence is; a₁₀ = ⁴⁹/₆
How to find the nth term of a sequence?The first term of the sequence is given by the expression;
2 ÷ ¹²/₃₁ = ³¹/₆
The second term of the sequence is given by the expression;
3 ÷ ⁶/₁₁ = ³³/₆
The third term of the sequence is given by the expression;
5 ÷ ⁶/₇ = ³⁵/₆
These are the first three terms of a sequence and so the sequence is;
³¹/₆, ³³/₆, ³⁵/₆,....
d = ³³/₆ - ³¹/₆ = ²/₆
Thus, term to term rule is given by the nth term of an arithmetic progression;
aₙ = ³¹/₆ + (n - 1)²/₆
The next three terms are; ³⁷/₆, ³⁹/₆, ⁴¹/₆
The 10th term in the sequence is;
a₁₀ = ³¹/₆ + (10 - 1)²/₆
a₁₀ = ³¹/₆ + ¹⁸/₆
a₁₀ = ⁴⁹/₆
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helppppppppppppppp
Ginny and Bob are both locksmiths.
Ginny uses the function f(x)=60x+80 to determine the charge to her customers, where x represents the number of hours of labor.
The table shows what Bob charges a customer for x hours of labor.
x (hours) 0 1 2 3 4
cost ($) 60 140 220 300 380
Which locksmith charges less for an initial fee for a service call?
Drag a value or name to the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Ginny charges Response area for an initial fee, and Bob charges Response area for an initial fee. Response area charges less for an initial fee.
For the initial fee, Bob charges less than Ginny.
What is unit rate?A unit rate means a rate for one of something.
Given that Ginny charges by uses the function f(x)=60x+80 where x represents the number of hours of labour.
Ginny initial charge = $80
Bob initial charge =$60
Hence, For the initial fee, Bob charges less than Ginny.
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How many real solutions does the system have ? y = - 3x - 1; y = x ^ 2 - 3x + 4
The only solution the system of the equation has is x = -1/3.
The number of solutions is one.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
The system of equations:
y = -3x - 1
y = x² - 3x + 4
The solutions of the equation.
y = 0
So,
-3x - 1 = 0
-3x = 1
x = -1/3
x² - 3x + 4 = 0
It is in the form of ax² + bx + c = 0
a = 1, b = -3, and c = 4
Now,
x = -b ± √(b² - 4ac) / 4a
x = 3 ± √(9 - 16) / 4
x = 3 ±√-7 / 4
x = 3 ±i√7 / 4
This is a complex root.
So,
These are not real solutions.
Thus,
The only solution the system of the equation has is x = -1/3.
The number of solutions is one.
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Dave borrowed $7400 from his uncle with simple interest of 6% and eventually repaid $8288 (principal and interest). What was the time period of the loan?
The time period of the loan was 1 year.
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below? On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (3.5, 3), and goes through (6, 0). Group of answer choices x – 3 x + 1 x – 1 x + 3
The answer choice which must be a factor of the polynomial in discuss is; (x - 1).
What must be a factor of the polynomial as described?It follows from the vertex form equation of a parabola; f(x) = a ( x - h )² + k where the vertex of the parabola is; (h, k).
Therefore, the equation of the parabola in discuss is;
f(x) = a (x - 3.5)² + 3.
Recall that the x coordinates of the vertex, h is given by; h = (p + q) / 2
where p and q are the zeroes of the quadratic function.
Therefore, since one of the zeroes is given as; 6 ( from (6, 0) ); it follows that the second zero can be determined as follows;
3.5 = ( 6 + q ) / 2
7 = 6 + q
q = 1
Therefore, since the second zero is; 1. It follows that the associated factor as required is; ( x - 1 ).
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The length of a sandwich is 36.2 inches. Skyler cut the sandwich into 4 equal-sized pieces for him and his friends to eat for lunch.
Which expression represents the length of each piece of the sandwiches?
Answer:
36.2/4=length of each sandwich piece