Resolviendo un sistema de ecuaciones, vemos que se venden 6 libros de secundaria 4 y 6 libros de secundaria 1.
¿Como escribir un sistema de ecuaciones?
Primero definimos dos variables:
x = numero de libros de secundaria 4 vendidos.k = número de libros de secundaria 1 vendidos.Sabemos que se venden 12 libros en total, entonces:
x + k = 12
Tambien sabemos que se recauda un total de $82, entonces:
x*$8 + k*$6 = $82
Entonces tenemos dos ecuaciones.
a) Usando la primer ecuacion, podemos aislar x para tener:
x = 12 - k
b) Ahora podemos reemplazar eso en la otra ecuación para solucionar el sistema.
(12 - k)*$8 + k*$6 = $82
$96 - $2*x = $82
$2*x = $12
x = $12/$2 = 6
Es decir se venden 6 libros de secundaria 4, y como se venden 12 libros en total, los otros 6 libros vendidos son de secundaria 1.
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Does this graph represent a function? Why or why not?
Answer:
no it does not pass the vertical line test choose D
Step-by-step explanation:
Sketch the region that is common to the graphs of x ≥ 2,
y ≥ 0, and x + y ≤ 6, and find its area.
a. Find the graph of their common region in the attachment
b. The area of the common region of the graphs is 8 units²
a. How to sketch the region common to the graphs?Since we have x ≥ 2, y ≥ 0, and x + y ≤ 6, we plot each graph separately and find their region of intersection.
The graph of x ≥ 2 is the region right of the line x = 2.The graph of y ≥ 0 is the region above the line y = 0 or x-axis.To plot the graph of x + y ≤ 6, we first plot the graph of x + y = 6 ⇒ y = -x + 6. Then the graph of x + y ≤ 6 is the graph of y ≤ - x + 6.So, the graph of x + y ≤ 6 is the region below the line y = - x + 6
From the graph, the regions intersect at (2, 0), (2, 4) and (6, 0)
Find the graph of their common region in the attachment
b. The area of the common regionFrom the graph, we see that the common region is a right angled triangle with
height = 4 units and base = 4 unitsSo, its area = 1/2 × height × base
= 1/2 × 4 units × 4 units
= 1/2 × 16 units²
= 8 units²
So, the area of the common region of the graphs is 8 units²
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(x + 2)*(x^2 -2*x+4) - (x^3 -12)
Answer:
[tex] \large{ \boxed{ \tt{20}}}[/tex]- Please see the attached picture for full solution!:)
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What is the area of the figure? Enter your answer in the box.
the answer is 30 because 3*4=12/2=6 and for the other triangle it is 8*6=48/2 =24 and 24+6=30
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, can the company build 10 child bikes and 12 adult bikes in a week. (2 points) Group of answer choices No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
The company cannot build 10 child bikes and 12 adult bikes No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 , Option A is the correct answer.
What is System of Inequality ?System of inequality represent system of inequalities that satisfies common condition.
It is given that
Each child bike requires 4 hours to build and 4 hours to test.
Each adult bike requires 6 hours to build and 4 hours to test.
Total building hours = 120
Total testing hours = 100
If c represents child bikes and a represents adult bikes, can the company build 10 child bikes and 12 adult bikes in a week.
6a + 4c ≤ 120
4a +4c ≤100
On solving this system of Inequality
a ≤ 10
which is less than required , and so
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Therefore Option A is the correct answer.
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Identify the domain and range of
each function.
y = 3.5x
The domain of this function is
The range of this function is
DONE
Answer:
Domain: [tex](-\infty, \infty)[/tex]Range: [tex](0, \infty)[/tex]Step-by-step explanation:
The domain of an exponential function is all real numbers.
The range of an exponential function that has not been vertically shifted is [tex](0, \infty)[/tex].
The domain of the function is all the real numbers and the range of the function is set of all positive real numbers
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
The domain of the given function is all real numbers. In other words, there are no restrictions on the possible values of x that we can plug into the function.
To see why, note that we can raise any real number to any power, so there are no values of x that are off-limits for this function.
The range of the function is all positive real numbers.
This is because the base of the exponential function is 5, which is positive, and raising 5 to any power results in a positive number. Multiplying a positive number by 3 also results in a positive number, so the function output is always positive.
Hence , we can write the domain and range of the function as:
Domain: all real numbers
Range: y > 0 (all positive real numbers)
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The large rectangle below represents one whole.
What percent is represented by the shaded area?
Answer:
40%
Step-by-step explanation:
so have 5 rectangles in a whole.we also have 2 shaded potions in that whole which represents 2/5 shaded potions.2/5 in fraction =0.4Now Change 0.4 to percentage by multiplying 0.4 by 1000.4 x 100 = 40Therefore the percentage represented by the shaded area is 40% Hope this helps.Good luck ✅.
how does the distance you determined in part c change if the radius of the small gear is 1.5 inches and the radius of the large gear is 45 inches?
If the radius of the smaller gear is 1.5 inches and the radius of the large gear is 4.5 inches then the bicycles can travel a distance of 62.83 inches.
Given radius of the small gear=1.5 inches and radius of the larger gear=4.5 inches.
Number of rotation of the small gear for each rotation of the larger gear=4.5/1.5=3
Distance which the bicycle can travel=3*2πr.
=3*2*π*10
=60π inches.
Difference in distance travelled=60π inches-40π inches.
=20π inches
put π=3.14
=20*3.14
=62.83 inches.
Hence the distance that the bicycle travels is 62.83 inches if the radius of smaller gear is 1.5 inches and radius of the larger gear is 4.5 inches.
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Question is incomplete as it should includes:
Description about the question that person is travelling through bicycle. That's why radius of gears has been given.
I am drinking beer and you are drinking light beer. Your light beer is 1/3 less filling than my regular beer. I drink 3 beers. How many do you have to drink to be equally full
Using proportions, it is found that you have to drink 9 beers to be equally full.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Your drink is 1/3 less filling, hence you have to drink 3 times the amount I drink to be equally full. I drink 3 beers, hence the number you drink is given as follows:
N = 3 x 3 = 9 beers.
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Can someone help with this
The measure of angle B = 31 degrees, measure of angle C
= 121 degrees, and b = 9. Then a =
to the
nearest tenth.
If Colorado Springs, Colorado, has 1.2 times as many days of sunshine as Boston, Massachusetts, how many days of sunshine does each city have if there are a total of 482 days of sunshine between the two in a year?
Colorado and Boston have 263 and 219 days of sunshine respectively.
What is the solution to the Equation?Let the number of days of sunshine in Colorado is x and the number of days of sunshine in Boston is y.
Total number of days of sunshine=482
Also, the number of days of sunshine in Colorado is 1.2 times the number of days of sunshine in Boston.
So, the equation is formed as follows:
x+y=482 -(1)
The other equation is formed as:
x=1.2y -(2)
Substitute the value x from equation (2) in (1),
1.2y+y=482
2.2y=482
y=482/2.2
y=219
Substitute the value of y in equation (1),
x+219=482
x=482-219
x=263
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A game club offers a special game to play. The tickets cost $5 for members and $10 for nonmembers. Write an expression to find the total cost of 6 member tickets and 4 nonmember tickets.
(6 + 5) + (4 + 10)
(6 * 5) + (4 * 10)
(4 * 5) + (6 * 10)
(6 + 5) * (4 + 10)
jurgen cuts 5 metre-long timber beam into 3 pieces,first piece 2.34metres second piece 1.85 work out the length of the third piece
The length of the third piece is 0.81 m if the Jurgen cuts 5 meter-long timber beam into 3 pieces, the first piece 2.34metres second piece 1.85.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
Jurgen cuts 5 meter-long timber beam into 3 pieces, first piece 2.34metres second piece 1.85.
Let the length of the third piece is x m.
2.34 + 1.85 + x = 5
4.19 + x = 5
x = 0.81 m
Thus, the length of the third piece is 0.81 m if the Jurgen cuts 5 meter-long timber beam into 3 pieces, the first piece 2.34metres second piece 1.85.
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what is -3 plus 1/2 ?
Answer:
-2.5
Step-by-step explanation:
Answer:
-5/2 or -2.5
you can type it in a calculator
Find the value of x in circle O.
55 ?
Answer:
x = 55°
Step-by-step explanation:
given 2 inscribed angles intercept the same arc then they are congruent, so
x = 55°
The atmospheric pressure at sea level is 14.7lb / i * n ^ 2 This pressure is reduced by half for each 3.6 miles above sea level Which graph correctly identifies the amount of atmospheric pressure based on height, in miles, above sea level?
Answer:graph b
Step-by-step explanation:
Leslie has 24 coins. They are all nickels and dimes. The total value of the coins is $1.85. How many dimes does Leslie have? Which of the following systems is correct for
this situation?
The number of dimes is 13.
The system of equation for the situation is as follows;
x + y = 24
0.1x + 0.05y = 1.85
How to solve system of equation?The coins are 24.
Therefore, they are all dimes and nickel.
Total value of the coins is $1.85.
Hence, let
x = number of dimes
y = number of nickels
Therefore,
x + y = 24
0.1x + 0.05y = 1.85
0.1x + 0.1y = 2.4
0.1x + 0.05y = 1.85
0.05y = 0.55
y = 0.55 / 0.05
y = 11
x = 24 - 11
x = 13
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Joe used random numbers to select boys from the alphabetized
version of the list shown to make a sample. The random numbers
were 17, 5, 1, and 12, so he selected the 17th, 5th, 1st, and 12th
names. Who was selected?
Alan, Craig, Dale, Eddie, Eugene, Glenn, Herbert, Howard, Jeremy,
Loren, Louis, Martin, Nathan, Randy, Ray, Russell, Sam, Steve, Victor,
Vincent
OA) Glenn, Howard, Nathan, Steve
OB) Craig, Eugene, Loren, Vincent
OC) Jeremy, Martin, Steve, Victor
OD) Alan, Eugene, Martin, Sam
Based on the numbers that Joe selected, the people selected were D) Alan, Eugene, Martin, Sam.
Who was selected?The 17th person was selected and if we assigned numbers from 1 to 20 to the alphabetized list, we would find that number 17 is Sam.
The 5th person is Eugene and the 1st person is Alan. The 12th person is Nathan.
In conclusion, option D is correct.
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Identify the type of function represented by f(x)=1/2(3)^x
A. increasing linear
B. exponential decay
C. decreasing linear
D. exponential growth
The function represented by f(x) = (1/2)(3)ˣ is an exponential growth
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.
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The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
If b > 1, it is an exponential growth but if b < 1, it is an exponential decay.
Given the function:
f(x) = (1/2)(3)ˣ
since 3 > 1, it is an exponential growth.
The function represented by f(x) = (1/2)(3)ˣ is an exponential growth
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GD Simpinying Radicals Simplify the number into simplest radical form. Use the factor tree to help determine the factors. √96 Warm-Up √6 O 2√6 0 4√6 0 4√3 Intro O Select a composite number to break into factors. Continue factoring until all factors are prime. 96 Done GD Simpinying Radicals Simplify the number into simplest radical form . Use the factor tree to help determine the factors . √96 Warm - Up √6 O 2√6 0 4√6 0 4√3 Intro O Select a composite number to break into factors . Continue factoring until all factors are prime . 96 Done
Answer:
Step-by-step explanation:
Writing Exercises
361. Explain how you solve a quadratic equation. How many answers do you expect to get for a quadratic equation?
Answer:
A quadratic equation can be solved using the quadratic formula, the factoring method, or completing the square. You expect to get either one or two answers.
Step-by-step explanation:
First, we have to understand how to solve a quadratic equation. There are three methods, the first of which is the quadratic formula. For any quadratic equation that takes the standard form of
[tex]f(x)=ax^2+bx+c[/tex]
you can solve for x by using the following formula:
x=(-b±√(b^2-4ac))/2a
Sometimes, however, the quadratic expression is factorable, meaning it can be converted into a product of two smaller expressions. For example:
[tex]x^2-4=(x-2)(x+2)[/tex]
As you can see, factoring gives you the roots easily (set each smaller expression to 0 and solve for x). If the quadratic is factorable, it would be easiest to use this method first.
Completing the square is another method that can be used to solve a quadratic function. It is often preferred because it converts the function into something factorable. In order to complete the square, you have to first ensure that the quadratic term's coefficient is 1. After that, you can take the linear term's coefficient, divide it by 2, and square it. Take the new term you found and add it to the equation. Because you are adding something to an equation, you must also subtract. Now, you can complete the square and factor. An example can be found below:
[tex]x^{2}-6=0\\\\(x^2-6+9)-9=0\\\\(x-3)^2-9=0\\\\(x-3-3)(x-3+3)=0\\\\x(x-6)=0\\\\x=0, x=6[/tex]
A quadratic equation can only have up to two solutions. You can imagine the graph of a quadratic. It looks like a parabola and only changes directions once. This means that it only crosses the x-axis two times. You can also look at the examples given and see that factoring only gives you two smaller expressions (leading to 2 roots). Sometimes, however, you might get a double root, leading to an equation with only one solution. This happens when the discriminant of the quadratic equation is 0. You can calculate this in advance to save yourself some time.
Assignment: generating frequencies for compound events investigation fill out this table to show the sample space for a roll of two dice (six-sided number cubes). 1 2 3 4 5 6 1 2 3 4 5 6
Total 36 outcomes are possible on rolling two dices simultaneously
A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment
A dice has 6 possibilities (1,2,3,4,5,6) , thus two when dices thrown together will have 36 outcomes in it's sample space. It's sample space is shown in picture attached below.
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What’s the sum of square root of square root of -2
The sum of the square root of -2 and -18 is 4i√2
How to determine the sum of square rootFrom the information given,
The sum square root of -2
√-2 + √-18
√-2 = √(-1*2) = √-1 * √2 = i√2 Note that the square root of -1 = i
√-18 = √(-1*18) = √-1 * √1`8 = i√18 Note that the square root of -1 = i
But we have that
√18 = √(9*2)
Using surd form. we have
= √9 * √2= 3√2
Then,
√-18 = i√18= i(3√2) = 3i√2
Let's add the sum of square root, we have
√-2 + √-18 = i√2 + 3i√2 = (i + 3i)√2 = 4i√2
Therefore, the sum of the square root of -2 and -18 is 4i√2
The complete question is;
What is the sum of square root of -2 and square root of -18?
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2 dogs, 4 horses 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground?.
Question 4 I need help to solve all 3
Answer:
[tex]x^{2} +12x+36[/tex] [tex]\\[/tex]----- factors [tex](x+6)^{2}[/tex][tex]4x^{2} +24x+36[/tex] ----- factors [tex](2x+6)^{2}[/tex][tex]2x^{2} +10x+8[/tex] ------ factors (2x+2)(x+4)[tex]y^{2} -4[/tex] --------- factor (y+2)(y-2)Step-by-step explanation:
First bullet is called Perfect Square Trinomial (PST), the first and last is a perfect square and the middle is twice the product of the squared first and last term. To factor, just copy the middle sign and square the first and last term.
---
2nd bullet is also a PST with a value on a. Likewise you just need to square the first and last term. Then, copy the middle sign.
--
3rd bullet is a trinomial. To get the factor, get the prime factor of the value of a. Then, find the factors of 8 that when add up results to the value of b.
-
4th bullet is a special case. First get the square root of the first and last term, and copy the sign, Then, copy the factors and change it to the opposite sign.
A sports team came to town. the stadium filled all 10,000 seats at two-level pricing. level 1 tickets are $50 each, and level 2 tickets are $150 each. the stadium made $75,000 in ticket sales. the system of equations that models this scenario is: x + y = 10,000 50x + 150y = 75,000 what do the x and y represent in the system?
x represents the number of tickets of level 1 and y represents the number of tickets of level 2 in the system given that there are 10,000 seats, level 1 tickets are $50 each, and level 2 tickets are $150 each and equation representing the situation:x + y = 10,000, 50x + 150y = 75,000. This can be obtained by understanding the question and observing the equations.
What do the x and y represent in the system?Given that total number of seats is 10,000 and there are two levels pricing.
Thus by observing the equation, x + y = 10,000,
10,000 is the sum of 2 variable which obviously will be the number of tickets in level 1 and number of tickets in level 2.
Since there are two level pricing,
50x + 150y = 75,000 represent the addition of total cost of tickets of level 1 and 2.
Hence x represents the number of tickets of level 1 and y represents the number of tickets of level 2 in the system given that there are 10,000 seats, level 1 tickets are $50 each, and level 2 tickets are $150 each and equation representing the situation:x + y = 10,000, 50x + 150y = 75,000.
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A manufacturer claims that a particular automobile model will get 50 miles per gallon on the highway. The researchers at a consumer-oriented magazine believe that this claim is high and plan a test with a simple random sample of 30 cars. Assuming the standard deviation between individual cars is 2.3 miles per gallon, what should the researchers conclude if the sample mean is 49 miles per gallon
A P-value of 0.0086 is sufficient evidence to refute the manufacturer's claim.
Suppose a particular vehicle gets 50 miles per gallon on the freeway and a simple random sample of 30 cars.
Let μ indicates the average number of miles per gallon of highway for a particular car model
Let [tex]\bar{x}[/tex] indicates the sample mean, σ indicates the population standard deviation and n indicates the sample size.
Given; [tex]\bar{x}[/tex]=49, σ= 2.3 and n = 30,μ₀ = 50
The significance level is α= 5%
Hypotheses: To test the null hypothesis: H₀: μ₀ = 50 Alternative hypothesis: H₁: μ <50
The test statistic can be written as:
[tex]z=\frac{\sqrt{n}(\bar{x}-50)}{\sigma}[/tex]
It follows a standard normal distribution under H₀.
Decision rule / rejection range: P-value <0.05 or because there is a test on the left
z <Ф⁻¹ (0.05) d. H. Z <-1.6449d. H.
[tex]\bar{x}[/tex] < μ₀+(σ÷√n )×-1.6449 = 49.3092725599558
Test statistic: Observations value of the test statistic,
[tex]\begin{aligned}Z_{stat}&=\frac{\sqrt{n}(\bar{x}-50)}{\sigma}\\ Z_{stat}&=\frac{\sqrt{30}(49-50)}{2.3}\\ Z_{stat}&=-2.3814\end[/tex]
critical value = Z critical = Z0.05 = -1.6449
P-value= P(Z < -2.3814)
P-value= P(Z < -2.3814)
P-value= (–2.3814)
P-value= 0.0086
Therefore, p-value = 0.0086 <0.05 and test statistic observations Zstat critical value [tex]\nleq[/tex] -1.6449, there is enough evidence to reject the null hypothesis.
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Complete the diagram by identifying the missing angles. Use the length of the ladder you chose for the missing length.
Since the length of the ladder is 40ft, the length of the zip line Z will be 222.47m.
What is the missing length about?Note that: one has to derive b using the law of sine.
[tex]\frac{b}{sin (15)} = \frac{40}{sin 90}[/tex]
b = [40 x Sin (15)] / sin (90)
So:
Sin (15) = √3−1)/(2√2
= 0.2588190451
Then: Sin (90) = 1
So, b = (0.2588190451 *40)/1
= 10.35/1
= 10.35
So one has to also derive for h
= [tex]\frac{b}{sin (15)} = \frac{h}{sin 75}[/tex]
Note that b = 10.35
Hence : h = 10.35 * [(√3 + 1) / 2√2] / [(√3−1)/(2√2)]
h = 10.35 * 3.73
h = 38.62
Using simple trigonometric analysis, we can say that:
∠ GJH = 90°; and
∠ GHJ = 10°
Therefore, to obtain Z
Z/ Sin (90) = h/Sin (10)
(Then make Z the subject of the formula)
Thus Z = h * Sin (90)/ Sin (10)
Z = 38.62 * 1/ 0.1736
Z = 222.47m
Therefore, Since the length of the ladder is 40ft, the length of the zip line Z will be 222.47m.
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The graph shows temperatures at different altitudes. Which choice describes the relationship between temperature and altitude?
A)Positive Linear Relationship
B) Non-Linear Relationship
C)Negative Linear Relationship
D)No Relationship
Answer:
Negative linear relationship
Step-by-step explanation:
The ___-if analysis checks the impact of a change in a variable or assumption on the model. Multiple choice question. what goal pivot sensitivity
what-if analysis
What-if analysis is a technique used to determine how the expected performance is affected by changing the assumptions underlying the prediction. Use What-if analysis to compare different scenarios and their possible outcomes based on fluctuating conditions.
What-if analysis allows project managers to identify event options and impacts, as well as change assumptions. When used properly, project managers can make more informed decisions and more accurately predict the outcome of those decisions.
Sensitivity analysis determines how different values of the independent variable affect a particular dependent variable under certain assumptions. In other words, sensitivity analysis examines how the causes of various uncertainties in a mathematical model contribute to the overall uncertainty of the model.
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