Here is a system of linear equations: Which would be more helpful for solving the system: adding the two equations or subtracting one from the other? Explain your reasoning. Solve the system without graphing. Show your work.
Answers
Okay, here we have this:
Considering the provided system we obtain the following:
The option more helpful for solving the system is add one equation to the other because in this way we can cancel the term of the "y", if we solve the system we obtain the following:
[tex]\begin{bmatrix}2x+\frac{1}{2}y=7 \\ 6x-\frac{1}{2}y=5\end{bmatrix}[/tex]Adding the equations:
[tex]\begin{gathered} 8x=12 \\ x=\frac{12}{8} \\ x=\frac{3}{2} \end{gathered}[/tex]Now, let's replacing in the first equation with x=3/2:
[tex]\begin{gathered} 2(\frac{3}{2})+\frac{1}{2}y=7 \\ 3+\frac{1}{2}y=7 \\ \frac{y}{2}=4 \\ y=8 \end{gathered}[/tex]Finally we obtain that the solution to the system is x=3/2 and y=8.
Related Questions
Rational and Irrational Numbers make up the____ system.
Answers
We have the following:
Therefore, the answer is real numbers
A cylinder has a height of 10 ft and a volume of 25,456 ft^3.The radius of the cylinder is approximately ___ feet.Round your answer to the nearest whole number.
Answers
From the question given, they provided us with the height,h = 10ft, and volume, V=25,456 cubic feet.
Thus, we have:
[tex]\begin{gathered} V=\pi\times r^2\times h \\ 25,456=\pi\times r^2\times10 \\ \frac{25,456}{10\pi}=r^2 \\ \text{Taking the value of }\pi\text{ as 3.142, we have:} \\ r^2=\frac{25,456}{10\times3.142} \\ r^2=810.1846 \\ r=\sqrt[]{810.1846} \\ r=28.46ft \end{gathered}[/tex]Hence, the radius of the cylinder is 28.46ft
Type the correct answer in each box. Use numerals instead of words.The exterior of a solid cone is painted. The height of the cone is 11.4 centimeters, and the diameter of its opening is 5 centimeters.What is the surface area of the solid cone requiring paint to the nearest square centimeter?The surface area of the solid cone requiring paint rounded to the nearest whole number is square centimeters.
Answers
The surface area of a cone with diameter d and height h is given by:
[tex]A=\pi(\frac{d}{2})^2+\pi\cdot\frac{d}{2}\cdot\sqrt[]{h^2+(\frac{d}{2})^2}[/tex]For d = 5 cm and h = 11.4 cm, we have:
[tex]\begin{gathered} A=\pi(\frac{5}{2})^2+\pi\frac{5}{2}\sqrt[]{11.4^2+(\frac{5}{2})^2} \\ A=\frac{25}{2}\pi+\pi\frac{25}{2}\sqrt[]{129.96+\frac{25}{2}} \\ A=12.5\pi+12.5\cdot\pi\cdot\sqrt[]{142.46} \\ A\approx12.5\pi+12.5\cdot11.94\cdot\pi \\ A\approx508cm^2 \end{gathered}[/tex]Suppose 2' is a normally distributed random variable with ft = 10.3 and 0 = 3.8. For the following probability,draw an appropriate diagram, shade the appropriate region and then determine the value:P(9 <2 ≤ 14) = Note: Enter your answer up to 4 decimal places.
Answers
GIVEN
The following values are given:
[tex]\begin{gathered} \mu=10.3 \\ \sigma=3.8 \end{gathered}[/tex]SOLUTION
The z-score for the x values 9 and 14 can be calculated using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]For x = 9:
[tex]\begin{gathered} z=\frac{9-10.3}{3.8} \\ z=-0.34 \end{gathered}[/tex]For x = 14:
[tex]\begin{gathered} z=\frac{14-10.3}{3.8} \\ z=0.97 \end{gathered}[/tex]The probability can be calculated as follows:
[tex]P(9\le x\le14)=Pr(-0.34The region that represents the solution is shown below:Therefore, the probability is given to be:
[tex]P(9\le x\le14)=0.4671[/tex]The probability is 0.4671.
Multiply. Write the result in standard form.(2 + 1)(3^4 + 7 + 2)
Answers
To multiply polynomials, we use the distributive law
[tex]\begin{gathered} (2x+1)(3x^4+7x+2)=(2x+1)(3x^4)+(2x+1)(7x)+(2x+1)(2) \\ =2x(3x^4)+1(3x^4)+2x(7x)+1(7x)+2x(2)+1(2)_{} \\ =6x^5+3x^4+14x^2+7x+4x+2 \end{gathered}[/tex]The last part follows by the laws of exponentials, finally we combine like terms
[tex]\begin{gathered} 6x^5+3x^4+14x^2+7x+4x+2=6x^5+3x^4+14x^2+(7+4)x+2 \\ =6x^5+3x^4+14x^2+11x+2 \end{gathered}[/tex]Two cards are drawn from a deck of 52 cards. The first card is replaced before drawing the second card. Find the probability that the first card is red and the second card is a 7
Answers
The probability that the first card is red and the second card is a 7 is 1/26.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability that the first card is a red and the second is a 7 = (number of red cards / total number of cards) x (number of 7 / total number of card)
Probability that the first card is a red and the second is a 7 = (26 / 52) x (4/52) = 1/26
To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ1
express 0.004 in scientific notation
Answers
We are asked to express 0.004 in scientific notation
The number 0.004 has the decimal point at the start, so we move this decimal point to the right until there is only one non-zero digit is left (4 in this case) and then count the number of times we moved.
[tex]0.0004=4\times10^{-3}[/tex]In this case, we moved 3 times so the exponent (power) is -3
The sign of exponent is negative when we move to the right (like in this case)
The sign of exponent is positive when we move to the left.
a teacher performing a demonstration find that a piece of court displaces 23.5 ml of water . the piece of cork had a density of 5.7 grams. what is the density of the cork
Answers
We are asked to determine the density of the cork. To do that we will use the following formula:
[tex]D=\frac{m}{V}[/tex]Where:
[tex]\begin{gathered} D=\text{ density} \\ m=\text{ mass} \\ V=\text{ volume} \end{gathered}[/tex]The volume of the cork is the same as the volume that it displaced of water, therefore, we have:
[tex]V=23.5ml[/tex]Now, we substitute the values and we get:
[tex]D=\frac{5.7g}{23.5ml}[/tex]Solving the operations:
[tex]D=0.24\frac{g}{ml}[/tex]Therefore, the density of the cork is 0.24 g/ml.
Multiply the following polynomials. Once simplified, name the resulting polynomial. (x + 2) (4x^2 - 3x - 2)name:
Answers
The resulting polynomial consists of four terms , it is called a quadrinomial.
A bag of numbered lottery balls contains the numbers 1 through 50. What is the probability that a randomly selected ball will be a number that is not a multiple of 8? Give your answer as a simplified fraction.
Answers
A bag of numbered lottery balls contains he numbers 1 through 50.
One ball is selected at random.
From 50 balls, one ball can be selected in 50 different ways.
So, the total number of points in sample space is 50.
Let us consider the event that the number is a multiple of 8 be A.
There are six numbers between 1 o 50 which are multiple of 8.
Therefore, one ball can be selected from 6 balls in 6 different ways.
So, the number of points in sample space in favour of the event A is 6.
Therefore, by the classical definition of probability,
[tex]\begin{gathered} P(A)=\frac{6}{50} \\ =\frac{3}{25} \end{gathered}[/tex]Then, the probability that the selected number is not a multiple of 8 is
[tex]\begin{gathered} P(A^C)=1-P(A) \\ =1-\frac{3}{25} \\ =\frac{22}{25} \end{gathered}[/tex]So, the required probability is 22/25.
Samuel is 10 years old. He moaned the neighbors lawn on Saturday and I and $40. It took him 2 hours come on the lawn in 2 hours to clean his room. How much money did Samuel earn an hour? A) $4.00B) $6.67C) $10.00D) 20.00
Answers
If he earned $40 in total and it took 4 hours to finish everything, he earns in an hour:
[tex]\frac{40}{4}=10[/tex]Answer: Samuel earns $10.00. Letter C.
Answer:
He got paid 10$ an hour. It does not say he gets paid for cleaning his room. Step-by-step explanation:10 x 4 = 40$
Step-by-step explanation:
46 = -6t - 8 what is t
Answers
t=9,
1) Solving for t we have:
46 = -6t - 8 Add 8 to both sides
46+8 = -6t
54 = -6t Divide both sides by -6
9 = t Flipping it
t=9
2) So the Solution Set is S={9} for this equation.
6(__+x)-8(-3+8x) = 30-58xfill in the blank
Answers
In this expression, we have the same value on the left side is equal to the same amount on the right side.
So, let's start operating it to simplify it
6(_+x) -8(-3+8x)=30-58x
6(_+x)+24-64x=30-58x
6( ) +6x +24 -64x =30 -58x
6( ) -58x+24=30-58x
6( )-58x +58x=30-24
6( ) =14 DIviding both sides by six
( ) =7/3
Testing:
6(7/3 +x) -8(-3+8x)=30-58x
14+6x +24 -64x =30-58x
38
If a bow requires 3/4 yards of lace how many bows can u make with 12 yards of lace
Answers
3/4 yards of a lace for each bow
for 12 yards of lace:?
Simply divide the 12 yards of lace by the lace required by each bow (3/4)
12 / (3/4) = 16 bows
The graph of g consists of two straight lines and a semi circle. Evaluate each
Answers
Given:
a)
[tex]\int ^1_0g(x)dx[/tex]Consider the shape included in the region from 0 to 1 of g(x).
The area is,
[tex]\int ^1_0g(x)dx=\frac{1}{2}\times1\times4=2[/tex]b) From x = to x = 6 includes the semi-circle. Its area is calculated as,
[tex]\int ^6_2g(x)dx=-\frac{1}{2}(\pi\times r^2)=-\frac{1}{2}(\pi\times2^2)=-2\pi=-6.28[/tex]Express - 345 asin simplest form, where m and n are integers.Enter the correct answer in the box.-345 =
Answers
As -345 is an integer, the simplest fraction form is:
[tex]\frac{-345}{1}[/tex]or -345/1 (m=-345, n=1).
find the area of the circle with a diameter of 8.6 ft
Answers
Given:
Diameter of the circle, d = 8.6 ft
To find the area of a circle, use the formula below:
[tex]undefined[/tex]Diameter of the circle, d
Hi so some of the problems I don't know like I can't but I did do some problem by myself you can tell me whether it's correct
Answers
The symmetric property of equality, if AB = YU. then YU = AB
As per the symmetric property of equality,
if AB = YU. then YU = AB
As per the symmetric property of congurence,
∠H ≅ ∠K then ∠K ≅ ∠H
As per the reflexive property of congurence,
∠PQR ≅ ∠PQR
As per the distibutive property, multiplying the sum of two or more term by a number produces the same result as when each term is multiplied individually by the number and the products are added together.
3(x - 1) = 3x - 3
As per the substitution property one value can replace another value in an expression or equation and the value will remain the same.
If LM = 7, EF + LM = NP
Then EF + 7 = NP
Therefore, the above bits are done as per the property mentioned.
To learn more about distributive property refer here
https://brainly.com/question/2807928
#SPJ9
Mariah needs to randomly select one of three groups of students to make their presentation first. Which simulation tools could she use in thissituation?O a bag containing 12 chips in three different colors, with four of each coloro a six-sided number cubea full standard deck of cardsa spinner divided evenly into four sections, with each section a different colorO two coins
Answers
the correct answer is a bag containing 12 chips in three different colors, with four of each color (option A)
Explanation:
number of groups of student = 3
We need to select one out of the three.
The option that can be used to simulate this choice is having 12 chips in three different colours. Each colour will have 4 each.
The 3 different colours represent the 3 different groups. While each 4 number of a colour represent the number of students in each group.
Hence, the correct answer is a bag containing 12 chips in three different colors, with four of each color (option A)
Solve the system of two linear inequalities graphically,2y <&- 1618v 2 - 7x+56Step 1 of 3: Graph the solution set of the festlinear InequallyAnswerThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawEnable ZoonpanChoose the type of boundary linesSolid (-) Dashed)Enter two points on the boundarytine:10Select the region you wish to be shaded:
Answers
Given
[tex]\begin{gathered} 2y<8x-16 \\ 8y\ge7x+56 \end{gathered}[/tex]The graph
Two boundary points
(0,7) (2,0)
The sum of the two numbers is 133. Four times the smaller of the two numbers equals three times the greater number find the numbers using one variable.
Answers
The Solution:
Let the two number be x and y133-x (
Such that:
[tex]\begin{gathered} x<133-x \\ x=small\text{ number} \\ 133-x=larger\text{ number} \end{gathered}[/tex]So,
[tex]\begin{gathered} 4x=3(133-x) \\ \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 4x=399-3x \\ \text{ Collect the like terms.} \\ 4x+3x=399 \\ 7x=399 \end{gathered}[/tex]Divide both sides by 7.
[tex]x=\frac{399}{7}=57[/tex]Therefore, the correct nswers are:
57 and 76
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
The given function's f(t) = (t - 4)(t + 1)(t - 7), f-intercept is f(t) = 28 and the t-intercepts are t = - 1, 4, 7.
What are intercepts?A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the y-axis of the coordinate system in analytic geometry using the widely used convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. Therefore, x = 0 is satisfied at these sites. The x-intercept and y-intercept are the points where a line crosses each axis.
An intercept is a location where an axis and a graph intersect. The x-intercept is the name given to this particular one.
Put t = 0 in the function f(t) = (t - 4)(t + 1)(t - 7)
f(t)= (0-4)(0+1)(0-7)
f(t) = (-4)(1)(-7)
f(t) = 28
So, the f-intercept is (0,28)
Put f(t) = 0 to find t- intercepts
0 = (t-4)(t+1)(t-7)
So, t - 4 = 0
t = 4
For t + 1 = 0
t = -1
For (t - 7) = 0
t = 7
So, the t intercepts are t = -1, 4, 7.
To know more about intercepts, visit:
brainly.com/question/14180189
#SPJ1
Victor took a survey of high school students to see how many had part-time jobs last summer. The results of the survey are shown in the table. Compare theprobability that a student in the sophomore class had a part-time job to the probability that a student in the junior class had a part-time job.
Answers
Answer:
A sophomore is less likely than a Junior to have a job.
Explanation:
Given the table in the attached image.
The total number of sophomores is
[tex]35[/tex]The number of sophomores with a job is;
[tex]12[/tex]The probability that a sophomore had a job is;
[tex]P_S=\frac{12}{35}[/tex]The total number of Juniors is
[tex]37[/tex]The number of Juniors with a job is;
[tex]27[/tex]The probability that a Junior had a job is;
[tex]P_J=\frac{27}{37}[/tex]From the derived Probability, we can observe that the probability that a Junior had a job is greater than the probability that a Sophomore had a job.
[tex]P_J>P_S[/tex]Therefore, A sophomore is less likely than a Junior to have a job.
Which two ratios are equivalent to 11/12?A. 4/5 and 12/13B. 22/24 and 33/36C. 22/33 and 33/34D. 23/24 and 35/36
Answers
Two ratios are equivalent if the division between them is equal to one. We need to look at the options to check for which these are true.
For A:
[tex]\frac{\frac{11}{12}}{\frac{4}{5}}=\frac{11}{12}\cdot\frac{5}{4}=\frac{55}{48}[/tex]Since the answer is different than one, this is not the correct option.
For B:
[tex]\frac{\frac{11}{12}}{\frac{22}{24}}=\frac{11}{12}\cdot\frac{24}{22}=\frac{264}{264}=1[/tex][tex]\frac{\frac{11}{12}}{\frac{33}{36}}=\frac{11}{12}\cdot\frac{36}{33}=\frac{396}{396}=1[/tex]Since the result of the division is one for both ratios, the correct option is "B".
Select all of the constraints that apply to this situation $1.25x when x <12$12.00 + $0.75(x-12) when X_>12$1.25x when x _>120.75x when x >12$12.00 + $0.75x when x >12
Answers
We want to write expressions that describe the cost of the cookies. Let say we sell x cookies. If x is less than 12, then the cost per cookie is 1.25. So the cost of x cookies would be the product of this numbers, so it would be
[tex]1.25x,x<12[/tex]Note that when x=12 the cost should be 12. Also note that for each extra cookie, starting at 12, each cookie costs 0.75. If we buy x cookies , to calculate the extra cookies, with respect to 12, we simply substract 12 from x and we multiply it by 0.75. This would be
[tex]0.75\cdot(x\text{ -12)}[/tex]as this is an additional cost to the 12, we add 12 to this expression. THen we get
[tex]12+0.75\cdot(x\text{ -12)}[/tex]Note that for this expression, when x=12, we get that the expression becomes
[tex]12+0.75\cdot(12\text{ -12)=12}[/tex]THis means that the expression applies from 12 and on, so we have the followin inequality12
[tex]12+0.75\cdot(x\text{ -12), x}\ge12[/tex]Find the standard deviation for the following wroup of data Hems, Round your answer to the nearest tenth for one decimal place), 7,9,11,14,15,16
Answers
The standard deviation of the groups of data is 3.3 .
The standard deviation is calculated using the formula [tex]{\displaystyle \sigma={\sqrt {{\frac {1}{N}}\sum _{i=1}^{N}\left(x_{i}-{\mu }\right)^{2}}}}[/tex]
Where σ is the standard deviation.
x denotes the data of the population.
N is the size of the population.
μ is the mean of the population.
The given population is 7,9,11,14,15,16
Here N= 6
Mean (μ) = (7+9+11+14+15+16)÷6 = 72/6=12
Now we will put the values in the above equation to calculate the sd.
[tex]{\displaystyle \sigma={\sqrt {{\frac {1}{6}}\sum _{i=1}^{6}\left(x_{i}-{12 }\right)^{2}}}}[/tex]
Simplifying we get:
σ = √(64/6)
σ = 3.2659..
σ = 3.3
The standard deviation is a statistic that indicates the degree of volatility or dispersion in a set of numerical values.
A low standard deviation shows that possibly the values tend toward being close to the mean, sometimes referred to as the expected value of the set, whereas a large standard deviation suggests that the values are distributed over a wider range.
To learn more about standard deviation visit:
https://brainly.com/question/28108712
#SPJ9
I inserted a picture of the question answer choices E. 15 F.x
Answers
Recall that two terms are called like terms if they have the same variables with the same exponents, in simpler words, two terms are like terms if when adding them the result is a simplification of the sum.
Answer: 8 and 12, 1, and 15 are like terms.
ANSWER QUESTION 3 PHOTO ATTACHEDFAST REPLY = BETTER RATINGTHANK YOU!
Answers
Given
[tex]f(x)=xe^{7x}[/tex]Calculate the second derivative of f(x), as shown below
[tex]\begin{gathered} \Rightarrow f^{\prime}(x)=e^{7x}+7xe^{7x} \\ and \\ \Rightarrow f^{\prime}^{\prime}(x)=7e^{7x}+7(e^{7x}+7xe^{7x}) \\ \Rightarrow f^{\prime}^{\prime}(x)=14e^{7x}+49xe^{7x} \end{gathered}[/tex]Then, find the interval such that f''(x)>0 in order to find where f(x) is concave up,
[tex]\begin{gathered} 14e^{7x}+49xe^{7x}>0 \\ \Rightarrow2e^{7x}+7x*e^{7x}>0 \\ and \\ e{}^{7x}>0,x\in\Re \end{gathered}[/tex]Then,
[tex]\begin{gathered} 2e^{7x}>-7xe^{7x} \\ \Rightarrow2>-7x \\ \Rightarrow x>-\frac{2}{7} \end{gathered}[/tex]Therefore, f(x) is concave up when x in (-2/7, +infinite).
In the case of concavity down,
[tex]\begin{gathered} f^{\prime}^{\prime}(x)<0 \\ \Rightarrow2e^{7x}+7x*e^{7x}<0 \\ \Rightarrow2+7x<0 \\ \Rightarrow-\frac{2}{7}>x \end{gathered}[/tex]Thus, f(x) is concave down when x in (-infinite, -2/7).
The answer is the fifth and last option (top to bottom).
Number 3.Light travels 1.9x10^5 kilometers per second.there are 6.4 x 10^5 seconds in one week .About how many kilometers does light travel.
Answers
helloo
from the question given, we have some variables
[tex]\begin{gathered} \text{speed}=1.9\times10^5\operatorname{km}\text{ /s} \\ \text{time}=6.4\times10^5s \\ \text{distance}=x \end{gathered}[/tex]now the formula for speed is given as
[tex]\begin{gathered} \text{speed}=\frac{\text{distance}}{\text{time}} \\ 1.9\times10^5=\frac{x}{6.4\times10^5} \\ x=(1.9\times10^5)\times(6.4\times10^5) \\ x=1.22\times10^{11}\operatorname{km} \end{gathered}[/tex]Maggie graphed a scatter plot of the numberof hours she drove, t, and the number of milesshe traveled, d. She then found a trend line ofher data to be d = 45.5t + 8. What is thepredicted distance Maggie will travel # shedrives for 4 hours?A 182 milesB 372 milesC 364 milesD 190 milesWhat’s the answer ?
Answers
WE have the following:
[tex]d=45.5t+8[/tex]When t = 4
[tex]undefined[/tex]