What is the solution to the system of equation?
-3x-4y-32= -7
2x-6y+2=3
5x-2y+5z=9
Answer:
[tex]x=\dfrac{38}{13},y=\dfrac{4}{13}\text{ and }z=-1[/tex]
Step-by-step explanation:
we are given three equation of variable x, y and z.
-3x-4y-3z= -7 ------------- (1)
2x-6y+z=3 ------------- (2)
5x-2y+5z=9 ------------- (3)
Using elimination method to eliminate z from equation (1) and (2)Make the coefficient of z same in both equation.
Multiply equation (2) by 3
-3x - 4y - 3z = -7
6x - 18y + 3z = 9
Add above equation to eliminate z
3x - 22y = 2 ---------------(4)
Using elimination method to eliminate z from equation (2) and (3)Make the coefficient of z same in both equation.
Multiply equation (2) by -5
-10x + 30y - 5z = -15
5x - 2y + 5z = 9
Add above equation to eliminate z
-5x + 28y = -6 ---------------(5)
Using elimination method to eliminate x from equation (4) and (5)Make the coefficient of x same in both equation.
Multiply equation (4) by 5 and equation (5) by 3
15x - 110y = 10
-15x + 84y = -18
Add above equation to eliminate x
-26y = -8
[tex]y=\dfrac{4}{13}[/tex]
Substitute y into equation (5) to get x
So, [tex]-5x+28(\frac{4}{13})=-6[/tex]
[tex]x=\dfrac{38}{13}[/tex]
Substitute x and y into equation (1)
[tex]-3\cdot \frac{38}{13}-4\cdot \frac{4}{13}-3z=-7[/tex]
[tex]z=-1[/tex]
Solution:
[tex]x=\dfrac{38}{13},y=\dfrac{4}{13}\text{ and }z=-1[/tex]
Find an expression in terms of n for the number of grey tiles in pattern n?
Suppose that y varies inversely with x. Write an equation for the inverse variation. y = 4 when x = 6
The equation for the inverse variation is y = 24/x.
Explanation:In an inverse variation, the equation can be represented as y = k/x, where k is a constant. To find the equation for the given scenario, we can substitute the values of y = 4 and x = 6 into the equation and solve for k.
4 = k/6
Cross-multiplying, we get k = 24. Therefore, the equation for the inverse variation is y = 24/x.
PLEASSEEE HELPPP
Daisy's friend calls her and asks her to meet at the park in exactly 40 minutes. Which method should Daisy use to most accurately determine when 40 minutes have passed?
A. Daisy should use a stopwatch with minutes and seconds.
B. Daisy should count the minutes in her head after she receives the call.
C. Daisy should use an hourglass and flip it over every time the sand runs out.
D. Daisy should look at a clock that shows hours and minutes only.
What is the value of 5^4 over 5^6
A rectangle has an area of 98 square inches. the length of the rectangle is double the width of the rectangle. find the dimensions of the rectangle
Mr. Yu applies 12 ounce of fertilizer to every 58 square meter of his lawn.How many ounces of fertilizer does Mr. Yu use per square meter for his lawn?Enter your answer in the box as a fraction in simplest form.
Answer: is 4/5
how i know because i did the quiz hope this helps
An angle measuring 22 degrees is bisected what is the measure of he angle that are formed?
What is the sum of the geometric sequence 1, 3, 9, … if there are 10 terms?
Answer: 29524
Step-by-step explanation:
Given geometric sequence : 1, 3, 9, …........................
First term of G.P. [tex]a = 1[/tex]
Second term of G.P.[tex]a_2=3[/tex]
Common ratio =[tex]r=\frac{a_2}{a}=\frac{3}{1}=3[/tex]
We know that the sum of the geometric sequence with n terms is given by :-
[tex]S=\frac{a(r^n-1)}{r-1}[/tex] for |r|>1
Substitute a = 1 , r =3 and n=10 , we get
[tex]S=\frac{1(3^(10)-1)}{3-1}\\\\=\frac{59049-1}{2}\\\\=-\frac{59048}{2}\\\\\Rightrrow\ S=29524[/tex]
I need this question answered asap! Thank you advance!!
The population in Rochester, New York, was 219,773 people in 2000 and 210,565 people in 2010. By about what percent did the population change? Did the population grow or shrink? Write the percent as a decimal.
Answer:
The population changed by 4.19%. The population shrank.
0.0419.
Step-by-step explanation:
We have been given that the population in Rochester, New York, was 219,773 people in 2000 and 210,565 people in 2010.
[tex]\text{Percent change}=\frac{\text{Final}-\text{Initial}}{\text{Initial}}\times 100[/tex]
[tex]\text{Percent change}=\frac{210,565-219,773}{219,773}\times 100[/tex]
[tex]\text{Percent change}=\frac{-9,208}{219,773}\times 100[/tex]
[tex]\text{Percent change}=-0.04189777\times 100[/tex]
[tex]\text{Percent change}=-4.189777\%[/tex]
[tex]\text{Percent change}\approx-4.19\%[/tex]
Therefore, the population changed by 4.19%.
Since the percent change is negative, therefore, the population decreased or shrank over the given period.
[tex]4.19\%=\frac{4.19}{100}=0.0419[/tex]
Please explain your answer thanks
Find the slope m of the tangent to the curve y = 8 + 4x2 − 2x3 at the point where x =
a.
Final answer:
The slope m of the tangent to the curve y = 8 + 4x² - 2x³ at the point where x = a is found by taking the derivative of y with respect to x, which yields m = 8a - 6a².
Explanation:
To find the slope m of the tangent to the curve y = 8 + 4x² − 2x³ at the point where x = a, we first need to compute the derivative of the function y with respect to x. The derivative of a function at a particular point gives us the slope of the tangent line at that point.
The derivative of y with respect to x is given by:
dy/dx = d(8 + 4x² - 2x³)/dx = 8x - 6x²
To find the slope at x = a, we substitute a into the derivative:
m = 8a - 6a²
So, the slope of the tangent line at the point x = a on the given curve is m = 8a - 6a²
How many squares with side length 1/4 inch will fit into 1 square inch?
How many squares with side length 1/4 inch will fit into 1 square inch?
A) 1
B) 16
C) 4
D) 25
The number of squares with side length 1/4 inch that would fit into a 1-square inch is 4
A square to a four-sided quadrilateral that has four equal sides. A square has four right angles. The sum of angles in a square add up to 360 degrees.
Area of a square = length²
Perimeter of a square = 4 x length
In order to determine how many squares would fit into the a 1 inch square, divide the length of the square by the 1/4
Number of squares = 1 ÷ 1 / 4
1 x 4 = 4 squares
Please find attached an image of a square. To learn more about a square, please check: brainly.com/question/21565373?referrer=searchResults
Describe how to graph a line given an equation in standard form.
Which ordered pair is the solution to the system of equations?
{y=x-4
{-4x+3y=-3
A.(0, −1)
B.(−9, −13)
C.(−6, −10)
D.(−6, 2)
Hope this helped...
MARK ME BRAINIEST PLEASE
Answer:
BThe center of the circle is A( -3,3) and B(1,6) is on the circle. Find the area of the circle in terms of pie
Find the average rate of change for f(x) = x2 + 9x + 18 from x = −10 to x = 10.
a.3
b.7
c.9
d.11
The average rate of change of the given function is 9.
Given that, a function f(x) = x²+9x+18, we need to find the average rate of change for the function given,
So, the average rate of change = f(b)-f(a) / b-a
Here, a and b are -10 and 10,
So, f(-10) = 100-90+18 = 28
f(10) = 100+90+18 = 208
So, the average rate of change = 208-28 / 10+10
= 180 / 20 = 9
Hence, the average rate of change of the given function is 9.
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Fran graphs the equations y = 2x2 – 2 and y = –0.5x + 4. Her graph is shown below.
Which value is an approximate solution of 2x2 – 2 = –0.5x + 4?
Answer:
A
Step-by-step explanation:
I just took the test
The point R is halfway between the integers on the number line below and represents the number ____. (Use the hyphen for negative numbers and write the answer as a decimal, such as -6.4).
The value of point R is -2.5 if point R is halfway between the integers on the number line; the answer is -2.5.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
It is given that:
The number line is shown in the picture.
Let the number is R which is halfway between the integers on the number line.
A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
R is between the integers -3 and -2:
R = (-3 + (-2))/2 = -5/2
R = -2.5
Thus, the value of point R is -2.5 if point R is halfway between the integers on the number line; the answer is -2.5.
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i will give brianliest
Lars bought 3 jars of marbles. Each jar has 42 marbles, of which 13 are red. Lars can use the calculation below to find the total number of red marbles.
3×(13×42)
How can Lars simplify the calculation using only the associative property of multiplication?
a1/3 b 3 c 42 d (3×13) e (13×42)
Answer:
3 times 1/3
Step-by-step explanation:
Help with number 6 and 7! Extra points and brainliest!!
Which is a rational function?
A. y=sqrt x-3
B. y=5
C. y=x^2-3x+5
D. y=x-5/x
Estimate the product of the expression below to the nearest whole number.
16.77 x 3.81
68
48
64
51
graph and solve the system
Y=-3x+3
Y=2x-7
In which sentence is the appositive phrase punctuated correctly?
A.) Raul’s new car the color of a ripe tomato sat in the driveway.
B.) Raul’s new car the color of a ripe tomato, sat in the driveway.
C.) Raul’s new car, the color of a ripe tomato, sat in the driveway.
D.) Raul’s new car, the color of a ripe tomato sat in the driveway.
The sentence that is an appositive phrase punctuated correctly is "Raul’s new car, the color of a ripe tomato, sat in the driveway." Option C is correct.
Given that,
Four punctuated phrases are given we have to determine which one is appositive.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
The sentence given in Options A, B. and D are not appositive.
Sentance Raul’s new car, the color of a ripe tomato, sat in the driveway is an appositive sentence because is differentiate the 3 string with 2 commas.
Thus, the sentence that is an appositive phrase punctuated correctly is "Raul’s new car, the color of a ripe tomato, sat in the driveway." Option C is correct.
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PLEASE PLEASE HELP IM LITERALLY CRYING.
Let f(x)=8x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down.
What is the equation for g(x)?
Enter your answer in the box.
g(x)= ????
Answer:
g(x) = 32x-7
Step-by-step explanation:
A vertical stretch is shown in an equation by multiplying the equation by a factor greater than 1. Since we are stretching by a factor of 4, we multiply the equation by 4:
g(x) = 4(8x) = 32x
A vertical translation is performed by subtracting a value from a function. To translate the function 7 units down, we will subtract 7 from the equation:
g(x) = 32x-7
The equation for g(x) = 32x - 7.
Given that,
Let f(x) = 8x,The graph of f(x) should be transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down.Based on the above information, the calculation is as follows:
g(x) = 4(8x)
= 32x
Now here we subtract 7 from the equation.
So, it is g(x) = 32x-7
Therefore we can conclude that the equation for g(x) = 32x - 7.
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Clara earns at least $36.75 but not more than $98 working. She earns $12.25 per hour. The number of hours it takes Clara to earn p dollars is modeled by a function. t(p)=p12.25 What is the practical range of the function?
The range of the function modelling the number of hours it takes clara to earn p dollars is;
A set of all real numbers from 3 to 8
Minimum dollars she earns working; p_min = $36.75
Maximum dollars she earns working; p_max = $98
number of hours it takes her to earn p dollars is given by;
t(p) = p/12.25
Now, range of a function is a set of all possible output values.
Thus, t(36.75) = 36.75/12.25
t(36.75) = 3 hours
Similarly;
t(98) = 98/12.25
t(98) = 8 hours
Since minimum time is now 3 hours and maximum time is now 8 hours, then the range of the function is;
3 ≤ t ≤ 8 which is a set of all real numbers from 3 to 8
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The product of the roots of 5 - 2m - 3m2 = 0 is:
Use Vieta's formulas:
[tex]ax^2+bx+c=0\\\\x_1\cdot x_2=\dfrac{c}{a}[/tex]
[tex]x_1;x_2[/tex]-the roots
We have
[tex]5-2m-3m^2=0\to a=-3;\ b=-2;\ c=5[/tex]
put the values of c and a to the expression:
[tex]m_1\cdot m_2=\dfrac{5}{-3}=-\dfrac{5}{3}[/tex]
Answer:
-2/3
Step-by-step explanation:
A political polling agency predicts candidate A will win an election with 54% of the votes. Their poll has a margin of error of 4% both above and below the predicted percentage. Which inequality represents the predicted possible percent of votes, x, for candidate A? 50 ≤ x ≤ 58 x ≥ 50 or x ≤ 58 x ≥ 52 or x ≤ 56 52 ≤ x ≤ 56
The inequality that represents the predicted possible percent of votes is 50 ≤ x ≤ 58
The margin of error (E) shows by how much the measured value can differ from the mean value.
Given that the probability of winning the election is 54% and there is a margin of error of 4%, hence:
Let x represent the predicted possible percent of votes.
x = 54% ± 4%
x = (54% - 4%, 54% + 4%)
x = (50%, 58%)
The inequality that represents the predicted possible percent of votes is 50 ≤ x ≤ 58
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The inequality representing the predicted possible percent of votes for candidate A is [tex]\( 50 \leq x \leq 58 \)[/tex].
The predicted possible percent of votes, x, for candidate A considering the margin of error can be represented as follows:
Given:
- Predicted percentage of votes for candidate A = 54%
- Margin of error = ±4%
The predicted range of percentages for candidate A can be expressed as:
[tex]\[ 54\% \pm 4\% \][/tex]
This translates to:
[tex]\[ 54\% - 4\% \leq x \leq 54\% + 4\% \][/tex]
Calculate the lower and upper bounds:
[tex]\[ 50\% \leq x \leq 58\% \][/tex]
Therefore, the inequality that represents the predicted possible percent of votes x for candidate A is [tex]\( \boxed{50 \leq x \leq 58} \)[/tex].
Complete question:- A political polling agency predicts candidate A will win an election with 54% of the votes. Their poll has a margin of error of 4% both above and below the predicted percentage. Which inequality represents the predicted possible percent of votes, x, for candidate A?
50≤ x≤ 58
x≥ 50 or x≤ 58
x≥ 52 or x≤ 56
52≤ x≤ 56
1. Which of the following could be an example of a function with a domain (-∞, ∞) and a range (-∞, 2)?
A. y= -(0.25)^x-2
B. y= -(3)^x-2
C. y= -(0.25)^x+2
D. y= -(3)^x+2