ANSWER
The set of equations has no solution
EXPLANATION
-3x + 5y = -8 ------ equation 1
6x - 10y = 16 -------- equation 2
These two equations can be solve simultaneously either by substitution method or elimination method
To solve for the value of x and y, we will be using the elimination method
-3x + 5y = -8
6x - 10y = 16
Let us eliminate x first.
We need to make the coefficient of x in both equation equal
Hence, multiply equation 1 by 2 and equation 2 by 1
-3x*2 + 5y*2 = -8 x 2
6x * 1 - 10y * 1 = 16 x 1
-6x + 10y = -16 ------------ equation 3
6x - 10y = 16 -------------- equation 4
To eliminate x , add equation 3 and 4 together
-6x + 6x + 10y + (-10y) = -16 + 16
-6x + 6x + 10y - 10y = -16 + 16
0 + 0 = 0
0 = 0
Hence, the set of equations has no solution
A researcher studied the relationship between the number of times a certain species of cricket will chirp in one minute and the temperature outside. Her data is expressed in the scatter plot and line of best fit below. What is the meaning of the yy-value on the line when x=80x=80?
The line of best fit approximates the relationship between the independent and the dependent variables. Here, the x-values give us the number of chirps per minute while the y-values give us the temperature in degrees Fahrenheit.
When x = 80, the number of chirps per minute is 80. The corresponding y is approximately 62.5 degrees Fahrenheit, which is the predicted temperature when the x-value is 80.
So, the answer is the first option: The predicted temperature in degrees Fahrenheit if the cricket has chirped 80 times.
Hello!I have (m^3n^5)^1/4 and I do not know how to take the n out since it is n^5/4.Thanks
We are given
[tex](m^3n^5)^{\frac{1}{4}}[/tex]
We want to take n out
Solution
Given
[tex]\begin{gathered} (m^3n^5)^{\frac{1}{4}} \\ (m^3\times n^4\times n)^{\frac{1}{4}} \\ (m^3)^{\frac{1}{4}}\times(n^4)^{\frac{1}{4}}\times(n)^{\frac{1}{4}} \\ (m^3)^{\frac{1}{4}}\times n^{}\times(n)^{\frac{1}{4}} \\ n\times(m^3)^{\frac{1}{4}}^{}\times(n)^{\frac{1}{4}} \\ n(m^3n)^{\frac{1}{4}} \end{gathered}[/tex]Describe how the graph of y = ln (-x) relates to the graph of its parent function y = ln x.
The graph of function f(-x) can be obtained from graph of pareant funcion f(x) by refecting the graph over y-axis.
We need to obtain the graph of ln (-x) from parent function ln x, which is nothing but replace of x by -x. So graph of ln (-x) is obtained by reflection of graph of function ln (x) over y-axis.
Answer: y-axis reflection
Q4 O center (-1,3), radius = 1 What is the center and radius of the circle, 2 2 r + y + 2x - 6y +9=0 - 9 center (1,-3), radius = 1 center (-1,3), radius = 9 center (1,-3), radius = 3
Step 1: Write out the formula
The equation of a circle given by
[tex](x-a)^2+(y-b)^2=r^2[/tex][tex]\begin{gathered} \text{where} \\ (a,b)\text{ is the center of the circle} \\ r\text{ is the radius of the circle} \end{gathered}[/tex]Step 2: Write out the given equation and rewrite it in the form shown above
[tex]x^2+y^2+2x-6y+9=0[/tex][tex]\begin{gathered} x^2+2x+y^2-6y+9=0 \\ \text{ By completing the square, we have} \\ (x+1)^2-(+1)^2+(y-3)^2-(-3)^2+9=0 \\ \end{gathered}[/tex][tex]\begin{gathered} (x+1)^2+(y-3)^2-1-9+9=0 \\ (x+1)^2+(y-3)^2=1=1^2 \end{gathered}[/tex]By comparing the equation with the formula above, we have
[tex]a=-1,b=3,r=1[/tex]Therefore,
center (-1,3), radius = 1
Find the sales tax.
Sales Tax
Selling Price Rate of Sales Tax Sales Tax
$70.00
3%
?
The sales tax is $.
Answer: $2.10
Step-by-step explanation: 3% of $70 is $2.10.
The total cost would be $72.10
How to calculate percentages:
Divide the number that you want to turn into a percentage by the whole. In this example, you would divide 2 by 5. 2 divided by 5 = 0.4. You would then multiply 0.4 by 100 to get 40, or 40%.
x + y + zX=5 y=3 z=7
please i need your help i will appreciate it
The value of c is 5/2 that satisfy the conclusions of the mean value theorem.
Given Function:
f(x) = x^2-3x+3 on interval [1,4].
The Mean Value Theorem states that for a continuous and differentiable function f(x)=x^2-3x+3 on the interval [1,4] there exists such number c from the interval [1,4] that [tex]f'(c)=\frac{f(4)-f(1)}{4-1}[/tex].
f(4) = 4^2-3*4+3
= 16-12+3
= 4+3
= 7
f(1)=1^2-3*1+3
= 1-3+3
= 1
f'(c) = 2c -3
2c-3 = 7 - 1 / 4 - 1
2c - 3 = 6/3
2c -3 = 2
2c = 5
c = 5/2
Therefore the value of c = 5/2 that satisfy the conclusions of the mean value theorem.
Learn more about the mean value theorem here:
https://brainly.com/question/1581272
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Determine which of the following statements is NOT correct
THe statement that is not correct is the first one
A bag contains 6 apples and 4 bananas. If two fruits are drawn one by one with replacement, find the probability that the first one is an apple and the second one is banana.
we have
probability first one is an apple:
[tex]\frac{6}{6+4}=\frac{6}{10}[/tex]probability the second one is banana:
[tex]\frac{4}{6+4}=\frac{4}{10}[/tex]therefore, the probability that the first one is an apple and the second one is banana:
[tex]\frac{6}{10}\times\frac{4}{10}=\frac{24}{100}=\frac{6}{25}[/tex]answer: 6/25
can you please help me
Answer
The graph of y = -3x + 1 is presented below
Explanation
We are asked to plot the graph of y = -3x + 1
We will use intercepts to obtain two points on the line and connect those two points
y = -3x + 1
when x = 0
y = -3x + 1
y = -3(0) + 1
y = 0 + 1
y = 1
First point on the line is (0, 1)
when y = 0
y = -3x + 1
0 = -3x + 1
3x = 1
Divide both sides by 3
(3x/3) = (1/3)
x = ⅓ = 0.333
Second point on the line is (⅓, 0) or (0.333, 0)
The graph of this question is presented under 'Answer' above.
Hope this Helps!!!
Liam wants to find the average of the following numbers. 53, 46, 57, 52, 49 He estimates the average as 50 and then finds the average. Which describes how close Liam is to his estimate?
You find the average by adding all of the numers and then divide by the ammount of numbers that were added:
[tex]A=\frac{53+46+57+52+49}{5}\Rightarrow A=51.4[/tex]So the average is 51.4 and therefore Liam was off by 1.4 units.
Given the definitions of f(x) and g(2) below, find the value of g(f(-3))f(x) = -3x – 12g(x) = 3x2 – 2x – 14
Given data:
Itis given that
[tex]\begin{gathered} f(x)=-3x-12 \\ g(x)=3x^2-2x-14 \end{gathered}[/tex]Now to calcualte g(f(-3)) first let us calculate f(-3)
[tex]\begin{gathered} f(-3)=-3(-3)-12 \\ =9-12 \\ =-3 \end{gathered}[/tex]Now, g(f(-3)) will be
[tex]\begin{gathered} g(f(-3))=g(-3) \\ =3(-3)^2-2(-3)-14 \\ =3(9)+6-14 \\ =27-8 \\ =19 \end{gathered}[/tex]So, value of g(f(-3)) is 19.
in the figure shown Sigma MN is parallel to y z what is the length of segment MX
We will solve for MX using similar angles theorem
Let line MX be= y
we have to find the ratio of the small triangle to that of the big triangle
Therefore we will have,
[tex]\begin{gathered} \frac{\text{xcm}}{(x+12)cm}=\frac{3.5\operatorname{cm}}{17.5\operatorname{cm}} \\ \text{when we cross multiply we wil have,} \\ 17.5\times x=3.5(x+12) \\ 17.5x=3.5x+42 \\ by\text{ collecting like terms we wll have} \\ 17.5x-3.5x=42 \\ 14x=42 \end{gathered}[/tex]to get x we divide both sides by the coefficient of x which is 14
[tex]\begin{gathered} \frac{14x}{14}=\frac{42}{14} \\ x=3.0\operatorname{cm} \end{gathered}[/tex]Hence ,
[tex]\vec{MX}=3.0\operatorname{cm}[/tex]Therefore,
The correct option will be OPTION A
According to a report from a particular university, 46% of female undergraduates take on debt. Find the probability that none of the female undergraduates have taken on debt if 9female undergraduates were selected at randomWhat probability should be found?MA PO female undergraduates take on debt)OB P(9 female undergraduates take on debt)OC P(1 female undergraduate takes on debt)OD P(2 female undergraduates take on debt)The probability that none of the female undergraduates take on debt is I(Type an integer or decimal rounded to three decimal places as needed)1}0vo(0.MorexHelp Me Solve ThisView an ExampleGet More HelpClear AllCheck Answer
For this exercise we use the probability function of the binomial distribution, also called the Bernoulli distribution function, is expressed with the formula:
[tex]P(x)=\frac{n!}{(n-x)!\cdot x!}\cdot p^x\cdot q^{n-x}[/tex]Where:
• n, = the number of trials
,• x, = the number of successes desired
,• p,= probability of getting a success
,• q, = probability of getting failure
From the exercise we can identify:
[tex]\begin{gathered} n=9 \\ x=0 \\ p=0.46 \\ q=1-p \\ q=0.54 \end{gathered}[/tex]Replacing in the equation of the binomial distribution:
[tex]\begin{gathered} P(0)=\frac{9!}{(9-0)!\cdot0!}\cdot(0.46)^0\cdot(0.54)^{9-0} \\ P(0)=0.0039 \\ P(0)=0.004 \end{gathered}[/tex]The answer is P(0 female undergraduates tak on debt)
5. Input Output 4 3 3 1
It is not a function because a function should assign one element in the domain to one and only one in the range.
Rewrite the equation below so that it does not have fractions. 3+ = x= = Do not use decimals in your answer.
First we have to find the least common multiple between the denominators ( 3 and 7). Since they are prime numbers the LCM is : 3*7 = 21
Then, multiply each term of the equation by 21 and simplify
[tex]\begin{gathered} 3\cdot21+21\cdot\frac{2}{3}x=\frac{2}{7}\cdot21 \\ 63+7\cdot2x=2\cdot3 \\ 63+14x=6 \end{gathered}[/tex]The answer is 63 + 14x = 6
Solve the system of two linear inequalities graphically.{x<5<2x - 4Step 1 of 3: Graph the solution set of the first linear inequality.Answer3 KeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. Theregions will be added once the line is drawn.HOANChoose the type of boundary line:O Solid (-)Dashed ---)SEnter two points on the boundary line:10-5ज510JOO5Select the region you wish to be shaded:ОАOB101
From the problem, we have :
[tex]\begin{gathered} x<5 \\ x\ge-4 \end{gathered}[/tex]For the first inequality, x < 5
Since the symbol is "<", the boundary line is dashed line.
The boundary line is at x = 5 which has points (5, 0) and (5, 2)
and the region is to left of x = 5.
The graph will be :
Next is to graph the second inequality, x ≥ -4
Since the symbol is "≥", the boundary line is a solid line
The boundary line is at x = 4 which has points (-4, 0) and (-4, 2)
and the region is to the right.
The graph will be :
The solution to the inequalities is the overlapping region when joined together.
This will be :
The overlapping region is the middle region or region in between the boundary line which is also -4 ≤ x < 5
Calculate the limitlim x => -4 [tex] \frac{x {}^{2} + 2x - 8}{x {}^{2} + 5x + 4} [/tex]
The limit to be calculated is:
[tex]\lim _{x\to-4}\frac{x^2+2x-8}{x^2+5x+4}[/tex]Notice that:
[tex]\begin{gathered} \frac{x^2+2x-8}{x^2+5x+4}=\frac{(x-2)(x+4)}{(x+1)(x+4)} \\ =\frac{(x-2)}{(x+1)},x\ne-4 \end{gathered}[/tex]Remember that, in the limit when x->-4, the value of x approaches to -4, but it never is -4. Thus, we can use the last line of the identity above,
[tex]\begin{gathered} \Rightarrow\lim _{x\to-4}\frac{x^2+2x-8}{x^2+5x+4}=\lim _{x\to-4}\frac{(x-2)(x+4)}{(x+1)(x+4)}=\lim _{x\to-4}\frac{(x-2)}{(x+1)}=\frac{(-4-2)}{(-4+1)}=-\frac{6}{-3}=2 \\ \Rightarrow\lim _{x\to-4}\frac{x^2+2x-8}{x^2+5x+4}=2 \end{gathered}[/tex]The answer is 2.
Use a net to find the surface area of the prism.25 cm3.5 cm13 cmThe surface area of the prism is (Simplify your answer.)
A rectangle prism of sides 25, 3.5 and 13 cm can be drawn as:
It will have 6 faces (4 lateral, a base and a top face)
Each face has a surface area that is the product of two of the sides. We have two faces for each pair of sides.
So if we have sides a, b and c, the surface area can be written as:
[tex]S=2(a\cdot b+a\cdot c+b\cdot c)[/tex]With the sides of our prism we can calculate the surface area as:
[tex]\begin{gathered} S=2(25\cdot3.5+25\cdot13+3.5\cdot13) \\ S=2(87.5+325+45.5) \\ S=2\cdot458 \\ S=916\operatorname{cm}^2 \end{gathered}[/tex]Answer: The surface area of the prism is 916 cm^2
The volume of a large tank is 350 ft. It is 65 ft wide and 4 ft high. What is the length of the tank?
The volume of a rectangular prism can be calculated by the formula
[tex]V=l\cdot w\cdot h[/tex]in which l, w and h represent the length, width, and heght respectively.
clear the equation for l
[tex]l=\frac{V}{w\cdot h}[/tex]replace with the data given
[tex]undefined[/tex]The Voronoi diagram below shows the locations of the four post offices P_{1} , P_{2} P_{3} , and P_{4}in a city.y(km)8P_{3}P2r (km)6P_{1}PKatie's apartment lies inside the shaded circle shown on the diagram.(a) Write down the post office nearest to Katie's apartment.P is located at coordinates (3-6), and the edge between P and P_{i} has the equation y = - 5/3 * x = 16/3(b) Determine the location of PPa is located at coordinates (1.7).3(c) Find the gradient. A. of the edge between P, and P.
Given -
Voronoi diagram:
To Find -
(a) Write down the post office nearest to Katie's apartment.
(b) Determine the location of P4
(c) Find the gradient k. of the edge between P3 and P4
Step-by-Step Explanation -
(a)
We can see from the voronoi diagram that the center of the x-axis where the circle covers is where Katie's apartment is located.
It is located near P4.
So,
P4 is nearest to Katie's apartment.
(b)
The location of P4:
(2, -3)
(c)
[tex]k\text{ = }\frac{Y_2\text{ - Y}_1}{X_2\text{ - X}_1}\text{ = }\frac{7}{50}[/tex]Final Answer -
(a) The post office nearest to Katie's apartment = P4
(b) The location of P4 = (2, -3)
(c) The gradient k of the edge between P3 and P4 = 7/50
Martha drove her car east for a total of 9 hours at a constant velocity. In one-third of that time, she drove 180 kilometers. What was her velocity?
time = one third of 9 hours = 1/3 x 9 = 3 hours
Distance = 180 km
Velocity = Distance / time
Replacing:
V = 180 km/3 h = 60 km per h
what is .8 divided by 40
Problem
0.8 divided 40
Solution
We can do the following:
[tex]\frac{0.8}{40}=\frac{0.8\cdot10}{40\cdot10}=\frac{8}{400}[/tex]and if we simplify we got:
[tex]\frac{8}{400}=\frac{4}{200}=\frac{2}{100}=\frac{1}{50}=0.02[/tex]Daniel and his mother flew fromMiami, Florida to Maine to visit family.When they left Miami, the temperaturewas 84°. When they arrived in Maine itwas -7°. What was the temperaturechange Daniel and his mother?
the temperature change will be the difference or the subtraction between bout temperatures so it will be:
[tex]84-(-7)=91º[/tex]so there are 91º of temperature difference
evaluate [tex]3 {x}^{2} - 4[/tex]when x=2.
3x^2 - 4 , at 2 is = 3•2^2 - 4
. = 12 - 4 = 8
Law of Exponents. Simplify each expression. Answers should be written with positive exponents.(-5p^6 times r^-9)^0
Solution:
Given the expression:
[tex](-5p^6\cdot r^{-9})^0[/tex]Simplifying using the law of exponents,
[tex]\begin{gathered} (-5p^6\cdot r^{-9})^0=(-5\times p^{-6}\times r^{-9})^0 \\ \end{gathered}[/tex]but
[tex]a^{-b}=\frac{1}{a^b}[/tex]thus, we have
[tex]\begin{gathered} (-5\times p^{-6}\times r^{-9})^0=(-5\times\frac{1}{p^6}\times\frac{1}{r^9})^0 \\ =(-\frac{5}{p^6r^9})^0 \end{gathered}[/tex]From the zero index law of exponents,
[tex]a^0=1[/tex]This implies that
[tex](-\frac{5}{p^6r^9})^0=1[/tex]Hence, the solution to the expression is 1
If x decreases by 3 units what is the corresponding change in y ?
We have the equation:
[tex]y=6x-2[/tex]The rate of change in linear functions like this is equal to the slope, which in this case is m = 6.
So, for each unit increase in x, y will increase in 6 units.
[tex]\Delta y=m\cdot\Delta x=6\cdot1=6[/tex]This rate of change is constant for linear functions, so when x decreases by 3 units, we expect y to decrease by 3*6 = 18 units, 3 times the slope. So y will be -18 of the previous value.
[tex]undefined[/tex]Answer: a) 6, b) -18.
chance the pilot of a boeing 727 flew e plane so it took off at an angle of elevation 21 degrees. after flying one kilometer, what is the altitude (height) of the plane that chance was flying rounded to the nearest meter? (1 km= 1000 meters)
To solve the exercise, it is convenient to first draw a picture of the situation posed by the statement:
As you can see, a right triangle is formed. So to find the height at which the plane was when the pilot had flown one kilometer, you can use the trigonometric ratio sin(θ):
[tex]\sin (\theta)=\frac{\text{Opposite side}}{\text{ Hypotenuse}}[/tex]Then, in this case, you have
[tex]\begin{gathered} \sin (21\text{\degree})=\frac{\text{ Altitude}}{1000m} \\ \text{ Multiply by 1000m on both sides of the equation} \\ \sin (21\text{\degree})\cdot1000m=\frac{\text{ Altitude}}{1000m}\cdot1000m \\ \sin (21\text{\degree})\cdot1000m=\text{ Altitude} \\ 358.37m=\text{ Altitude} \\ \text{ Rounding to the nearest meter} \\ 358m=\text{ Altitude} \end{gathered}[/tex]Therefore, the altitude or height of the plane after flying one kilometer is 358 meters.
Solve each system of equations using linear combination.1.3x +5y = 82x - 5y = 22
x = 6, y = -2
Explanations:The given system of equations is:
3x + 5y = 8..................................(1)
2x - 5y = 22................................(2)
Add equations (1) and (2) together
(3x + 5y) + (2x - 5y) = 8 + 22
3x + 2x + 5y - 5y = 30
5x = 30
x = 30/5
x = 6
Substitute x = 6 into equation (1)
3x + 5y = 8
3(6) + 5y = 8
18 + 5y = 8
5y = 8 - 18
5y = -10
y = -10/5
y = -2
The solution to the system of equations is:
x = 6, y = -2
find the equation of the line with slope 6 and containing the point (3,1). Write the equation in function notation
ANSWER
f(x) = 6x - 17
EXPLANATION
The equation of a line with slope m and y-intercept b is:
[tex]f(x)=mx+b[/tex]We know the slope of this line, m = 6, so we have this equation:
[tex]f(x)=6x+b[/tex]To find the y-intercept we have to replace f and x with the given point: f(3) = 1:
[tex]\begin{gathered} 1=6\cdot3+b \\ 1=18+b \\ b=1-18 \\ b=-17 \end{gathered}[/tex]The equation is:
[tex]f(x)=6x-17[/tex]