In the equation, the value of x is 4 and y is 1.
How to get the values?From the information given,
2x - y = 7. ...... i
x + 2y = 6 ....... ii
Multiply equation i by 1
Multiply equation ii by 2
2x - y = 7.
2x + 4y = 12
Subtract both equations
-5y = -5
y = -5/-5
y = 1
From equation i
2x - y = 7.
2x - 1 = 7
2x = 7 + 1
2x = 8
x = 8/2
x = 4
Therefore, x = 4 and y = 1
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Solve the system of equations using elimination: -x+3y=-24− and -4x+2y=4
Answer:
[tex]\begin{cases}x=-6\\y=-10\end[/tex]
Step-by-step explanation:
[tex]\begin{cases}-x+3y=-24 \left(1)\right\\-4x+2y=4 \left(2)\right\end[/tex]
Make x the subject in (1)
[tex]x=3y+24 \left(3)\right[/tex]
Sub into (2)
[tex]-4(3y+24)+2y=4\\\\\implies-12y-96+2y=4\\\\\implies10y=-100\\\\y=-10[/tex]
Sub into (3)
[tex]x=-30+24\\\\x=-6[/tex]
Hence
[tex]\begin{cases}x=-6\\y=-10\end[/tex]
Answer:
[tex]\left \{ {{x=-6} \atop {y=-10}} \right. .[/tex]
Step-by-step explanation:
[tex]\left \{ {{-x+3y=-24\ \ (1)} \atop {-4x+2y=4\ \ \ (2)}} \right. \ \ \ \ \\[/tex]
We multiply equation (1) by -4:
-x+3y=-24 |*(-4)
-x*(-4)+3y*(-4)=-24*-(-4)
4x-12y=96. (3) ⇒
[tex]\left \{ {{4x-12y=96\ \ (3)} \atop {-4x+2y=4\ \ \ (2)}} \right.[/tex]
We summarize equations (2) and (3):
[tex]-10y=100\ |:(-10)\\y=-10.\\Make\ y \ the\ subject\ in\ (1):\\-x+3*(-10)=-24\\-x-30=-24\\-x=-24+30\\-x=6\ |*(-1)\\x=-6.[/tex]
in the rectangle abcd, AC= -6x-2, BP= -4x-3, DP+ -6y-19 find the value of y
is that 2.11 I think so
Step-by-step explanation:
I don't know explain it to you and
In general, the greater the between group variance compared to the within group variance, the more likely you are to:
In general, the greater the between-group variance compared to the within-group variance, the more likely you are to find statistical significance.
Unlike the inside group version, where the focus is on the differences among a population and its implication, the between-organization variant is concerned with finding how the method of corporations differ from each other.
Inside-organization version (on occasion referred to as mistakes organization or error variance) is a time period used in ANOVA tests. It refers to variations because of variations within individual businesses (or ranges). In other words, no longer all of the values within every group (e.g. method) are equal.
With the purpose to examine multiple groups right away, we can study the ANOVA, or analysis of Variance. not like the t-test, it compares the variance within every sample relative to the variance between the samples.
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please help
PART A
(length of the foot) = 0.860 • (length of the forearm) + 3.302
17= 0.860 x 17 + 3.302= 17.922
If you let y = length of the foot and x = length of the forearm, this equation can be simplified to y = 0.860x + 3.302.
y = 0.860 (17) + 3.302= 17.922
PART B
Could the equation in Part A represent a function? Would this be a linear function? Why or why not? Explain your answer.
Answer:
PART A
length of foot = y
length of forearm = x = 17
Equation: y = 0.860x + 3.302
Plug in 17 for x in the equation, and simplify. Remember to follow PEMDAS, first multiply, then combine like terms:
y = (0.860)(17) + 3.302
y = 14.62 + 3.302
y = 17.922
length of foot = y = 17.922 inches long
f(x)=6x^3-4, g(x)=2x+2, find (g-f)(x)
The value of (g-f)(X) is 2x - 6x³ +6.
what is Function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
f(x)= 6x³-4, g(x)= 2x+2
Now,
(g-f)(x)= g(x)-f(x)
= 2x+2-( 6x³-4)
=2x+2- 6x³+4
=2x - 6x³ +6
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The graph represents a system of linear equations comparing the outside and inside temperatures y, in degrees Fahrenheit, recorded at a school one day x hours after 8:00 a.m.
A coordinate grid showing Daily Temperature with Hours after 8:00 a m on the horizontal, x axis and Temperature in degrees Fahrenheit on the vertical, y, axis. One line labeled Inside passes through (0, 70) and (8, 70). The second line passes through (0, 58) and passes through (8, 70).
After how many hours were the inside and outside temperatures equal?
6 hours
7 hours
8 hours
10 hours
Using linear functions, it is found that the temperatures would be equal after 8 hours.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Two functions are equal when they intersect. In this problem, both lines pass through point (8,70), that is, they have the same temperature(of 70 degrees) after 8 hours.
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Find the quotient:
15x²-3x
————
-3x
Enter the correct answer.
Answer:
-5x + 1
Step-by-step explanation:
Hello!
We can find the quotient by factoring the numerator, and cancelling common factors.
Simplify[tex]\frac{15x^2 - 3x}{-3x}[/tex][tex]\frac{(-3x)(-5x + 1)}{-3x}[/tex][tex]\frac{\not{(-3x)}(-5x + 1)}{\not{-3x}}[/tex][tex]-5x +1[/tex]The quotient is (-5x + 1).
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{\dfrac{15x^2 - 3x}{-3x}}[/tex]
[tex]\huge\textbf{Simplify the current equation:}[/tex]
[tex]\mathbf{= \dfrac{-3x(-5x + 1)}{-3x}}[/tex]
[tex]\huge\textbf{Cancel out \boxed{\bf -3x} \& simplify it:}[/tex]
[tex]\mathbf{= \dfrac{-15x + 3}{3}}[/tex]
[tex]\huge\textbf{Simplify that above:}[/tex]
[tex]\mathbf{= -5x + 1}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{-5x + 1 }}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Please please please help i need help asap im so lost
if x^3 - 7x + 16x - 12 + (x-a) (x-b) (x-c) for all values of x, what is the value of abc?
[tex](x - a)(x - b)(x - c) \\ (x {}^{2} - bx - ax + ab)(x - c) \\ x {}^{3} - bx {}^{2} - ax {}^{2} + abx - cx {}^{2} + cbx + cax - abc[/tex]
[tex]x {}^{3} + ( - a - b - c)x {}^{2} + (ab + cb + ca)x - abc [/tex]
[tex] - a - b - c = - 7 \\ ab + ac + bc = 16 \\ - abc = - 12 \: \: \: \: \: abc = 12[/tex]
( a , b , c ) = ( 2 , 2 , 3 )A graph titled Cost of a Lunch in a School's Cafeteria has Days since school started on the x-axis and cost of lunch (dollars) on the y-axis. A horizontal line is at y = 2.5.
Which is correct about the graph’s slope?
Its slope is positive.
Its slope is negative.
Its slope is zero.
It has no slope.
The true statement about the graph's slope is (c) Its slope is zero.
How to determine the true statement?From the question, we have:
A horizontal line is at y = 2.5.
The horizontal line implies that the cost of lunch do not change
Horizontal lines have a slope of 0
Hence, the true statement about the graph's slope is (c) Its slope is zero.
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In Mr. Romano's class, the ratio of the number of girls to the number of boys is 3:2. A student is selected at random from
the class. The probability that the selected student is a boy is
F. 1/6
G. 1/3
H. 2/5
J. 3/5
K. 2/3
PLEASE HELP ME ASAP!!!!!
find the mean of factors of 16
Answer:
The answer is 6.2
Step-by-step explanation:
The factors of 16 are 1,2,4,8, and 16.
get the sum of the factors which is 31, then divide it to number of the addends which is 5.
31/5 = 6.2
Simplify the expression write the answer using scientific notation (8x10^7)(2x10^6)
Answer:
Second option 1.6x10^14
Step-by-step explanation:
Can I Please Get Help I Need The Units With The Answer Too
The rate of change of the the given table is: 3/4soda per dollar.
What is the Rate of Change?Rate of change = change in total cost / change in number of sodas.
Using (24, 18) and (28, 21), we would have:
Rate of change = (21 - 18)/(28 - 24)
Rate of change = 3/4
Therefore, the rate of change is 3/4soda per dollar.
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Question 8 c
A bag of tokens contains 7 red, 9 green, and 6 blue tokens. What is the probability that
a randomly selected token is not red? Enter your answer as a fraction.
11. Find the slope of the line that passes through the pair of points. (2, 6), (7, 0)
[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]
Find the slope of the line that passes through the pair of points.
[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]
In this problem we have two points given to us, which are...
(2,6)(7,0)... and we should find the slope.
[tex]\bf{We\;will\;use\;the\;Slope-Equation:}\\m=\dfrac{y2-y1}{x2-x1}[/tex]
[tex]\bf{\dfrac{0-6}{7-2}=\dfrac{-6}{5} =-\dfrac{6}{5}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Slope:}[/tex]
[tex]\bf{=-\dfrac{6}{5}}[/tex]
[tex]\boxed{\bf{aesthetic \not101}}[/tex]
2. Match each transformation with the correct description
A. (x,y) → (3x, y)
B. (x,y) → (x + 3, y)
C. (x,y) → (x, 3y)
D. (x,y) →
(x, y + 3)
E. (x,y) → (3x, 3y) d
—
—▬▬▬▬▬
dilation with scale factor 3
translation 3 units up
translation 3 units right
horizontal stretch by a factor of 3
vertical stretch by a factor of 3
PLS IF YOU CAN HELP WITH THE TWO QUESTION THAT WOULD BE GREAT
Answer:
Step-by-step explanation:
The Matching for each transformation is
1. (x,y) → (3x, y)
horizontal stretch by factor 3.
2. (x,y) → (x + 3, y)
translation 3 unit right
3. (x,y) → (x, 3y)
Vertical stretch by factor 3.
4. (x,y) → (x, y + 3)
translation 3 unit up.
5. (x,y) → (3x, 3y)
dilation with Scale factor 3.
What is Transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
1. (x,y) → (3x, y)
It is horizontal stretch by factor 3.
2. (x,y) → (x + 3, y)
It is translation 3 unit right because the rule for translation for 3 unit right is x - > x + a
3. (x,y) → (x, 3y)
It is Vertical stretch by factor 3.
4. (x,y) → (x, y + 3)
It is translation 3 unit up.
5. (x,y) → (3x, 3y)
It is dilation with Scale factor 3.
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Which numbers are the means of the proportion shown below?
213
818
3 30
A. 2 and 30
B. 3 and 30
C. 2 and 20
D. 3 and 20
The numbers which are the means of the proportion as given in the task content are in; Choice D; 3 and 20
Which numbers are the means of the proportion shown below?It follows from the task content that the proportion whose mean is to be evaluated in the task content is; 2/3 = 20/30.
On this note, it follows that the numbers 2 and 30 are the lower and upper extremes of the property and hence, 3 and 20 are the mean of the proportion.
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What is the equation of a line passing through (-3, 7) and having a slope of 5 ?
Answer:
B
Step-by-step explanation:
since the slope is 5, 1/5x or -1/5x cannot be the slope. since the slope isn't negative it also cancels out -5x. 5x can be your only slope and that is in answer B.
A shopkeeper bought two watches for rs. 400.he sold them to gain 5 percent on one and lose 5 percent on the other .calculate his final gain or loss lercent if the sp of both watches is the same.
The final loss percent is 0.25%.
What is the final loss percent?The gap between the cost price and the selling price is what is referred to as a loss. And the loss percent is the loss as a percentage of the actual cost.
Total CP=Rs. 400
Let the CP of the first watch be Rs. x
So, CP of the second watch=Rs.(400-x)
For the first watch,
Gain Percent=5%
SP = [tex](1+\frac{5}{100})*x[/tex]
SP=105x/100
For the second watch,
Loss Percent=5%
SP=[tex](1-\frac{5}{100})(400-x)[/tex]
SP=95(400-x)/100
As the SP of both the watches is the same.
[tex]\frac{105}{100}x=\frac{95}{100}(400-x)[/tex]
105x=38000-95x
105x+95x=38000
200x=38000
x=38000/200
x=190
CP of the first watch=Rs. 190
CP of the second watch=Rs. (400-190)=Rs. 210
SP of first watch=[tex]\frac{105}{100}*190[/tex] =Rs. 199.50
SP of second watch=[tex]\frac{95}{100}*210[/tex]=Rs. 199.50
Total SP=Rs. 399
Final Loss=Total CP-Total SP
=Rs.(400-399)
=Rs. 1
Final Loss Percent=100/400
=0.25%
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The lighthouse and the boat shown below
are 24.6 km apart.
The boat is 13.5 km east of the lighthouse.
Work out the bearing of the lighthouse from
the boat.
Give your answer to the nearest degree.
|FFFFLD
Lighthouse
N
Boat
Not drawn accurately
Answer:
213°
Step-by-step explanation:
Consider the angle measured at the lighthouse between North and the Boat. The lengths given in the problem statement are the lengths of the side opposite that angle, and the length of the hypotenuse of the right triangle shown. The trig function that relates the angle and those sides is ...
Sin = Opposite/Hypotenuse
ApplicationThe sine of the angle at the lighthouse is ...
sin(bearing to boat) = (13.5 km)/(24.6 km) = 45/82
The value of the angle is found using the inverse sine function, called the arcsine function:
bearing to boat = arcsin(45/82) ≈ 33°
Reverse bearingThe bearing from the boat to the lighthouse is in the opposite direction. It can be found by adding 180° to this angle:
bearing to lighthouse = 33° +180° = 213°
__
Additional comment
The attached image shows a calculator making this calculation. Note that the angle mode is set to DEG (lower left corner). The arcsine function is usually found as the 2nd function of the Sin key.
Guys help me with this problem, please. I really need help right now.
Answer:
A
Step-by-step explanation:
So whenever you're finding the difference between two numbers you generally use the equation: |a-b| since a-b may or may not be negative, but |a-b| will always equal |b-a|. Since the only thing that differs is the sign. So when you have: [tex]|-\frac{2}{3}-\frac{5}{3}|[/tex], in this case a=-2/3 and b=5/3 (b is positive since you're subtracting b, so if b appeared positive in the equation, it's actually negative, since the negative sign in |a-b|, which would make the two negatives cancel out). This means A is the correct answer. You could also calculate what the value is. Calculating gives you: [tex]|-\frac{7}{3}| = \frac{7}{3}[/tex]. And as you can see the top one, has two numbers separated by 7 one thirds.
Answer:
A
Step-by-step explanation:
It is absolute value and when it is absolute value, it is positive.
Determine the vertex of the quadratic relation y=2(x+2)(x-6).
Answer:
vertex = (2, - 32 )
Step-by-step explanation:
given a quadratic function in standard form
y = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
given
y = 2(x + 2)(x - 6) ← expand factors using FOIL
= 2(x² - 4x - 12 ) ← distribute parenthesis
y = 2x² - 8x - 24 ← in standard form
with a = 2, b = - 8 , then
x = - [tex]\frac{-8}{4}[/tex] = 2
substitute x = 2 into the function for corresponding y- coordinate
y = 2(2 + 2)(2 - 6) = 2(4)(- 4) = 8 × - 4 = - 32
vertex = (2, - 32 )
In Washington County, 850 homes were sold in 2017. How many homes were sold in the Southwest region?
A)102
B)1,020
C)1,231
D)588
Option A is correct answer; i.e. 102 homes were sold in 2017.
What is Pie Chart?A pie chart is a type of graph that records data in a circular manner that is further divided into sectors for representing the data of that particular part out of the whole part.
Here,
Total Homes sold in 2017 = 850 homes.
Homes sold in Southwest region = 12 % of the total.
= 0.12 X 850
= 102.
Thus, option A is correct answer; i.e. 102 homes were sold in 2017.
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1. The following diagram shows a slide at a park. a. Find the vertical distance from the ground to the top of the slide. b. Find the length of the slide. c. What is the area of the space under the slide. Steps 2 m /70* Slide 40° H
The area of the space under the slide is 2.10 square meters
The vertical distanceThe diagram in the question is added as an attachment
The vertical distance is represented by h.
So, we have:
sin(70) = h/2
Solve for h
h = 2 * sin(70)
Evaluate
h = 1.88 m
Hence, the vertical distance is 1.88 m
The length of the slideThis is calculated using
sin(40) = h/Slide
This gives
sin(40) = 1.88/Slide
Solve for Slide
Slide = 1.88/sin(40)
Evaluate
Slide = 2.92
Hence, the length of the slide is 2.92 m
The area of the space under the slideThis is calculated using:
A = 0.5 * h * slide * sin(∅)
Where
∅ = 90 - 40 = 50
So, we have:
A = 0.5 * 1.88 * 2.92 * sin(50)
Evaluate
A = 2.10
Hence, the area of the space under the slide is 2.10 square meters
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Perpendicular bisector: put the following steps in order using what you know about constructing a perpendicular bisector.
In order to draw a perpendicular bisector you must have ruler , compass and a pencil.
Given nothing and we have to show the steps to draw a perpendicular bisector.
Perpendicular bisector is the line which divides the line into two equal parts and makes 90° angle on other line.
If we want to make a perpendicular bisector on a line then we have to follow the following steps:
1) First draw a line with the help of ruler on which we want to make perpendicular bisector.
2) Now take a compass and a pencil.
3) Put the pencil in the compass and strech the compass equal to half or little more of the length of the line.
4) Now put the compass on one end of the line and draw an arc on the line or may be just upward.
5) Now repeat the step 4 from other end.
6) Now draw a line from the point where two arcs intersects on the line.
7) It is the perpendicular bisector of the line.
Hence to draw a perpendicular bisector we require compass, ruler and a pencil.
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Mackenzie is a waitress at a restaurant. Each day she works, Mackenzie will make a guaranteed wage of $25, however the additional amount that Mackenzie earns from tips depends on the number of tables she waits on that day. From past experience, Mackenzie noticed that she will get about $15 in tips for each table she waits on. How much would Mackenzie expect to earn in a day on which she waits on 13 tables? How much would Mackenzie expect to make in a day when waiting on tt tables?
Answer: If she waits on 13 tables than she should expect to earn $220
Step-by-step explanation:
15*13=195
195+25=220
Below is the graph of y=b^x. Find b.
b=
Answer: 1
Step-by-step explanation:
When [tex]x=0[/tex], [tex]y=\boxed{1}[/tex]
please can someone help me
Answer: A=48 squared centimeters
Step-by-step explanation: First you need to find the area of the whole rectangle. Area equals length times width (9*8), which is 72. Next you find the area of the white region: 4*6=24. Finally, you subtract the smaller region from the whole: 72-24=48. BOOM: you got the exact right answer :)
Work out the volume of the cone, giving your answer
to 3 significant figures.
Answer: 1010
Step-by-step explanation:
[tex]V=\frac{1}{3}(\pi)(8^{2})(15) \approx \boxed{\text{ } 1010 \text{ cm}^{3}}[/tex]