Answers
-3x + y = 2 Equation (1)
7x -8y = 1 Equation (2)
Let us solve the system of equations with the elimination method.
-24x + 8y = 16 (Multiplying the equation 1 by 8)
+ 7x - 8y = 1 (Adding the equation 2 to the last form of the equation 1)
------------------
-17x = 17 (Adding like terms)
x = 17/(-17) ( Dividing by -17 on both sides of the equation)
x= -1
Replacing x=-1 in the equation 1,we have:
-3(-1) + y = 2
3 + y = 2 (Multiplying and using the sign rules)
y = 2- 3 (Subtracting 3 from both sides of the equation)
y = -1 (Subtracting)
The answers are x=-1 and y=-1
Related Questions
A small bicycle manufacturer has daily fixed costs of $1913 and each bicycle costs $80 to manufacture. Let x represent the number of bicycles manufactured and C(x) represents the cost of manufacturing. (a) Write a linear function that models this situation.C(x)= _____(b) Find C(5). Interpret your answer in the context of this problem.C(5)=____. This means that the cost of manufacturing ____ bicycles in a day is $_____
Answers
From the question we can derived the folllowing:
Fixed cost of manufacturing the bicycles = $1913
Variable cost of manufacturing one bicycle = $80
So let's the number of bicycles manufactured = x
Total cost of manufacturing bicycles = C(x)
(a) C(x) can be expressed as:
C(x) = 1913 + 80 * x
C(x) = 1913 + 80x
(b) Find C(5)
Recall, C(x) = 1913 + 80x
C(5) = 1913 + 80 * 5
C(5) = 1913 + 400
C(5) = 2313
(c) C(5)___ This means that the cost of manufacturing ______ bicycles in a day is $_____?
This means that the cost of manufacturing 5 bicycles in a day is $2313
IM BAD AT GEOMETRY I NEED ALL THE HELP I CAN GET
Answers
a )
m < DOA
X + 30 + 30 =180
X + 60 = 180
X = 180 -60
X =120 degrees
b) m < COD
112/2 = 56 degrees
If a BNC your digits for which of the following holds in a
Answers
Given:
We use the digit places to compute the value of a,b and c.
subtracting unit place.
[tex]1-b=6[/tex]If we get 1-b=6, b must be greater than 1.
We need to take one from the tenth place that is a in 9a1.
So now we get 11
[tex]11-b=6[/tex]If we put b=5, this equation will satisfy.
[tex]11-5=6[/tex]So the value of b is 5.
Subtracting tenth place values.
[tex]a-2=8[/tex]If we put a=10, we get
[tex]10-2=8[/tex]a already reduced one value.
so here a should be 11, so we take the unit digit from 11. and it takes 1 from the hundredth place is 9.
Hence the value of a is 1.
subtracting the hundredth place.
a take 1 from 9, so in this stage we have
[tex]8-6=c[/tex][tex]2=c[/tex]Hence the value of c is 2.
Adding a,b, and c, we get
[tex]a+b+c=1+5+2=8[/tex]The answer is 8.
1. A number that can be written using exponents is called a(n)
Answers
Answer:
Your answer is powers.
Factor.(6x+4) 3x + 22(x+2)2(3x+2)3(2x+1)
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EXPLANATION
[tex]\mathrm{Rewrite\: }6\mathrm{\: as\: }2\cdot\: 3[/tex][tex]\mathrm{Rewrite\: }4\mathrm{\: as\: }2\cdot\: 2[/tex][tex]=2\cdot\: 3x+2\cdot\: 2[/tex][tex]\mathrm{Factor\: out\: common\: term\: }2[/tex][tex]=2\mleft(3x+2\mright)[/tex]In conclusion, the factored expression is 2(3x+2)
whats 3.141, 3 2/3 π √3 3.11111 from least to greatest
Answers
start by writing all numbers like decimals
[tex]\begin{gathered} 3\frac{2}{3}=3.66666667 \\ \pi\cong3.1416 \\ \sqrt[]{3}=1.732 \end{gathered}[/tex]then using the decimals we can say that the least is square root 3 and the greatest is 3 2/3
The correct order should be
[tex]\sqrt[]{3};\bar{3.1};3.141;\pi;3\frac{2}{3}[/tex]Hi, can you help me answer this question please, thank you
Answers
Given:
An organization reported that teenagers spent 3.75 hours per day on an average using their phones.
The claim is that the mean time teenagers spend using their phones is greater than 3.75 hours.
The null and alternative hypothesis respectively is,
[tex]\begin{gathered} H_o=\mu=3.75\text{ hours} \\ H_a=\mu>3.75\text{ hours } \end{gathered}[/tex]Find the area of this triangle. Round tothe nearest tenth.20 ft15 ft[? ]ft²9 ft110⁰EnterHelpSkip
Answers
Step 1
The formula the area is given as;
[tex]\frac{1}{2}absinC[/tex]Where;
[tex]\begin{gathered} a=9,b=15\text{ C=110}^o \\ \frac{1}{2}\times9\times15\times s\imaginaryI n110 \\ \end{gathered}[/tex][tex]Area\approx63.4ft^2[/tex]Answer;
[tex]undefined[/tex]which of the following represents the difference of the polynomial below? (x^4+8x^3+9x^2)-(5x^4+4x^3+2x^2)A. 5x^4+12x^3+11x^2B.-4x^4+12x^3+11x^2C.4x^4+4x^3+7x^2D.-4x^4+4x^3+7x^2
Answers
Given:
The objective is to find the difference between the polynomial equations (x^4+8x^3+9x^2)-(5x^4+4x^3+2x^2).
The difference can be calculated as,
[tex]\begin{gathered} =(x^4+8x^3+9x^2)-(5x^4+4x^3+2x^2) \\ =x^4+8x^3+9x^2-5x^4-4x^3-2x^2 \\ =x^4-5x^4+8x^3-4x^3+9x^2-2^2 \\ =-4x^4+4x^3+7x^2 \end{gathered}[/tex]Hence, option (d) is the correct answer.
Answer:
D. -4x^4+4x^3+7x^
x^4+8x^3+9x^2-(5x^4+4x^3+2x^
distribute the negative to the whole second equation
x^4+8x^3+9x^2-5x^4-4x^3-2x^2
combine like terms and the answer is
Step-by-step explanation:
find the value of x (3x+6) (6x+3)
Answers
we have
[tex]\begin{gathered} (3x+6)+(6x+3)=180 \\ 3x+6+6x+3=180 \\ 9x+9=180 \\ 9x+9-9=180-9 \\ 9x=171 \\ \frac{9x}{9}=\frac{171}{9} \\ x=19 \end{gathered}[/tex]answer: B. 19
[tex]undefined[/tex]Violet has $1.60 worth of nickels and dimes. She has a total of 21 nickels and dimes altogether. Determine the number of nickels and the number of dimes that Violet has.
Answers
The number of nickels and the number of dimes that Violet has is 10 nickles and 11 dimes.
Given:
Violet has $1.60 worth of nickels and dimes. She has a total of 21 nickels and dimes altogether.
Let nickles be n and dimes be d.
From statement given:
n + d = 21
n = 21 - d
1 dimes = 10 cents , 1 nickle = 5 cents and $1 = 100 cents.
n + d = $1.60
convert into cents
5n + 10d = 160
divide by 5 on both sides
n + 2d = 32
n = d - 21 substitute in n + 2d = 32
21 - d + 2d = 32
d + 21 = 32
d = 11
Hence number of dimes = 11
substitute d = 11 in n = 21 - d
n = 21 - 10
n = 10
Hence number of nickles = 10
Therefore the number of nickels and the number of dimes that Violet has is 10 nickles and 11 dimes.
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please help me with my question
Answers
The volume of a triangular prism is given by the following expression:
[tex]V=A_{\text{base}}\cdot h[/tex]Where V is the volume, Abase is the area of the base and h is the height of the prism. For this prism the base has a rectangular shape, so it can be calculated as shown below:
[tex]A_{\text{base}}=\text{length}\cdot\text{width}=18\cdot12=216cm^2[/tex]Using this value on the first expression:
[tex]V=216\cdot9=1944cm^3[/tex]The correct option is A.
Use a number line to find 1-5 .Then write a related addition sentence for the subtraction sentence. -5 -4 -3 -2 -1 0 1 Difference: Addition Sentence:
Answers
We need to use the number line to find the result of 1-5.
The steps to do this are:
• First start at number 1 in the number line.
,• Jump to left five times, becuase we have to subtract 5 to 1.
Graphically this is:
In the picture above you can see the red circle marks the start at number 1, then we jump five times to the left, in yellow, and we reach the number -4 in a green circle. So the result of 1-5 is -4.
So, the Difference is 1-5=-4 and the Addition sentence is -4+5=1.
The Addition sentences is the opposite, you start at -4 and jump to rigth until reach the number 1, the number of jumps is the same to the Difference, 5 jumps.
determine equation of line passing through the points 3 1 5 -1
Answers
y = -x + 4
Explanation:uisng equation of ;line: y = mx + b
m = slope, b = y-intercept
points: 3, 1 and 5, -1
Slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} x_1=3,y_1=1,x_2=5,y_2\text{ = -1} \\ m\text{ = }\frac{-1-1}{5-3} \\ m\text{ = -2/2 = -1} \end{gathered}[/tex]To get the y-intercept, we would pick any of the points:
using: (3, 1) = (x, y)
y = mx + b
1 = -1(3) + b
1 = -3 + b
1 + 3 = b
b = 4
The equation becomes:
y = -1(x) + 4
y = -x + 4
The equation V=23.4+2.8xgives the value (in thousands of dollars) of an investment after xmonths.
Answers
Given the following equation:
[tex]\text{ V = 23.4 + 2.8x}[/tex]In the standard slope-intercept form, y = mx + b, m represents the slope of the equation.
If the slope is positive, it is increasing.
If the slope is negative, it is decreasing.
From the given equation, V = 23.4 + 2.8x, it appears that 2.8 is the slope in this equation. Since it is a positive number, it is increasing.
Therefore, we can say that:
The value of this investment is increasing at a rate of 2.8 thousand dollars per month.
Find the x-intercept and the y-intercept of the graph of the equation. Do not graph the equation. -4x + 4y = 8x - intercept = y - intercept =
Answers
Given the equation:
[tex]-4x+4y=8[/tex]We will find the intercepts of the given equation.
The x-intercept is the value of (x) when y = 0
So, substitute with y = 0 and solve the equation to find (x)
[tex]\begin{gathered} -4x+4(0)=8 \\ -4x=8 \\ x=\frac{8}{-4}=-2 \end{gathered}[/tex]So, the x-intercept = -2
The y-intercept is the value of (y) when x = 0
So, substitute with x = 0 and solve the equation to find (y):
[tex]\begin{gathered} -4(0)+4y=8 \\ 4y=8 \\ y=\frac{8}{4}=2 \end{gathered}[/tex]So, the y-intercept = 2
The complex fraction 3/2 4/7 can be simplified into which of the following
Answers
Simplify the complex fraction,
[tex]\frac{\frac{3}{2}}{\frac{4}{7}}[/tex]This can be re-written as:
[tex]\frac{3}{2}\div\frac{4}{7}[/tex]Simplify,
[tex]\frac{3}{2}\times\frac{7}{4}=\frac{21}{8}[/tex]Simplify further,
[tex]\frac{21}{8}=2\frac{5}{8}[/tex]help meeeeeeeeeeeeeeee pleasee
Answers
The side of the square whose area of square is 18 square inches is 4.23 inches.
According to the question,
We have the following information:
Area of the square = 18 square inches
We know that the following formula is used to find the area of square and it is also given in the question:
Side*side = 18
Side = √18
Side of the square = 3√2 inches
(The square root of 2 is 1.41 approximately.)
Side of the square = 3*1.41
Side of the square = 4.23 inches
Hence, the side of the square whose area of square is 18 square inches is 4.23 inches.
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Which values of x in the set {−5,0,8,9,10,14} are solutions to the inequality 2(x−4)<10?
Answers
Answer:
-5, 0, 8
Step-by-step explanation:
[tex]2(x-4)<10 \\ \\ x-4<5 \\ \\ x<9 \\ \\ \therefore x=-5,0,8[/tex]
helpppppppppppppppp-
Answers
Answer: 5.668
The decimal point for both values is in the same place so you would just add them up like any other number.
Answer:
5.668
Step-by-step explanation:
Check the above picture
anthonys sink is shaped like a half-sphere, and it has a volume of 700 pi cubic inches. it is compltely full of water, and he has two different cylindrical cups he can use to scoop out. The blue cup has a diameter of 4 inches and a height of 8 inches in the green cup has a diameter of 8 inches and a height of 8 inches. How many cupfuls of water will it take for him to empty his sink using each cup? In your answer, give the number of cupfuls it will take to empty the sink using each cup, and then explain how you calculate it.
Answers
To answer this question the first step is to find the volume of each of the cylindrical cups.
The volume of a cylinder is given by the following equation:
[tex]V=\pi r{}^2h[/tex]Where V is the volume, r is the radius and h is the height.
Find the radius of each of the cups by dividing their diameters by 2:
[tex]\begin{gathered} rb=\frac{4}{2}=2 \\ rg=\frac{8}{2}=4 \end{gathered}[/tex]Calculate the volume of each of the cups using the given values:
[tex]\begin{gathered} Vb=\pi rb^2hb \\ Vb=\pi(2)^2(8) \\ Vb=32\pi \\ Vg=\pi(4)^2(8) \\ Vg=128\pi \end{gathered}[/tex]It means that the blue cup has a volume of 32pi cubic inches and the green cup has a volume of 128pi cubic inches.
To find how many cupfuls of water will it take for him to empty his sink using each cup, divide the volume of the sink by each of the volumes of the cups:
[tex]\begin{gathered} nb=\frac{700\pi}{32\pi}=21.88 \\ ng=\frac{700\pi}{128\pi}=5.47 \end{gathered}[/tex]It will take 21.88 (22) blue cups for him to empty the sink.
It will take 5.47 (6) green cups for him to empty the sink.
20 points can you just do both or 1 of them
Answers
Answer
C.
[tex]\frac{9}{49}units^2[/tex]D.
[tex]\frac{121}{64}inches^2[/tex]Explanation
The area of a square is found by multiplying side by side, which corresponds to squaring because all sides of the square are equal, so:
[tex]\frac{3}{7}\cdot\frac{3}{7}=\frac{9}{49}[/tex]And
[tex]\frac{11}{8}\cdot\frac{11}{8}=\frac{121}{64}[/tex]hello whoever my tutor is i just wanted to say just tell me what to fill in the boxes thats will be enough. thank you : )
Answers
Given that, Katie has four grape candies and 3 cherry candies.
Thus, the total number of candies is 7.
Calculate the ratio of grape candies to total number of candies.
[tex]G\colon C=4\colon7[/tex]Therefore, ratio is 4:7.
New-Home Prices If the average price of a new one-family home is $246300 with a standard deviation of $ 15000, find the minimum and maximum prices of the houses that a contractor will build to satisfy the middle 70% of the market. Assume that the variable is normally distributed. Use a graphing calculator and round the answers to the nearest dollar.Minimum price: $=Maximum price: $=
Answers
Answer:
Minimum Price: $230,700
Maximum Price: $261,900
Explanation:
To find the minimum and maximum prices, we need to find the z-score of the middle 70%
70% = 0.7
1 - 0.7 = 0.3
0.3/2 = 0.15
Then the inverse normal of 0.15 is -1.04
[tex]z=\pm1.04[/tex]Therefore,
[tex]\frac{x-246300}{15000}=\pm1.04[/tex][tex]\begin{gathered} x-246300=\pm15600 \\ x=246300\pm15600 \end{gathered}[/tex][tex]\begin{gathered} x=246300+15600 \\ =261900 \\ \text{MAXIMUM} \end{gathered}[/tex]and
[tex]\begin{gathered} x=246300-15600 \\ =230700 \\ \text{MINIMUM} \end{gathered}[/tex]11. The scale of a dollhouse is l in: 2 ft. Which of the following would most likely be the measurement of the heightof the dollhouse's front doorA 21in2No - - -B. 3-Ft2O c. 14 inO D. 14H12. A flagpole casts a shadow 5 ft. long. At the same time, a 3 ft. yardstick casts a shadow 1.5 ft. long. How tall isthe flagpole?O A. 5 ft.B. 10 ft.O C. 20 ft.O D. 15 ft
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We want to find the height of the dollhouse's front door.
Since the dollhouse's measures is given in inches, we have just two possible right choices:
because the answer should be given in inches.
If the correct option were the third one, 14 in,
then the real door measure would be twice in feet: 28 feet.
If the correct option were the first one, 3 1/2 in,
then the real door measure would be twice in feet: 7 in.
28 feet is a really big door. It is more likely for a house to have a 7 in door.
Answer: A. 3 1/2 in. Using ratios and the Pythagorean Theorem the approximate width is 23.5 inches and the height is inches.
Answers
Given:
There is a ratio given as 16:9 of width to height and diagonal is 27 iniches
Required:
We need to find the value of height
Explanation:
By ratio
[tex]\begin{gathered} \frac{w}{h}=\frac{16}{9} \\ \\ h=\frac{9}{16}w \end{gathered}[/tex]where w is width and h is height
by using pythagorean theorem
[tex]\begin{gathered} 27^2=h^2+w^2 \\ 729=\frac{81}{256}w^2+w^2 \\ \\ 186624=81w^2+256w^2 \\ w^2=553.78 \\ w=23.5\text{ in} \end{gathered}[/tex]to find h
[tex]h=\frac{9}{16}*23.5=13.24\text{ in}[/tex]Final answer:
height is 13.24 inches
Horses age more rapidly than humans.Suppose that the "horse age" and"human age"
Answers
Let x represent the horse age
Let y represent the human age
Since the horse age and human age vary directly, we have the relation
[tex]x\text{ }\alpha\text{ y}[/tex]Introducing an equality sign, we
[tex]x\text{ =Ky}[/tex]Where K is a proportionality constant, evaluated as
[tex]K\text{ = }\frac{x}{y}----\text{ equation 1}[/tex]Since a 5-year-old horse is equivalent to 15-year old human,
x = 5
y = 15
we have
[tex]\begin{gathered} K\text{ = }\frac{5}{15} \\ \Rightarrow K=3 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} K=\frac{x}{y} \\ 3\text{ = }\frac{x}{y} \\ \Rightarrow x\text{ = 3y ----- equation 2} \end{gathered}[/tex]Thus, for a horse who has lived 16 years
x = 16
Write and equation that relates the variable. Then find X when y= -6.
Answers
Answer;
We can have the equation as;
[tex]\begin{gathered} y\text{ = 3x} \\ \text{if y = -6, then x = -2} \end{gathered}[/tex]where 3 is k which is the proportionality constant
Explanation;
Firstly, we need to understand the relation of being directly proportional
When two variables are proportional, the relationship between them is of the nature;
[tex]y\text{ = kx}[/tex]where K is the proportionality constant
We can have k as 3, and that means we have the relationship as;
[tex]y\text{ = 3x}[/tex]So, from the question, x is ? and y = -6; we can have x calculated as;
[tex]\begin{gathered} -6\text{ = 3x} \\ x\text{ = }\frac{-6}{3} \\ x\text{ = -2} \end{gathered}[/tex]I need help with my homework please it’s 3 parts to this question I will post the rest into the answer tab
Answers
Since there are a adults and c children
Since there are 187 tickets sold
Then the number of adults and children is 187
Add a and c, then equate the sum by 187
[tex]a+c=187\rightarrow(1)[/tex]Since the price of each adult's ticket is $25
Since the price of each child ticket is $13
Since the total revenue is $3223
Then multiply a by 25, c by 13, then add the products and equate the sum by $3223
[tex]25a+13c=3223\rightarrow(2)[/tex]Now, we have a system of equations to solve it
Multiply equation (1) by -13 to make c equal in values and opposite in signs to eliminate it
[tex]\begin{gathered} -13(a)+-13(c)=-13(187) \\ -13a-13c=-2431\rightarrow(3) \end{gathered}[/tex]Add equations (2) and (3)
[tex]\begin{gathered} (25a-13a)+(13c-13c)=(3223-2431) \\ 12a=792 \end{gathered}[/tex]Divide both sides by 12
[tex]\begin{gathered} \frac{12a}{12}=\frac{792}{12} \\ a=66 \end{gathered}[/tex]Substitute a by 66 in equation (1) to find c
[tex]66+c=187[/tex]Subtract 66 from both sides
[tex]\begin{gathered} 66-66+c=187-66 \\ c=121 \end{gathered}[/tex]The answers are:
a) The system of equations is
[tex]\begin{gathered} a+c=187 \\ 25a+13c=3223 \end{gathered}[/tex]b) There were 66 adult tickets sold
c) There were 121 children's tickets sold
bal.com Look at this graph. 10 8 6 4 Su N -B -6 0 N 10 -2 7. -6 -10 What is the equation of the line in slope-intercept form? Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
First, locate the coordinates of two points
(8, -2) and (2, -8)
Find the slope
x₁=8 y₁=-2 x₂=2 y₂=-8
Using the slope formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\frac{-8+2}{2-8}[/tex][tex]=\frac{-6}{-6}[/tex][tex]=1[/tex]slope (m) = 1
Find the intercept
substitute x = 8 y=-2 and m = 1 in y=mx+ b and then solve for intercept b
-2 = 1(8) + b
-2 -8 = b
b = -10
Substitute the value of m and b into y=mx+b to form the equation
y = 1x - 10
Hence the equation is;
y = x - 10