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The solution of the system of equations is where both lines cross each other.
solution = (0,1)
Related Questions
Graph the solution set of each system of inequalities.19. 4x-y52x + 2y <6
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The graph is given by:
a chemist has 30% and 60% Solutions of acid available how many liters of each solution should be mixed to obtain 120 liters of 34% acid solution
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Answer:
104 litres of 30% solution and 16 litres of 60% solution.
Explanation:
Let us call x the litres of 30% solution and y the litres of 60% solution.
Now, we know that the end result is 120 litres of a solution; therefore, we have
[tex]x+y=120[/tex]Morover, we are also
What’s 51,053 minus 12,947?
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Answer:
The answer you're looking for would be 38,106.
Step-by-step explanation:
May I have Brainliest please? I am so close to getting my next ranking! I just need 3 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
- 12,947
—————
38106
Aline has a slope of -3/4 and a y-intercept of 5. Write an equation insiope-intercept for that could represent this situation."
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Here, we want to write an equation in the slope-intercept form
Mathematically, we have this as;
[tex]y\text{ = mx + b}[/tex]b is the slope and m is the y-intercept
Thus, substituting the values we have in the question;
m = -3/4 and b = 5
Thus, we have the equation as;
[tex]y\text{ = -}\frac{3}{4}x\text{ + 5}[/tex]need help with the the association property etc
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Line 1:
[tex](2+x)x[/tex]Line 2:
[tex]x(2+x)[/tex]Line 1 to Line 2 is:
Commutative property of Multiplication.
Line 3:
[tex]x(x+2)[/tex]Line 2 to Line 3 is:
Commutative property of Addition
Scott borrowed $8000 at a rate of 19%, compounded annually. Assuming he makes no payments, how much will he owe after 8 years? Round your answer to the nearest cent
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To answer this question we will use the following formula for compounded interest:
[tex]A=A_0(1+r)^t,[/tex]where A is the final amount, A₀ is the initial amount, r is the interest rate as a decimal number, and t is the number of times that the interest rate is applied.
Substituting A₀=8000, r=0.19, and t=8 we get:
[tex]A=8000(1+0.19)^8\text{.}[/tex]Simplifying the above result we get:
[tex]\begin{gathered} A=8000(1.19)^8, \\ A\approx32171.08 \end{gathered}[/tex]Answer: $32171.08.
A certain college has been raising tuition every year since the year it opened. The function T = 12,000 (1+.03)* represents the tuition, T, after x years. If the college opened in the year 1990, what was the tuition in 2020?
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19. A wooden box has 20 cm on each edge. Find its volume.A. 875 cu. cmB. 8 000 cu. cmC. 8 875 cu. cm
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Given:
Length of the edge of wooden box = 20 cm
Required:
The volume of wooden box.
Explanation:
The volume of cubical box is given as,
[tex]\begin{gathered} Volume\text{ = Edge}^3 \\ Volume\text{ = 20 cm }\times\text{ 20 cm }\times\text{ 20 cm} \\ Volume\text{ = 8000 cm}^3 \end{gathered}[/tex]Answer:
Thus the volume of the wooden box is 8000 cu. cm. The correct answer is option B.
write 77.56 as a scientific notation
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The scientific notation/standard form of 77.56 can be represented below
[tex]7.756\times10^1[/tex]The logic behind it is we shift the dot backward until it get to the last number. The number of step we took represent the exponential of 10.
10,720MasteryLook at the image below.4Course suRatios, rateArithmetic10Course cheTest yourthe skillsWhat is the area of the triangle?
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The given triangle is not the regular drawing of a triangle. We need to identify the height and base.
From the diagram, the height = 10
base = 4
Substitute the values:
[tex]\begin{gathered} \text{Area of the triangle = }\frac{1}{2}\times\text{ 10}\times4 \\ \text{Area of the triangle = 20 units}^2 \end{gathered}[/tex]how does you solve Vertices: (0,7), (0,-7) Co vertices: (2,0), (-2,0)
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As according to given conditions let us draw these 4 points on the graph:
So the center is (0,0)
So the equation is:
[tex]\frac{(x-0)^2}{4}+\frac{(y-0)^2}{49}=1[/tex]Using y= sin x OR y= cos x [Sinusoidal function] as the parent function, make your own transformations (5 units right, reflect on x axis, 2 units down, horizontal compression with factor 2). Then graph and state domain and range.
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Using
[tex]y=\sin (x)[/tex]5 units right: Let's use the following rule:
[tex]\begin{gathered} y=f(x-5) \\ so\colon \\ y=\sin (x-5) \end{gathered}[/tex]Reflect on x-axis: Let's use the following rule:
[tex]\begin{gathered} y=-f(x) \\ so\colon \\ y=-\sin (x-5) \end{gathered}[/tex]2 units down: Let's use the following rule:
[tex]\begin{gathered} y=f(x)-2 \\ so\colon \\ y=-\sin (x-5)-2 \end{gathered}[/tex]Horizontal compression with factor 2: Let's use the following rule:
[tex]\begin{gathered} y=f(2x) \\ so\colon \\ y=-\sin (2x-5)-2 \end{gathered}[/tex]Let's graph the parent function, and the new function:
The blue graph is the parent function and the red graph is the new function after the transformations applied.
The domain and the range of the new function are:
[tex]\begin{gathered} D\colon\mleft\lbrace x\in\R\mright\rbrace_{\text{ }}or_{\text{ }}D\colon(-\infty,\infty) \\ R\colon\mleft\lbrace y\in\R\colon-3\le y\le-1\mright\rbrace_{\text{ }}or_{\text{ }}R\colon\lbrack-3,-1\rbrack \end{gathered}[/tex][4]How many solutions does the system of equations have?y = 7x-4y = 7x + 2 One Soluton Infinite Solutions No Solution
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Given system of equations:
[tex]\begin{gathered} y\text{ = 7x - 4} \\ y\text{ = 7x + 2} \end{gathered}[/tex]Let us attempt to solve the equations
From equation 1:
[tex]y\text{ = 7x -4}[/tex]Substituting the expression for y into equation 2:
[tex]\begin{gathered} y\text{ = 7x + 2} \\ 7x\text{ -4 = 7x + 2} \\ \text{Collect like terms} \\ 7x\text{ - 7x = 2 + 4} \\ 0\text{ = 6} \end{gathered}[/tex]This imples that there is no solution to the system of equations.
We can plot the graph of the equations to better visualize and see that the lines don't intersect
The lines are parallel and do not intersect. Hence, there is no solution to the system of equations
what is the x intercept?
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Answer:
x intercept is -2
Step-by-step explanation:
I need some help please Find the inverse function of the given function.1. F(x)= x^2-4/2x^2
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to solve this problem, we can follow some steps
step 1
replace f(x) with y
[tex]\begin{gathered} f(x)=\frac{x^2-4}{2x^2} \\ y=\frac{x^2-4}{2x^2} \end{gathered}[/tex]step 2
replace every x with a y and every y with an x
[tex]\begin{gathered} x=\frac{y^2-4}{2y^2} \\ \end{gathered}[/tex]step 3
solve for y
[tex]\begin{gathered} x=\frac{y^2-4}{2y^2} \\ \text{cross multiply both sides} \\ 2y^2\times x=y^2-4^{} \\ 2y^2x=y^2-4 \\ \text{collect like terms} \\ 2y^2x-y^2=-4 \\ \text{factorize y}^2 \\ y^2(2x-1)=-4 \\ \text{divide both sides by 2x - 1} \\ \frac{y^2(2x-1)}{(2x-1)}=-\frac{4}{(2x-1)} \\ y^2=-\frac{4}{2x-1} \\ \text{take the square root of both sides} \\ y=-\sqrt[]{\frac{4}{2x-1}} \end{gathered}[/tex]therefore the inverse of f(x) is
[tex]f^{-1}(x)=-\sqrt[]{\frac{4}{2x-1}}[/tex]There are 110 calories per 177.4 grams of Cereal X. Find how many calories are in 246.5 grams of this cereal There are ? calories in 246.5 grams of this cereal ( round to the nearest whole number as needed )
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We can solve this question by means of the rule of three, which can be stated as
[tex]\begin{gathered} 110\text{ calories ----------- 177.4 grams} \\ \text{ x ---------------- 246.5 grams} \end{gathered}[/tex]then by using cross-multiplication to calculate x, we have
[tex]x\cdot177.4\text{ grams=(110 calories)}\cdot(246.5\text{ grams)}[/tex]so, by dividing both sides by 117.4 grams, x is given as
[tex]\begin{gathered} x=\frac{\text{(110 calories)}\cdot(246.5\text{ grams)}}{177.4\text{ grams}} \\ x=152.54667\text{ calories} \end{gathered}[/tex]Therefore, by rounding this result to the nearest whole nuymber, there are 153 calories in 246.5 grams of cereal
CAN SOMEONE HELP WITH THIS QUESTION?✨
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The value of sin Ф will be [tex]2\sqrt{6} /5[/tex] .
What are trigonometric function?A right-angled triangle's angle can be related to side length ratios using trigonometric functions, which are real functions in mathematics. They are extensively employed in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more. The term "Circular" is another name for trigonometric functions. A triangle's angle functions can be used to define functions. It implies that these trig functions can be used to determine the relationship between a triangle's angles and sides. There are several trigonometric identities and formulas that show the relationship between the functions and aid in determining the triangle's angles. Here is an in-depth explanation of all these trigonometric functions and their formulas.
sin²Ф + cos²Ф = 1
sinФ = [tex]\sqrt{1 - 1/25}[/tex]
= [tex]2\sqrt{6} /5[/tex]
To know more about trigonometric function, visit:
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The distance d (in inches) that a beetle travels over time + (inseconds) is given by the function d (t) = 2t^3 . Find the averagespeed of the beetle from t1 = 0 second to t2 = 2 seconds.inches/second
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Given distance,
[tex]d(t)=2t^3[/tex]Let v is the speed of the beetle.
It is given by
[tex]v=\frac{d(t)}{t}[/tex]Now,
[tex]\begin{gathered} v=\frac{2t^3}{t} \\ v=2t^2 \end{gathered}[/tex]At t = 0 sec.
[tex]\begin{gathered} v=2t^2 \\ v=2\times0 \\ v=0 \end{gathered}[/tex]At t = 2 sec.
[tex]\begin{gathered} v=2t^2 \\ v=2\times2^2 \\ v=8\text{ m/sec} \end{gathered}[/tex]So, the average speed of the beetle is 8 m/sec.
Hello, I need help simplifying question 16 i please, thanks
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Given -
i. 5cot²θ + 5
To Find -
Simplification =?
Step-by-Step Explanation -
We know that
[tex]cot\theta\text{ = }\frac{\cos\theta}{\sin\theta}[/tex]So, simply putting it in the given equation:
[tex]\begin{gathered} =\text{ }5\frac{\cos^2\theta}{\sin^2\theta}\text{ + 5 } \\ \\ =\text{ 5}\frac{\lparen\cos^2\theta+\sin^2\theta\rparen}{\sin^2\theta} \\ \\ We\text{ know taht }\sin^2\theta\text{ + }\cos^2\text{ = 1} \\ \\ So,\text{ } \\ \\ =\text{ }\frac{5}{\sin^2\theta} \end{gathered}[/tex]Final Answer -
= 5/sin²θ
if ace of 21 = 856 find ace 20 and ace of 22 given a common ratio of 1/4.
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Answer:
[tex]a_{20}=214,a_{22}=3424[/tex]Explanation:
We are told that the common ratio between the numbers is 1/4, meaning each consquetive number is
17. Write the equation of the line in slope-intercept form with the given information. 17. Passes through (-2, 6) with a slope of (-1/4)
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Given:
Slope of line is m = -1/4 and passes through point (-2,6).
Explanation:
The general equation of line with slope m and passing through point (x_1,y_1) is,
[tex]y-y_1=m(x-x_1)[/tex]Determine the equation of line passing through point (-2,6) and have slope of -1/4.
[tex]\begin{gathered} y-6=-\frac{1}{4}(x-(-2)) \\ y-6=\frac{-1}{4}\cdot x-\frac{1}{4}\cdot2 \\ y=-\frac{x}{4}-\frac{1}{2}+6 \\ y=-\frac{x}{4}+\frac{11}{2} \end{gathered}[/tex]So equation of line is,
y = -x/4 + 11/2
Mrs. Thornton asked her students to draw a figure with a perimeter of 4x + 4. Shown below are 4 drawings madeby her students. (They are not drawn to scale.) Which one is NOT correct?А2x+11B2x2C.X + 4XDX+ 1X+ 1сdba
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The perimeter is 4x+4
the formula of the perimeter of a rectangle is
[tex]P=2l+2w[/tex]for the first drawing
[tex]P=2(2x+1)+2(1)=4x+2+2=4x+4[/tex]It is correct
for the second drawing
[tex]P=2(2x)+2(2)=4x+4[/tex]It is correct
for the third drawing
[tex]P=2(x+4)+2x=2x+8+2x=4x+8[/tex]It is not correct
for the fourth drawing
[tex]P=2(x+1)+2(x+1)=2x+2+2x+2=4x+4[/tex]it is correct
As we can see the incorrect draw is C.
find the values for A and B. explain of show your reasoning
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Answer:
The value of a is 5, and b is 6.
Explanation:
The points on the line are (6,10), (a,8), (4,b) and (2,2).
• The slope of a straight line is always constant.
First, determine the slope using the points (6,10) and (2,2).
[tex]\begin{gathered} \text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{10-2}{6-2} \\ =\frac{8}{4} \\ =2 \end{gathered}[/tex]Next, using points (6,10) and (a,8):
[tex]\begin{gathered} m=\frac{10-8}{6-a} \\ 2=\frac{2}{6-a} \\ \text{Cross multiply} \\ 2(6-a)=2 \\ 12-2a=2 \\ -2a=2-12 \\ -2a=-10 \\ a=-\frac{10}{-2} \\ a=5 \end{gathered}[/tex]Next. using points (6,10) and (4,b):
[tex]\begin{gathered} m=\frac{10-b}{6-4} \\ 2=\frac{10-b}{2} \\ \text{Cross multiply} \\ 10-b=2\times2 \\ 10-b=4 \\ b=10-4 \\ b=6 \end{gathered}[/tex]The value of a is 5 and b is 6.
Find the distance between each pair of points using the distance formula - round to the nearest 10th
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Explanation: Below we have the distance formula
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step 1: Now let's identify the values of the variable as follows
Step 2: Now we can substitute the values on the distance formula as follows
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(-4_{}-(-2))^2+(4_{}-0_{})^2} \\ d=\sqrt[]{(-4_{}+2)^2+(4_{}_{})^2} \\ d=\sqrt[]{(-2)^2+16^{}} \\ d=\sqrt[]{4^{}+16} \\ d=\sqrt[]{20} \\ d=4.472135955 \\ d\cong4.5 \end{gathered}[/tex]Final answer: So the distance between the pair of points rounded to the nearest tenth is 4.5
The volume of the oceans and their seas is nearly 1.5 . 109 cubic kilometers. Write this number in Standard Form A:0.00000000015km³ B: 1,500,000,000km³ C: 0.0000000015km³ D: 15,000,000,000km³
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Given data:
[tex]\text{1}.5\cdot10^9[/tex]the above number in standard form is.
1,500,000,000km³.
The answer is option c. 1,500,000,000km³
Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Find a) A ∩ B ∩ C. b) A ∪ B ∪ C. c) (A ∪ B) ∩ C. d) (A ∩ B) ∪ C.
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b) AuBuC = {0,1,2,3,4,5,6,7,8,9,10}
c) (AuB)nC ; (AuB) = {0,1,2,3,4,5,6,8,10}
:. (AuB)nC = {4,5,6,8,10}
d) (AnB)uC ; (AnB) = {0,2,4,6}
:. (AnB)uC = {0,2,4,5,6,7,8,9,10}
The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90%pure fruit juice. The company is attempting to produce a fruit drink that contains 75% pure fruit juice. How many pints of each ofthe two existing types of drink must be used to make 170 pints of a mixture that is 75% pure fruit juice?First fruit drink:pintsХ5?Second fruit drink: pints
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Let
x ----> number of pints of the First fruit drink
y ----> number of pints of the Second fruit drink
we have that
x+y=170 -------> x=170-y ----> equation A
65%=0.65
90%=0.90
75%=0.75
so
0.65x+0.90y=0.75(170) -----> equation B
Solve the system of equations
substitute equation A in equation B
0.65(170-y)+0.90y=0.75(170)
solve for y
110.5-0.65y+0.90y=
What is the slope of a line that goes through (2,6) and (4,12)?
Answers
Answer:
Slope = 3
Explanation:
To determine the slope of the line that goes through the given points: (2,6) and (4,12), we use the slope formula.
[tex]\text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}[/tex]Substituting the points, we have:
[tex]\begin{gathered} \text{Slope}=\frac{12-6}{4-2} \\ =\frac{6}{2} \\ =3 \end{gathered}[/tex]The slope of the line is 3.
-3x^2 – 24x – 13 = -13
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oh,
7. On Friday, Stock 1 dropped 3/4 point and Stock 2 dropped 5/8 point. Based on this information, which statement is true? Stock 2 dropped more Stock 1 dropped more The stocks dropped the same amount O Both stocks sold at the same price Clear selection
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Let's divide each fraction
[tex]\begin{gathered} \frac{3}{4}=0.75 \\ \frac{5}{8}=0.625 \end{gathered}[/tex]As you can observe, 3/4 is greater than 5/8.
Hence, Stock 1 dropped more.