Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given equations
[tex]\begin{gathered} y=-\frac{4}{3}x \\ y=\frac{3}{2}x \end{gathered}[/tex]STEP 2: Define the point that is the solution for the given functions on the graph
The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
STEP 3: Determine the solution for the system of equations
It can be seen from the image below that the two lines intersect at the origin and hence they are given as the solutions to the given system of equations.
Hence, the solutions are:
[tex]x=0,y=0[/tex]
Related Questions
A radio announcer asked her listeners which type of music they preferred. The results are below. which answer choice lists the results from greatest to least perefence?F. 0.10, 25%, 0.20, 45/100G. 25%, 45/100, 0.20, 0.10H. 0.10, 0.20, 25%, 45/100J. 45/100, 25%, 0.20, 0.10
Answers
To compare the preferences is best to express them using the same form, for example, express all values as decimal values:
To express 25% as a decimal value you have to divide it by 100:
[tex]\frac{25}{100}=0.25[/tex]To express the fraction 45/100 as a decimal value you have to divide 45 by 100
[tex]45\div100=0.45[/tex]So, the observations expressed as decimal values are:
Rap 0.25
Norteno 0.45
Kazz 0.20
Tejano 0.10
Now that all numbers are on the same form you can order them from greatest to least. To do so, you have to compare the digit on the first decimal place, if the first digit is equal, you have to compare the digit on the second decimal place.
The number with the greatest decimal value is 0.45
Then you have 0.20 and 0.25 both have the same first digit, so you have to compare the second digits. "0" is less than "5" so, 0.20 is less than 0.25.
The least value is 0.10.
So ordered from greatest to least the values are:
[tex]\begin{gathered} 0.45;0.25;0.20;0.10= \\ \frac{45}{100};25\%,0.20;0.10 \end{gathered}[/tex]The correct option is J.
An athlete runs at a speed of 9 miles per hour. If one lap is 349 yards, how many laps does he run in 22 minutes
Answers
The athlete will cover 17 yards in 22 minutes of his running.
What is unitary method?The unitary method is a method in which you find the value of a single unit and then the value of a required number of units.
Given is an athlete who runs at a speed of 9 miles per hour and one lap is 349 yards.
We will use the unit conversions to solve the given problem.
The speed of the athlete is 9 mph. We can write it as -
9 mph = (9 x 1760) yards per hour = 15840 yards per hour.
15840 yards per hour = (15840/60) yards per minute = 264 yards per min.
Total yards covered in 22 minutes = 22 x 264 = 5808 yards
one lap is equivalent to 349 yards.
1 yard is equivalent to (1/349) laps
5808 yards are equivalent to (5808/349) or 16.6 yards or approximately 17 yards.
Therefore, the athlete will cover 17 yards in 22 minutes of his running.
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What is the value of x if x + 15 = 38 ? Enter answer below
Answers
x=23
1) Evaluating x +15=38
x +15=38 Subtract 15 from both sides
x+15-15 = 38 -15
x=23
2) So the quantity of x = 23
x=23
1) Evaluating x +15=38
x +15=38 Subtract 15 from both sides
x+15-15 = 38 -15
x=23
2) So the quantity of x = 23
In ACDE, J is the centroid. If JG=21 find CG. D F G C E H
Answers
Let's begin by identifying key information given to us:
We have triangle CDE
J is the centroid
[tex]\begin{gathered} JG=21 \\ \text{The centroid of a triangle divides }\frac{2}{3\text{ }}\text{the distance from}verte\text{x to midpoint of the sides} \\ \Rightarrow JG=\frac{2}{3}CG \\ \Rightarrow21=\frac{2}{3}CG=\frac{63}{2} \\ \therefore CG=\frac{63}{2}=31.5 \end{gathered}[/tex]Find the annual fixed expense for car insurance if John makes
six payments in a year at $174.45 each?
Answers
The annual fixed expense for car insurance is $ 1,046.70.
It is given in the question that John makes six payments in a year at $174.45 each.
We have to find the annual fixed expense for car insurance.
We know that,
The annual fixed expense for the car insurance will be 6 times the individual payment given in the question.
Hence, by simple multiplication, we can write,
Annual fixed expense for the car insurance = 6*174.45 = $ 1,046.70
Car insurance
Car insurance is a type of financial protection that covers the cost of another driver’s medical bills and repairs if you cause an accident with your car, or in case your car is stolen or damaged some other way.
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F(x)=x+1 and g(x)=x^3 -1Find (fg)(5)
Answers
Solution
[tex](fg)(x)=f(x)\times g(x)[/tex]So
[tex]\begin{gathered} f(5)=5+1=6 \\ g(5)=5^3-1=125-1=124 \end{gathered}[/tex]and
[tex]\begin{gathered} (fg)(5)=f(5)\times g(5) \\ (fg)(5)=6\times124=744 \end{gathered}[/tex]Answer: (fg)(5) = 744
3. If you ordered a pizza to share with others, which of the following sets ofnumbers would best describe the part of the pizza you ate.a. Integerb. WholeC. Naturald. Rational
Answers
rational, because you've split the pizza
So for example if you cut the pizza into 12 pieces to one of your friends you gave 1/12
Find the component form of the sum of u and v with direction angles u and v.
Answers
We will have the following:
[tex]\begin{gathered} U_x=14cos(45) \\ \\ U_y=14sin(45) \\ \\ V_x=80cos(180) \\ \\ V_y=80sin(180) \end{gathered}[/tex]Then:
[tex]\begin{gathered} \sum_x=\frac{14\sqrt{2}}{2}+(-80)\Rightarrow\sum=7\sqrt{2}-80 \\ \\ \sum_y=\frac{14\sqrt{2}}{2}+(0)\Rightarrow\sum=7\sqrt{2} \end{gathered}[/tex]So, the component form for the sum of the vectors will be:
[tex]u+v=(7\sqrt{2}-80)i+(7\sqrt{2})j[/tex]Type the correct answer in each box use numerals instead of words What are the values of the function
Answers
Given the following function:
[tex]h(x)=\begin{cases}{3x-4;x<0} \\ {2x^2-3x+10;0\leq x<4} \\ {2^x};x\ge4\end{cases}[/tex]We will find the value of the function when x = 0 and when x = 4
First, when x = 0, the function will be equal to the second deifinition
So, h(0) will be as follows:
[tex]h(0)=2(0)^2-3(0)+10=10[/tex]Second, when x = 4, the function will be equal to the third definition
So, h(4) will be as follows:
[tex]h(4)=2^4=16[/tex]So, the answer will be:
[tex]\begin{gathered} h(0)=10 \\ h(4)=16 \end{gathered}[/tex]First use the Pythagorean theorem to find the exact length of the missing side. Then find the exact values of the six trigonometric functions for angle 0.
Answers
The trigonometric functions are given by the following formulas:
[tex]\begin{gathered} \sin \theta=\frac{a}{h} \\ \cos \theta=\frac{b}{h} \\ \tan \theta=\frac{a}{b} \\ \cot \theta=\frac{b}{a} \\ \sec \theta=\frac{h}{b} \\ \csc \theta=\frac{h}{a} \end{gathered}[/tex]Where we call a to the opposite leg to the angle θ (the side whose measure equals 20), b is the adjacent leg to angle θ (the side whose measure equals 21) and we call h to the hypotenuse (the larger side, whose measure equals 29).
By replacing 20 for a, 21 for b and 29 for h into the above formulas, we get:
[tex]\begin{gathered} \sin \theta=\frac{20}{29} \\ \cos \theta=\frac{21}{29} \\ \tan \theta=\frac{20}{21} \\ \csc \theta=\frac{29}{20} \\ \sec \theta=\frac{29}{21} \\ \cot \theta=\frac{21}{20} \end{gathered}[/tex]8) Remus earns $.15 per unit for the work he does. For all units heproduces in a week, over 1,000, he receives $.20. What were his weeklyearnings if he produced 1,420 units?
Answers
You have the following information:
- Remus earns $.15 per unit
- For units he produced over 1,000 he receives $.20
- He produced 1,420 units
In order to determine what were the weekly earnings, you first take into account the earnings for the first 1,000 units:
0.15 x 1,000 = 150
Next, you calculate the earnings for the units over 1,000, which are 420:
0.20 x 420 = 84
Next, you sum both contributions:
150 + 84 = 234
Hence, the weekly earning os Ramus were of $234
This figure shows two similar polygons; DEFG∼TUVS. Find the value of x.
Answers
According to the question, both polygons are similar. It means you can use proportions to find the value of x.
[tex]\frac{DE}{TU}=\frac{EF}{UV}[/tex]Replace for the given values in the picture
[tex]\begin{gathered} \frac{x}{6}=\frac{4}{12} \\ x=\frac{4}{12}\cdot6 \\ x=2 \end{gathered}[/tex]x has a value of 2.
A board game that normally costs $30 is on sale for 25 percent off. What is the sale price of the game?
$22.50
$27.50
$32.50
$37.50
Answers
30.00 times 0.25= 7.5
30.00-7.50=22.50
A boutique in Lanberry specializes in leather goods for men. Last month, the company sold 56 wallets and 63 belts, for a total of $3,920. This month, they sold 94 wallets and 22 belts, for a total of $3,230. How much does the boutique charge for each item?
Answers
Let w represent the cost of each wallet.
Let b represent the cost of each belt.
Last month, the company sold 56 wallets and 63 belts, for a total of $3,920. This means that
56w + 63b = 3920
This month, they sold 94 wallets and 22 belts, for a total of $3,230. This means that
94w + 22b = 3230
We would solve the equations by applying the method of elimination. To eliminate w, we would multiply the first equation by 94 and the second equation by 56. The new equations would be
5264w + 5922b = 368480
5264w + 1232b = 180880
Subtracting the second equation from the first, we have
5264w - 5264w + 5922b - 1232b = 368480 - 180880
4690b = 187600
b = 187600/4690
b = 40
Substituting b = 40 into 56w + 63b = 3920, we have
56w + 63(40) = 3920
56w + 2520 = 3920
56w = 3920 - 2520 = 1400
w = 1400/56
w = 25
Thus, the boutique charges $25 for each wallet and $40 for each belt
Rewrite the fallowing as an exponential expression in simplest form.
Answers
SOLUTION
[tex]\begin{gathered} 5x\sqrt[]{x} \\ 5x\times\sqrt[]{x} \\ 5x^1\times x^{\frac{1}{2}} \\ 5x^{1+\frac{1}{2}} \\ 5x^{\frac{3}{2}} \\ \end{gathered}[/tex]Y=1/3x+2 standard form
Answers
3y - x = 6 is standard form for the given equation
What is standard form of linear equation ?The typical form for linear equations with two variables is Ax+By=C.For instance, the linear equation 2x+3y=5 is in standard form. Finding both intercepts of an equation in this style is quite easy (x and y).This form is also very useful when trying to solve systems of two linear equations.Calculationy = 1/3x + 2
3y = x + 6
3y - x = 6 is standard form
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write an equation in slope -intercept form for the line with y- intercept -1 and slope -3/2
Answers
The line equation in the slope -intercept form can be written as,
[tex]y=mx+b[/tex]Here, m is the slope and b is the y intercept.
Given,
m = -3/2 and b = -1, therefore we can write the equation as,
[tex]y=-\frac{3}{2}x-1[/tex]The equation is, y =(-3/2)x-1.
What’s the correct answer answer asap for brainlist please
Answers
Answer:
A.it can't be endeavor.
Find the y-coordinate of point P that lies 1/3 along segment CD, closer to C, where C (6, -5) and D (-3, 4).
Answers
SOLUTION:
The given ratio is:
[tex]1:3[/tex]• The given points are ,C(6, -5) and D (-3, 4).
Using the section formula, the coordinate of P is:
[tex]\begin{gathered} P=(\frac{1(-3)+3(6)}{1+3},\frac{1(4)+3(-5)}{1+3}) \\ P=(\frac{-3+18}{4},\frac{4-15}{4}) \\ P=(\frac{15}{4},\frac{-11}{4}) \end{gathered}[/tex]Therefore the coordiantes of P
[tex]P=(\frac{15}{4},\frac{-11}{4})[/tex]Solve the system of linear equations by substitution:x - y = -2 and 3x - y = 2
Answers
To solve the system by substitution, isolate one variable from one equation and substitute the expression obtained for that variable into the other equation.
[tex]\begin{gathered} x-y=-2 \\ 3x-y=2 \end{gathered}[/tex]Isolate x from the first equation:
[tex]\begin{gathered} x-y=-2 \\ \Rightarrow x=y-2 \end{gathered}[/tex]Substitute x=y-2 into the second equation:
[tex]\begin{gathered} 3x-y=2 \\ \Rightarrow3(y-2)-y=2 \end{gathered}[/tex]Solve for y:
[tex]\begin{gathered} \Rightarrow3y-6-y=2 \\ \Rightarrow2y-6=2 \\ \Rightarrow2y=2+6 \\ \Rightarrow2y=8 \\ \Rightarrow y=\frac{8}{2} \\ \Rightarrow y=4 \end{gathered}[/tex]Substitute y=4 into the expression of x to find its value:
[tex]\begin{gathered} x=y-2 \\ \Rightarrow x=4-2 \\ \Rightarrow x=2 \end{gathered}[/tex]Therefore, the solution to the given system is:
[tex]\begin{gathered} x=2 \\ y=4 \end{gathered}[/tex]An extrasolar planet is observed at a distance of 4.2 x 10° kilometers away. A group of scientists has designed a spaceship that can travel at the speed of 7 x 108 kilometers per year. How many years will the spaceship take to reach the extrasolar planet?
Answers
Speed is the time rate at which an object is moving along a path. Then 0.6×10-8 years will the spaceship take to reach the extrasolar planet.
What is Speed?Speed is the time rate at which an object is moving along a path.
The formula for speed is distance/time
Given that
An extrasolar planet is observed at a distance of 4.2 x 10° kilometers away.
Distance= 4.2 x 10°
A group of scientists has designed a spaceship that can travel at the speed of 7 x 10⁸ kilometers per year
Speed = 7 x 10⁸
Time we need to calculate
Time =Distance/speed
Time = 4.2 x 10°/7 x 10⁸
=0.6×10⁻⁸
Hence 0.6×10-8 years will the spaceship take to reach the extrasolar planet.
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Solve the following inequality for t. Write your answer in the simplest form.6t + 3 < 7t + 10
Answers
Therefore, the solution is t > -7.
Simplify 6+ √-80.
06+16√5i
06+4√5
06+16/ √5
06+4√ √5i
Answers
Answer:
6 + 4[tex]\sqrt{5}[/tex]i
Step-by-step explanation:
The prime factorization of 80 is 2x2x2x2x5
6 + [tex]\sqrt{-2x2x2x2x5}[/tex] We can take out 2 pairs of 2 which would be 4 and [tex]\sqrt{-1}[/tex] is i
6 + 4[tex]\sqrt{5}[/tex] i
which expression could be substituted for x in the second equation to find the value of y?
Answers
Substitution
We have the system of equations:
x + 2y = 20
2x - 3y = -1
To solve it with the substitution method, we need to solve the first equation for x and substitute it in the second equation.
Subtracting 2y to the first equation:
x = -2y + 20
This expression corresponds to choice B.
Cindy eats 12 oz of candy in 4 days how long will it take her to eat 1 pound of candy
Answers
We should know that:
1 pound = 16 oz
given Cindy eats 12 oz in 4 days
She will eat 1 pound in x days
So, we need to find the number of days to eat 1 pound which is equal to 16 oz
Using the ratio and proportion
12 : 4 = 16 : x
[tex]\begin{gathered} 12\colon4=16\colon x \\ \frac{12}{4}=\frac{16}{x} \\ x=\frac{4\cdot16}{12}=\frac{16}{3}=5\frac{1}{3} \end{gathered}[/tex]so, the number of days = 5 1/3
Which of the following is not a valid way of starting the process of factoring60x² +84x +49?Choose the inappropriate beginning below.O A. (x )(60)OB. (2x (30%)O C. (6x X10x)OD. (2x (5x )
Answers
Given the equation:
60x^2 + 84x + 49
We are to determine among the options which is not a process of factorizing.
In factorizing, you get factors of the given numbers of the equation that when they are being multiplied or added, they give the numbers in the equation.
So, looking at the options, the only option that does not satisfies the requirement for starting a factorization process is B, which is (2x (30%)
Therefore, the inappropriate process of starting factorization among the option is option B which is (2x (30%).
find the equation of the circle with the given center and radius:center (-1,-6), and radius = 6
Answers
ANSWER:
[tex](x+1)^2+(y+6)^2=36^{}[/tex]STEP-BY-STEP EXPLANATION:
We have that the equation of the circle is given as follows:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where (h, k) is the center and r is the radius } \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} (x-(-1))^2+(y-(-6))^2=6^2 \\ (x+1)^2+(y+6)^2=36^{} \end{gathered}[/tex]i inserted a picture of the question, could you please take the short way.
Answers
Recall the following property of exponents:
[tex](a\cdot b)^x=a^x\cdot b^x\text{.}[/tex]Therefore:
[tex](14\cdot(-58))^{16}=14^{16}\cdot(-58)^{16}\text{.}[/tex]Answer: Option A.
The equation of a line that is perpindicular to y=10x but passes through (1, -3)
Answers
The equation of line is y = -x/10 + -29/10.
Given,
The equation of a line that is perpendicular to y = 10x
and, passes through the (1, -3)
To find the equation of line.
Now, According to the question:
Find the slope of the line that is perpendicular to y = 10x;
m = - 1/10
We know that, Slope of line is ;
y = mx + c
m = -1/10
x = 1
y = -3
Substitute and calculate
- 3 = -1/10 + b
b = -29/10
Now, y = mx + b
Substitute all the values in above slope equation:
y = -x/10 + -29/10
Hence, The equation of line is y = -x/10 + -29/10.
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If triangle ABC with C =90°,if C = 31MM & B equals 57° then a equals
Answers
SOLUTION
Step1; Draw the Triangle and locate the angles
We are to obtain the value of a that is the side |BC|
Applying trigonometry ratios we have
[tex]\begin{gathered} \text{hypotenuse}=c=31 \\ \text{Adjacent}=a \\ \theta=57^0 \end{gathered}[/tex][tex]\begin{gathered} \cos \theta=\frac{adjacent}{Hypotenuse} \\ \cos 57^0=\frac{a}{31}\ldots.\text{ cross multiply} \\ a=31\times cos57^0 \end{gathered}[/tex][tex]\begin{gathered} a=31\times0.8999 \\ a=27.89 \end{gathered}[/tex]Then the value of a = 28mm to the nearest whole number