The equation of line passing through two points (x_1,y_1) and (x_2,y_2) is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Substitute the points in the equation to obtain the equation of line.
[tex]\begin{gathered} y-3=\frac{-7-3}{3-(-3)}(x-(-3)) \\ y-3=\frac{-10}{6}(x+6) \\ 3(y-3)=-5(x+6) \\ 3y-9+5x+30=0 \\ 3y+5x+21=0 \end{gathered}[/tex]So equation of line is 3y+5x+21=0.
Simplify 6+ √-80.
06+16√5i
06+4√5
06+16/ √5
06+4√ √5i
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
following: Find the locus of points whose: ordinate is 1 greater than twice the abscissa
ordinate is 1 greater than twice the abscissa :
[tex]\begin{gathered} x=abscissa \\ y=ordinate \\ y=2x+1 \end{gathered}[/tex]The equation of a line that is perpindicular to y=10x but passes through (1, -3)
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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Y=1/3x+2 standard form
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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Select the polynomial functions for which (x+3) is a factor. Select all that apply.
If x+3 is a factor, then the result of replacing x=-3 in each equation would be 0.
Replacing x=-3 in the polynomials, we have:
Option A
[tex]\begin{gathered} f(-3)=(-3)^4-12(-3)^3+54(-3)^2-108(-3)+81=1296\text{ } \\ \text{ We see that option A is incorrect.} \end{gathered}[/tex]Option B
[tex]\begin{gathered} f(-3)=(-3)^4-3(-3)^3-(-3)+3=168\text{ } \\ \text{We see that option B is incorrect.} \end{gathered}[/tex]Option C
[tex]\begin{gathered} f(-3)=(-3)^5+2(-3)^4-23(-3)^3-60(-3)^2=0\text{ } \\ \text{We see that option C is correct.} \end{gathered}[/tex]Option D
[tex]\begin{gathered} f(-3)=(-3)^5+5(-3)^4-3(-3)^3-29(-3)^2+2(-3)+24=0\text{ } \\ \text{We see that option D is correct.} \end{gathered}[/tex]The answers are options C and D.
Solve the following inequality for t. Write your answer in the simplest form.6t + 3 < 7t + 10
Therefore, the solution is t > -7.
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).
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]helpppppp!!!!!!!!!!!!!!!!!!!!
Answer
D. Observations of constellations show that stars have moved over time.
Explanation:
A scientific claim is basically an observation in science.
Constellation changes there position over time because of earth's rotation around sun. So, observation of constellations shows that stars have moved over time is a scietific claim. If stars would not move then constellation will not form.
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?
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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What’s the correct answer answer asap for brainlist please
Answer:
A.it can't be endeavor.
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
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.
Can You Teach Me How To Multiple Fractions ?
Let's suppose we are given two fractions:
[tex]\frac{a}{b},\frac{c}{d}[/tex]In order to multiply them we simply multiply the numerators and denominators, like this:
[tex]\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}[/tex]For example, let's say we are given the following fractions:
[tex]\frac{1}{2},\frac{3}{5}[/tex]We can multiply them following the previous rule:
[tex]\frac{1}{2}\times\frac{3}{5}=\frac{1\times3}{2\times5}=\frac{3}{10}[/tex]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
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
write an equation in slope -intercept form for the line with y- intercept -1 and slope -3/2
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.
Cindy eats 12 oz of candy in 4 days how long will it take her to eat 1 pound of candy
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
Solve the system of linear equations by substitution:x - y = -2 and 3x - y = 2
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]Consider the circle x ^ 2 + y ^ 2 = 100 and the line x + 3y = 10 and their points of intersection (10, 0) and B = (- 8, 6) . Find coordinates for a point C on the circle that makes chords AB and AC have equal length . Be sure to justify your answer.
The equation of circle is given by,
[tex]x^2+y^2=100\text{ ---(1)}[/tex]The equation of line is given by,
[tex]x+3y=10\text{ ---(2)}[/tex]The points of intersection of the circle and line is,
A=(Xa, Ya)=(10, 0)
B=(Xb, Yb)=(-8, 6)
The length of chord AB can be calculated using distance formula as,
[tex]\begin{gathered} AB=\sqrt[]{(X_b-X_a)^2+(Y_b-Y_a)^2} \\ =\sqrt[]{(-8-10)^2+(6-0)^2} \\ =\sqrt[]{(-18)^2+6^2} \\ =\sqrt[]{324+36} \\ =\sqrt[]{360} \\ =6\sqrt[]{10} \end{gathered}[/tex]Let (Xc, Yc) be the coordinates of point C on the circle. Hence, using equation (1), we can write
[tex]X^2_c+Y^2_c=100\text{ ---(3)}[/tex]Using distance formula, the expression for the length of chord AC is given by,
[tex]AC=\sqrt[]{(X_c^{}-X_a)^2+(Y_c-Y_a)^2_{}}[/tex]Since (Xa, Ya)=(10, 0),
[tex]\begin{gathered} AC=\sqrt[]{(X^{}_c-10_{})^2+(Y_c-0_{})^2_{}} \\ AC=\sqrt[]{(X^{}_c-10_{})^2+Y^2_c} \end{gathered}[/tex]It is given that chords AB and AC have equal length. Hence, we can write
[tex]\begin{gathered} AB=AC \\ 6\sqrt[]{10}=\sqrt[]{(X^{}_c-10_{})^2+Y^2_c} \end{gathered}[/tex]Squaring both sides of above equation,
[tex]\begin{gathered} 360=(X^{}_c-10_{})^2+Y^2_c\text{ } \\ (X^{}_c-10_{})^2+Y^2_c=360\text{ ----(4)} \end{gathered}[/tex]Subtract equation (4) from (3) and solve for Xc.
[tex]\begin{gathered} (X^{}_c-10_{})^2-X^2_c=360-100 \\ X^2_c-2\times X_c\times10+100-X^2_c=260 \\ -20X_c=260-100 \\ -20X_c=160 \\ X_c=\frac{160}{-20} \\ X_c=-8 \end{gathered}[/tex]Put Xc=-8 in equation (3) to find Yc.
[tex]\begin{gathered} (-8)^2+Y^2_c=100 \\ 64+Y^2_c=100 \\ Y^2_c=100-64 \\ Y^2_c=36 \\ Y^{}_c=\pm6 \\ Y^{}_c=6\text{ or }Y_c=-6 \end{gathered}[/tex]So, the coordinates of point C can be (Xc, Yc)=(-8, 6) or (Xc, Yc)=(-8, -6).
Since (-8, 6) are the coordinates of point B, the coordinates of point C can be chosen as (-8, -6).
Therefore, the coordinates of point C is (-8, -6) if chords AB and AC have equal length.
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?
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
F(x)=x+1 and g(x)=x^3 -1Find (fg)(5)
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
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?
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
Kentaro mixed 3.5 gallons of cranberry juice with 3 quarts of orange juice to make a punch.1 gallon = 4 quarts1 gallon = 16 cups1 cup = 8 fluid OuncesHow many fluid ounces of punch did Kentaro make? Enter the answer in the box.
The total volume made is 544 fluid ounces of punch
Here, we want to get the amount of fluid ounces of punch made
What we have to do here is to convert each of the volumes to fluid ounces and add together
From the Cranberry juice;
[tex]\begin{gathered} 1\text{ gallon = 16 cups} \\ 3.5\text{ gallons will be = 3.5 }\times\text{ 16 = 56 cups} \\ 1\text{ cup = 8 fluid oz} \\ 56\text{ cups will be; 56}\times\text{ 8 = 448 fluid oz} \end{gathered}[/tex]Now, for the orange juice;
[tex]\begin{gathered} 1\text{ gallon = 4 quarts} \\ 4\text{ quarts = 16 cups} \\ 3\text{ quarts = }\frac{3\times16}{4}\text{ = 12 cups} \\ \\ 1\text{ cup = 8 fluid oz} \\ 12\text{ cups = 12 }\times\text{ 8 = 96 fluid oz} \end{gathered}[/tex]Here, to get the total number, we simply add
That will be;
[tex]96\text{ + 448 = 544 fluid ounces}[/tex]There are 2 liters of soda left after a class party. Laura, Gavin, Anita, Emmett, and Rebecca are on the clean-up crew, and decide to split the soda equally.
How much soda does each student get?
Write your answer as a proper fraction or mixed number.
0.4 liters or 2/5
Step-by-step explanation:
Dividing the soda equally, Each student would get 0.4 liters or 2/5
In ACDE, J is the centroid. If JG=21 find CG. D F G C E H
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 equation of the circle with the given center and radius:center (-1,-6), and radius = 6
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.
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.
What is the value of x if x + 15 = 38 ? Enter answer below
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
Christine is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of Math is Fun she sells. Suppose that x and y are related by the equation 70x + 1700= y.Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What is the change in Christine’s total pay for each copy of Math is Fun she sells? What is Christine’s total pay if she doesn’t sell any copies of Math is Fun?
From the information given, the equation relating her total pay (in dollars), y to the number of copies of Math is Fun she sells, x is expressed as
y = 70x + 1700
This is a linear equation. The slope intercept form of a linear equation is expressed as
y = mx + b
where
m = slope or rate of change
b = y intercept of the value of y when x = 0
By comparing both equations,
m = 70
b = 1700
a) Thus, the change in Christine’s total pay for each copy of Math is Fun she sells 70 dollars per copy
b) Christine’s total pay if she doesn’t sell any copies of Math is Fun is the value of y when x = 0. thus,
Christine’s total pay if she doesn’t sell any copies of Math is Fun = $1700
Find the annual fixed expense for car insurance if John makes
six payments in a year at $174.45 each?
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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This is very hard for me I need to know how to do it
The zeros of a function are the values of x that make the function be equal to zero.
When graphing a quadratic equation, the graph is a parabola, and the zeros of the function are the x-intercepts of the graph, which are the points where the graph intersects the x-axis.
So, if the zeros of this function are x = -8 and x = 2, that means the parabola crosses the x-axis at x = -8 and x = 2.
Therefore the correct option is the first one.
Rewrite the fallowing as an exponential expression in simplest form.
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]