Which is an equation of the line with a slope of2323 passing through the point (4,-1).Group of answer choices=14+23 =−4+23 =23−53 =23−113
Answers
Given that the slope of a line is 2/3, that passes through the point (4, -1), i.e
[tex]\begin{gathered} m=\frac{2}{3} \\ (x_1,y_1)\Rightarrow(4,-1) \end{gathered}[/tex]The formula to find the equation of straight line is
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where m is the slope of the line} \end{gathered}[/tex]Substitute the values into the formula of the equation of a straight line
[tex]y-(-1)=\frac{2}{3}(x-4)[/tex]Solve for y i.e make y the subject
[tex]\begin{gathered} y-(-1)=\frac{2}{3}(x-4) \\ y+1=\frac{2}{3}(x-4) \\ \text{Open the bracket} \\ y+1=\frac{2}{3}x-\frac{2}{3}(4) \\ y+1=\frac{2}{3}x-\frac{8}{3} \\ y=\frac{2}{3}x-\frac{8}{3}-1 \\ y=\frac{2}{3}x-(\frac{8}{3}+1) \\ y=\frac{2}{3}x-(\frac{8+3}{3}) \\ y=\frac{2}{3}x-\frac{11}{3} \end{gathered}[/tex]Thus, the answer is
[tex]y=\frac{2}{3}x-\frac{11}{3}[/tex]Thus, the answer is the last option.
Related Questions
(4,0) and (0,2) write an equation in standard form for the line that passes through the given points
Answers
We have the following:
The first thing is to find the slope of the line, like this:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]replacing:
[tex]m=\frac{2-0}{0-4}=\frac{2}{-4}=-\frac{1}{2}[/tex]now, the equation has the following form:
[tex]y=mx+b[/tex]for b,
m = -1/2
y = 2
x = 0
replacing:
[tex]\begin{gathered} 2=-\frac{1}{2}\cdot0+b \\ b=2 \end{gathered}[/tex]Therefore, the equation in standard form is:
[tex]\begin{gathered} y=-\frac{1}{2}x+2 \\ y+\frac{1}{2}x=2 \\ 2y+x=4 \end{gathered}[/tex]Walnuts make up half of the nuts in this nut bread:
It has exactly 2 pecans
The number of walnuts is double the number of pecans.
Write an equation to show how many of each nut this nut bread contains.
Answers
The equation to show how many of each nut this nut bread contains is w = 2p and there are 4 walnuts.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The number of walnuts is double the number of pecans. This can be illustrated as:
w = 2p
Therefore, the number of buts will be:
w = 2p
w = 2(2)
w = 4
Therefore, ther are 4 walnuts
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Alision has an interest in entomology, the study of insects. Her collection of insects from around the world includes the four specimens shown in the table below.
Answers
we know that
the mass of Alison's Emperor Scorpio is
[tex]2^{-5}=(\frac{1}{2})^5=\frac{1}{2^5}=\frac{1}{32}\text{ kg}[/tex]The answer is the second option1 x(x-2) how I do this
Answers
x(x-2)
Apply the distributive property:
x(x)+x(-2)
x^2-2x
If licorice costs $6.59 a pound, how much would it cost to buy a quarter-pound of licorice?
If a 10-foot piece of electrical tape has 0.037 feet cut from it. What is the new length of tape?
A director replayed 231 of the 1000 scenes filmed for a movie. Write a decimal to represent the part of the movie the director replayed.
If you had half a dollar, three quarters, eight dimes, six nickels, and nine pennies, how much money would you have altogether?
What is the combined thickness of these shims: 0.008, 0.125, 0.15, 0.185, and 0.005 cm?
All the people of a neighborhood pooled together and won the lottery. They won $10,000,000 and each person got a 0.02 share. How much money did each person receive?
Answers
Answer:
1. 1.6475.
2. 9.963.
3. 0.231
4. $1.69
5. 0.473 cm.
6. x = $200,000
Step-by-step explanation:
1.$6.59 ÷ 4 = 1.6475.
2. 10-0.037 = 9.963
3. 231 divided by 1000.
4. $0.50 + $0.80 + $0.30 + $0.09 = $1.69
5. 0.008 + 0.125 + 0.15 + 0.185 + 0.005
6. x =$10,000,000(0.02) where x is the amount of money each person will receive. x=$200,000 (multiply)
Find the equation of the line passing through point (3,5) and with a slope ⅓
Answers
hello
we are given 1 point with x and y co-ordinate and a slope, we can easily write down the equation of the line
standard equation of a straight line is
[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ c=\text{intercept} \end{gathered}[/tex]to solve this problem, we need to find the intercept first
substitute the x and y co-ordinates in the equation
[tex]\begin{gathered} y=mx+c \\ m=\frac{1}{3} \\ y=5 \\ x=3 \\ 5=\frac{1}{3}(3)+c \\ 5=1+c \\ c=4 \end{gathered}[/tex]we know our intercept is equal to 4 and we can proceed to write out our equation
[tex]y=\frac{1}{3}x+4[/tex]we can leave it this way or multiply through by 3
[tex]3y=x+12[/tex]How does a graph of quadratic function (f(x) = ax2 + bx + c) vary when the a,b, c changes from -1 to +1?
Answers
When a, b, c changes from -1 to +1, the parabolas opens and widens.
Given,
The quadratic function, f(x) = ax² + bx + c
We have to find the change in graph when a, b, c changes from -1 to 1.
First lets consider:
a and b as constants and c is varying.
That is,
x² + x + c
Then, the parabola will move up and down.
Now, lets consider:
a and c as constants and b is varying.
That is,
x² + bx + 1
Then, the vertex will move but all parabolas passes through the points (0, c)
Now, we can move to the question.
What happens to graph when +1 changes to -1.
So,
b and c should keep constant and a is varying.
Then,
ax² + x + 1
Here, the parabolas opens and widens.
That is,
When a, b, c changes from -1 to +1, the parabolas opens and widens.
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Write a quadratic function in intercept form whose graph passes through the points (-5,0)(-1,0) and (-7,-24)
Answers
EXPLANATION
The intercept-form of a quadratic function is as follows:
y = a(x - p)(x - q)
Now, as the roots are (-5,0)
Since the parabola passes through the point (−5,0), then 0=25a−5b+c
Since the parabola passes through the point (−1,0), then 0=a−b+c.
Since the parabola passes through the point (−7,−24), then −24=49a−7b+c.
Thus, we have obtained the following system:
Solving it we get that a=−2, b=−12, c=−10.
Thus, the equation of the parabola is y=(−2x−10)(x+1)
Select the three expressions that are equivalent to 410
Answers
Answer:
A, C, E
Step-by-step explanation:
4^10 = 1048576
A: (4^5)^2 = 1048576
C: 4^20 / 4^10 = 1048576
E: (4^2 x 4^3)^2 = 1048576
What is the area of the blue shape?
Pls help :(
Answers
Answer:
38.5 sq units
Step-by-step explanation:
Hello!
We can split the shape into two rectangles.
The small rectangle at the top has an area of 14 sq units (2 * 7).
The middle rectangle has an area of 49 sq units ( 7*7).
Since the blue part in the middle rectangle is half of the whole rectangle, the area of the blue part there is 24.5 sq units.
Adding that to 14 sq units will give us 38.5 sq units.
Can you help me solve my homework question I will follow along the steps
Answers
Notice that both fractions have the same denominator, therefore, we can simply add the numerators:
[tex]\frac{-5a-3x-2a+9x}{6a}.[/tex]Adding like terms, we get:
[tex]\frac{-7a+6x}{6a}.[/tex]Answer: [tex]\begin{gathered} \frac{-7a+6x}{6a},\text{ or equivalently} \\ -\frac{7}{6}+\frac{x}{a}. \end{gathered}[/tex]Solve for u.u + 8 = 16
Answers
In this case the answer is very simple. .
We must apply algebraic rules to find the solution.
u + 8 = 16
u = 16 - 8
u = 8
The answer is:
u = 8
In which graph does the height difference between Winter Hill and Frozen Field equal the height of BlizzardRun?Choose 1 answer:605040Height (in meters)30.©20100Blizzard RunSnow SlopeWinter HillFrozen FieldSledding hill
Answers
In graph A, you can see that:
• The height of Frozen Field is 50 meters
,• The height of Winter Hill is 15 meters
,• The height of Blizzard Run is 35 meters
Now, we can write the equation that describes the height difference between Winter Hill and Frozen Field.
[tex]\text{ Height of Frozen Field }-\text{ Height of Winter Hill }=50m-15m=35m_{}=\text{ Height of Blizzard Run }[/tex]In graph B, you can see that:
• The height of Frozen Field is 45 meters
• The height of Winter Hill is 10 meters
• The height of Blizzard Run is 55 meters
Now, we can write the equation that describes the height difference between Winter Hill and Frozen Field.
[tex]\text{ Height of Frozen Field }-\text{ Height of Winter Hill }=45m-10m=35m\ne55m_{}=\text{ Height of Blizzard Run }[/tex]Therefore, the graph where the height difference between Winter Hill and Frozen Field is equal to the height of Blizzard Run is graph A.
y−10=2(x−8)Write in Standard Form
Answers
The standard form of a linear equation in two variables is given by the expresssion:
[tex]Ax+By=C[/tex]So, rewriting the equation:
y-10=2x-16
y-2x=-16+10
y-2x=-6
2x-y=6
Calculate each percent increase or percent decreases Round to the nearest whole percent if necessary 1. original amount: 30, new amount: 45 2. original amount: 12, new amount: 16 3. original amount: 17 new amount: 21 4. original amount: 85, new amount: 56 5. original amount: 48, new amount: 37 6. original amount: 124, new amount: PLS HELP ME!!!
Answers
The percentage increase is 50%
Here, we want to calculate the percentage increase or decrease
To know if it is a decrease or an increase, we use the following simple logic.
If new amount is greater than original amount, then it is an increase.
If new amout is less than original amount, then it is a decrease
For the first question, we can see that the new amount is greater than the old amount
This indicates an increase
Mathematically;
[tex]\text{percentage increase = }\frac{(new\text{ amount - original amount)}}{\text{old amount}}\text{ }\times\text{ 100 percent}[/tex]According to the first question, new amount = 45 while old amount = 30
so;
percentage increase = (45-30)/30 * 100%
= 15/30 * 100% = 100%/2 = 50%
Put the following equation of a line into slope-intercept form, simplifying all fractions.
3y-3x=15
Answers
Answer:
[tex]y=x+5[/tex]
Step-by-step explanation:
[tex]3y-3x=15 \\ \\ y-x=5 \\ \\ y=x+5[/tex]
Prove that every differentiable function is continuous
Answers
To prove :
every differentiable function is continuous.
thus, every differentiable function is continuous.
REDUCE 48/96 TO THE LOWEST TERMS
Answers
Sketch the graph of each line.
24)
y=3/5x-4
Answers
The graph of the given line is attached below.
We are given the line:-
y = (3/5)x - 4
We will find the x and y intercepts of the line to plot in the graph.
As the equation is already in the slope intercept form, we can write,
The y-intercept of the line is -4.
Hence, the coordinates of the point will be (0,-4).
To find the x - intercept of the line we will put y = 0 in the given line.
0 = (3/5)x - 4
4 = 3x/5
x = 20/3
The coordinates of the point will be (20/3,0).
We can plot these points to get the desired graph.
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i need immediate help.The exercise consists of finding the axis of symmetry for the equation below.
Answers
Our equation
[tex]y=\frac{1}{3}(x+2)^2-1,[/tex]is a quadratic equation. In simple words, it's a parabola, whose graph (red curve) is the following:
The axis of symmetry of a parabola is just the line dividing the parabola into its two arms. In the graph, the axis of symmetry is the blue vertical line. It's usually represented algebraically by
[tex]x=\text{ The first component of the vertex}[/tex]AnswerThe axis of symmetry of our quadratic equation is
[tex]x=-2[/tex]How to put 7^3/4 in radical form
Answers
Given:
[tex]7^{\frac{3}{4}}[/tex]Resolving it to its radical form can be gotten based on the general laws of indices.
We have:
[tex]A^{\frac{x}{y}}=\sqrt[y]{A^x}[/tex]I.e. the number is raised to the power of the numerator and then we get the denominator's root of the number obtained.
Thus:
[tex]\begin{gathered} 7^{\frac{3}{4}}=\sqrt[4]{7^3}=\sqrt[4]{343} \\ \sqrt[4]{343}=343^{\frac{1}{4}}=343^{(\frac{1}{2}\times\frac{1}{2})} \\ =343^{(\frac{1}{2}\times\frac{1}{2})}=\sqrt[]{343^{\frac{1}{2}}} \end{gathered}[/tex]Now, we have our value in the square root form as:
[tex]\sqrt[]{343^{\frac{1}{2}}}=\sqrt[]{7^{\frac{3}{2}}}[/tex]May I please help with this. I have tried to find the correct answers but still couldn’t get them right
Answers
Solution
[tex]1cm\text{ to 7in}[/tex]We can use ratio to solve the problem
Part A
5cm to x in
[tex]\begin{gathered} 1cm\colon7in \\ 5cm\colon x\text{ in} \end{gathered}[/tex]Now
[tex]\begin{gathered} 1\colon7 \\ 5\colon x \\ \therefore\frac{1}{7}=\frac{5}{x} \\ \\ \text{cross multiply} \\ 1\times x=5\times7 \\ x=35 \end{gathered}[/tex]The final answer
[tex]5cm\text{ to 35inches}[/tex]Part B
Similar step as part a
[tex]\begin{gathered} 1\colon7 \\ y\colon63 \\ \frac{1}{7}=\frac{y}{63} \\ \\ \text{cross multiply} \\ 7y=63 \\ \text{divide both sides by 7} \\ \frac{7y}{7}=\frac{63}{7} \\ y=9 \end{gathered}[/tex]The final answer
[tex]9cm\text{ to 63inches}[/tex]Summary
use matrices D, E, and F to find each sum or product
Answers
Problem
Solution
5. E-D
Procedure
-3-2 =-5
-4-1=-5
0-7=-7
1-5=-4
2-3=-1
6- (-4)=10
And the answer would be:
-5 -5
-7 -4
-1 10
6. 3F
Procedure
3* -2=-6
3 *5 = 15
3* 1= 3
3*3 = 9
3*14=12
3 * -6= -18
And the answer would be:
-6 15 3
9 12 -18
13) An airline weighed the carry-on luggage of all its 1,106 passengers in a single day. How many of these passengers had carry-on luggage that weighed less than 20 lb? *
Answers
we know that
4 lb or less ------> is less than 20 lb ------> 120
5-9 lb------------> is less than 20 lb -------> 222
10-14 lb -------> is less than 20 lb ------->378
15-19 lb ------> is less than 20 lb-------> 256
Adds the number of passenger
120+222+378+256=976
thereforethe answer is 976Use log, 20.356, log, 3 0.503, and log, 5 0.835 to approximate the value of the given logarithm to 3 decimal places. Assume that b>0 and b + 1.
log, 625
X
A
Answers
Answer:
3.34
Step-by-step explanation:
625 is 5^4
Using the log rule [tex]log_b(x^a)=alog_b(x)[/tex],
log_b(5^4) = 4*log_b(5)
4*0.835 = 3.34
Match each function on the left with the ordered pairs on the right.
Answers
We have to match the functions with the corresponding ordered pair.
The easiest way is to pick an ordered pair and replace (x,y) in the function to verify if the equality stands or not. If it does stand, then the ordered pair is part of the function.
Then, we start with (-8,9) and function y = 6x+9. Replacing x and y, we get:
[tex]\begin{gathered} (x,y)=(-8,9) \\ y=6x+9 \\ 9=6\cdot(-8)+9 \\ 9=-48+9 \\ 0=-48\longrightarrow\text{False} \end{gathered}[/tex]As this equation does not verify for (-8,9), this ordered pair does not belong to the function.
We repeat the same process with the next function, y = -9x-1:
[tex]\begin{gathered} (x,y)=(-8,9) \\ y=-9x-1 \\ 9=-9(-8)-1 \\ 9=72-1 \\ 9=71\longrightarrow\text{False} \end{gathered}[/tex]As with the previous function, the equation does not verify.
The next function is y = -1x+1:
[tex]undefined[/tex]I need help with question 12 please in a hurry I understand already
Answers
Trigonometric Ratios
The figure is a triangle with hypotenuse of h = 25 feet. The angle of elevation is 35°.
In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 4 boys and 5 girls are competing, how many different ways could the six medals possibly be given out?
Answers
ANSWER
1,440
EXPLANATION
We have that 4 boys are competing and also 5 girls are competing. 3 medals are given to the boys and 3 medals are given to the girls.
For the boys, the gold medal can be awarded to one of 4 boys, then the silver medal can be awarded to 3 boys because 1 of them already got the gold medal. Finally, the bronze medal can be awarded to one of 2 boys, since the gold and silver medals are already taken. The number of ways the medals can be given to the boys is,
[tex]permutations_{boys}=4\cdot3\cdot2=24[/tex]This situation is similar for the girls, but in this case, there are 5 girls in total,
[tex]permutations_{girls}=5\times4\times3=60[/tex]The total ways the six medals can be given is,
[tex]permutations_{boys}\times permutations_{girls}=24\times60=1,440[/tex]Hence, there are 1,440 ways to give the six medals to the 4 boys and 5 girls.
WILL GIVE BRIANLYEST 100 POINTS ACULLY 200 BC IM GIVING EXTRA POINTS
Answers
Answer:
the mean would increase to a value to about 24.6
Q2: median is 7.
Step-by-step explanation:
Answer:
Q1) the mean would increase in value to about 24.6
Q2) 7
In triangle ABC, angle A is 44 degrees and angle B is 76 degrees. What is the measure of the third angle?
Answers
Answer:
60 degrees
Step-by-step explanation:
Total of angles of a triangle is 180
180-76-44= 60