Standard form of a line:
Ax + By = C
where A is a positive integer, B is an integer and C is a constant.
10. y + 1 = x + 2
y + 1 - y = x + 2 - y subtracting y at both sides
1 = x + 2 - y
1 - 2 = x + 2 - y - 2 subtracting 2 at both sides
-1 = x - y
13. y - 4 = -(x - 1)
(y - 4)*(-1) = -(x - 1)*(-1) Multiplying by -1 at both sides
-y + 4 = x - 1
-y + 4 + y = x - 1 + y Adding y at both sides
4 = x - 1 + y
4 + 1 = x - 1 + y + 1 Adding 1 at both sides
5 = x + y
16. y - 10 = -2(x - 3)
(y - 10)/(-2) = -2(x - 3)/(-2) Dividing by -2 at both sides
y/-2 +5 = x - 3
2*(y/-2 +5) = 2*(x - 3) Multiplying by 2 at both sides
-y + 10 = 2x + 6
-y + 10 + y = 2x + 6 + y Adding y at both sides
10 = 2x + 6 + y
10 - 6 = 2x + 6 + y - 6 subtracting 6 at both sides
4 = 2x + y
Danny uses an app that shows him how many kilometers he has ran to prepare for a marathon. The app said he ran 8.045 kil. He wants to post online how many miles he ran. Danny ran _____ miles.
1 kilometer is equivalent to 0.62 miles. To find how many miles are 8.045 kilometers, we can use the next proportion:
[tex]\frac{1\text{ km}}{8.045\text{ km}}=\frac{0.62\text{ mi}}{x\text{ mi}}[/tex]Solving for x,
[tex]\begin{gathered} 1\cdot x=0.62\cdot8.045 \\ x=5\text{ miles} \end{gathered}[/tex]Another way to solve this, is the next one:
[tex]8.045\text{ km}\cdot\frac{0.62\text{ miles}}{1\text{ km}}=5\text{ miles}[/tex]Danny ran 5 miles.
which of the following Roots would be between 8 and 7
To find which of the following roots is between "8" and "7" we can calculate the root of which numbers result in 8 and 7. To do this we will power them by 2, this is done because power is the oposite operation to the root. Doing this gives us:
[tex]\begin{gathered} 8^2=64 \\ 7^2=49 \end{gathered}[/tex]So the root of 64 is 8 and the root of 49 is 7. We need to find the number that is between 49 and 64.
From the options the only one that qualifies is 52. The correct option is b.
which values are in the domain of the function F(X)= -6x + 11 with a range of (-37 ,-25, -13, -1)? select all that apply a)1b)4c)8d)5e)2f)6g)3h)7
Answers:
2
4
6
8
Explanation:
The domain of the function with a range {-37, -25, -13, -1} will be the set of values of x when f(x) is -37, -25, -13, and -1. So, to find the correct answers, we need to solve the following equations:
If f(x) = -37, we get:
[tex]\begin{gathered} f(x)=-6x+11 \\ -37=-6x+11 \\ -37-11=-6x+11-11 \\ -48=-6x \\ \frac{-48}{-6}=\frac{-6x}{-6} \\ 8=x \end{gathered}[/tex]If f(x) = - 25, we get:
[tex]\begin{gathered} -25=-6x+11 \\ -25-11=-6x+11-11 \\ -36=-6x \\ \frac{-36}{-6}=\frac{-6x}{-6} \\ 6=x \end{gathered}[/tex]If f(x) = - 13, we get:
[tex]\begin{gathered} -13=-6x+11 \\ -13-11=-6x+11-11 \\ -24=-6x \\ \frac{-24}{-6}=\frac{-6x}{-6} \\ 4=x \end{gathered}[/tex]If f(x) = -1, we get:
[tex]\begin{gathered} -1=-6x+11 \\ -1-11=-6x+11-11 \\ -12=-6x \\ \frac{-12}{-6}=\frac{-6x}{-6} \\ 2=x \end{gathered}[/tex]Therefore, the domain is the set of the values of x: {2, 4, 6, 8}
i do not know how to get the stuff it is asking me for
We can check in the graph the the parabola touches the x-axis in only one point, which is (5,0). Therefore, the quadratic function has 1 solution.
Solution: x = 5 and x = 5
Question: Ramona wrote down an expression that was equivalent to... 3 . 15 + 10 (8 - 1) -82.(please look at the photo the numbers are different.)
ANSWER
[tex]45+70-64[/tex]EXPLANATION
We want to find the equivalent expression to:
[tex]3\cdot15+10(8-1)-8^2[/tex]To do this, first simplify the bracket:
[tex]\begin{gathered} 3\cdot15+10(7)-8^2 \\ 3\cdot15+70-8^2^{} \end{gathered}[/tex]Now, simplify the exponent:
[tex]3\cdot15+70-64[/tex]Finally, simplify the muiltiplication:
[tex]45+70-64[/tex]That is the answer.
I need help with my math
Given the equation:
[tex]y=\frac{2}{3}x-3[/tex]We will graph the equation using the intercepts
The X-intercept is the value of x when y = 0
so,
[tex]\begin{gathered} y=0\rightarrow0=\frac{2}{3}x-3 \\ \frac{2}{3}x=3 \\ x=\frac{9}{2}=4.5 \end{gathered}[/tex]The y-intercept is the value of y when x = 0
so,
[tex]x=0\rightarrow y=-3[/tex]So, the graph of the line passes through the points (0, -3) and (4.5, 0)
The graph of the equation is as shown in the following picture:
The correct option is:
Find the z-scores for which 70% of the distribution's area lies between - Z and z.
The values given by z-score tables represent the fraction of the area under a normal curve between -∞ and z. For example, for a given z, the value given by a table represents the following area:
However, in this exercise we must find the area under the curve between -z and z and not between -∞ and z. We are basically looking for an area like this one:
So the z in a z-score table that corresponds to 70% of the area is not the answer.
However, we still can find the value of z using a z-score table. Remember that the total area under this curve is equal to 1. We are told that the area between -z and z is the 70% so this area is equal to 0.7. Then the remaining area i.e. the sum of the areas at the left of -z and at the right of z is equal to 1-0.7=0.3. Another important property of the normal distribution curve is that it's symmetric so the area at the right of z is equal to that at the left of -z then the two green areas are equal and their sum is 0.3. This means that each green area is equal to 0.3/2=0.15. So basically we have the following:
- The area between -∞ and -z is equal to 0.15.
- The area between z and ∞ is equal to 0.15.
Remember that the z-scores tables give us the z-score associated with the area under the curve between -∞ and z. Then if we look at a z-score table and look for the value 0.15 the table will give us the value of -z and with it the value of z. So we must look for 0.15 in a z-score table:
0.14917 is the closest value to 0.15 in this table so it is useful. As you can see it's located at row -1 and column 0.04 which means that it corresponds to -1.04. Then -z=-1.04 and therefore z=1.04. Then the answer is:
[tex]-1.04,1.04[/tex]Which of the following represents vector vector u equals vector RS in linear form, where R (–22, 6) and S (–35, 14)?
Given two points R(xR, yR) and S(xS, yS), the vector v = RS is found as follows:
[tex]v=[/tex]In this case, the points are R (–22, 6) and S (–35, 14), then the vector is:
[tex]\begin{gathered} v=<-35-(-22),14-6> \\ v=<-13,8> \\ Or \\ v=-13i+8j \end{gathered}[/tex]how would you find the absolute value of 5.23? i do not know how. my child is using a number line.
The absolute value is to write the nubmer as a positive number
For example:
|-4| = 4
|-2.5| = 2.5
| 6| = 6
So, the number if was negative, we will make it positive
And the number if positive, will remain as it is
There is no need to use the number lines
So, the absolute value of 5.23 = | 5.23 | = 5.23
on the beach boardwalk there are 20 different places to get food this year the World War II Saturday of 25% more places to get food how many total places to get food this year
Originally 20 places
Now there are 25% more
25% of 20 = 25(20)/100 = 500/100 = 5
25% of 20 = 25 times 20 and divided by 100 = 500/100 = 5
[tex]\frac{25\cdot20}{100}\text{ = 5}[/tex]Original quantity = 20
25% of 20 is 5
Ttotal quantity = original quantity + 25% = 20 + 5 = 25
Answer:
There are 25 places to get food this year
20 old plus 5 new
A sandwich shop has 70 stores and 90% of the stores are in California. The rest of the stores are in Nevada. How many stores are in California and how many are in Nevada?There are ____ stores in California and ____ in Nevada.
The sandwich shop has a total of 70 stores, this is the 100% of their stores.
90% of the stores are in California
The rest of the stores, 10%, are in Nevada.
To calculate how many stores correspond to the 90% you can use cross multiplication
100%_____70 shops
90%______x shops
[tex]\begin{gathered} \frac{70}{100}=\frac{x}{90} \\ x=(\frac{70}{100})90 \\ x=63 \end{gathered}[/tex]So the 90% of 70 is 63, this means that there are 63 stores in California.
Now subtract the number of stores in California from the total number of stores
[tex]70-63=7[/tex]And we get that there are 7 stores in Nevada
What is the probability that the spinner lands on blue?
Answer:
Concept:
The total number of angles in a circle is
[tex]\begin{gathered} =360^0 \\ =120^0+60^0+180^0=360^0 \end{gathered}[/tex]The angle of the sector that represents blue is
[tex]=60^0[/tex]To calculate the probability, we will use the formula below
[tex]\begin{gathered} P(\text{blue)}=\frac{n(\text{blue)}}{n(S)} \\ n(\text{blue)}=60^0,n(S)=360^0 \\ P(\text{blue)}=\frac{n(\text{blue)}}{n(S)}=\frac{60}{360} \\ P(\text{blue)}=\frac{1}{6} \end{gathered}[/tex]Hence,
The final answer is = 1/6
x is inversely proportional to y, and x = 18 when y = 4. a. Write an equation relating x and y b. Find x when y = 30
Here, we want to solve a proportional relationship problem
a) We have the proportion as follows;
[tex]\begin{gathered} x\propto\frac{1}{y} \\ \\ k\text{ as constant} \\ \\ k\text{ = xy} \\ \\ \text{for x = 18 and y = 4} \\ \\ k\text{ = 18}\times4\text{ = 72} \\ xy\text{ = 72} \end{gathered}[/tex]b) X, when y = 30
[tex]\begin{gathered} xy\text{ = 72} \\ x\text{ = }\frac{72}{y} \\ x\text{ = }\frac{72}{30} \\ x\text{ = 2.4} \end{gathered}[/tex]What is the equation of the line passing through the points( 29 ) and 2) in slope-intercept form?O y-zx-3O y-3x+o y = 2 x - 22O x- x+Mark this and retumSave and ExitNexSubmit
The slope-intercept form is
[tex]y=mx+b[/tex]First we find m which is defined as rise / run
[tex]m=\frac{\text{rise}}{\text{run}}=\frac{y_1-y_2}{x_1-x_2}[/tex][tex]\Rightarrow m=\frac{(\frac{11}{12})-(\frac{19}{20})}{(\frac{1}{3})-(\frac{2}{5})}[/tex][tex]m=\frac{1}{2}[/tex]And finally, we find the y-intercept b from one of the points given.
Let us use the point (1/3, 11/12).
[tex]\frac{11}{12}=\frac{1}{2}(\frac{1}{3})+b[/tex][tex]\frac{11}{12}=\frac{1}{6}+b[/tex][tex]b=\frac{11}{12}-\frac{1}{6}[/tex][tex]b=\frac{3}{4}[/tex]Hence, the equation of the line in slope-intercept form is
[tex]y=\frac{1}{2}x+\frac{3}{4}[/tex]which is the second choice in the column.
Which is an equation of the line perpendicular to y+5X=7and passes through (10,-4)[A] y = 1/5x +7[B] y = 5x + 25/4[C] y = 1/5x - 6[D] y = 5x + 7
Given the equation:
[tex]y+5x=7[/tex]we can find its slope if we write it in the y=mx+b form:
[tex]\begin{gathered} y+5x=7 \\ \Rightarrow y=-5x+7 \end{gathered}[/tex]Now, we know as a general rule, that the slope of the perpendicular of the line that has slope m, is -1/m, more clearly:
[tex]\begin{gathered} \text{if m is the slope of the line} \\ \Rightarrow m_p=-\frac{1}{m}\text{ is the slope of the perpendicular line} \end{gathered}[/tex]So, in this case we have:
[tex]\begin{gathered} m=-5 \\ \Rightarrow m_p=-\frac{1}{m}=-\frac{1}{-5}=\frac{1}{5} \\ m_p=\frac{1}{5} \end{gathered}[/tex]now we use the slope-point formula to find the equation of the perpendicular line:
[tex]\begin{gathered} (x_0,y_0)=(10,-4) \\ m_p=\frac{1}{5}_{} \\ y-y_0=m(x-x_0)_{} \\ \Rightarrow y-(-4)=\frac{1}{5}(x-10) \\ \Rightarrow y+4=\frac{1}{5}x-\frac{10}{5} \\ \Rightarrow y=\frac{1}{5}x-2-4=\frac{1}{5}x-6 \\ y=\frac{1}{5}x-6 \end{gathered}[/tex]therefore, the line perpendicular to y+5x=7 that passes through (10,-4) is y=1/5x-6
A van with seven people drove 422 miles six hours. About how many miles did they travel each hour?
Distance travelled by van in six hours is 422 miles.
Determine the distance travelled by the van in one hour.
[tex]\begin{gathered} \frac{422}{6}=70.333 \\ \approx70.3\text{ miles} \end{gathered}[/tex]So, they travel approximately 70.3 miles in each hour.
If you shift the function F(x) = log10 x right three units, what is the newfunction, G(x)?O A. G(x) = log, (x-3)O B. G(x) = log, (x+3)O C. G(x) = 109, *-3O D. G(x) = 109,X+3
Given the function:
[tex]F\mleft(x\mright)=log_{10}x[/tex]You need to remember that, according to the Transformation Rules for Functions:
1. If:
[tex]f(x+h)[/tex]The function is shifted left "h" units.
2. If:
[tex]f(x-h)[/tex]The function is shifted right "h" units.
In this case, you know that F(X) is shifted right three units to obtain the new function G(x), then the transformation has this form:
[tex]F(x-3)[/tex]Therefore, you can determine that:
[tex]G(x)=\log _{10}\mleft(x-3\mright)[/tex]Hence, the answer is: Option A.
To construct a square, match the corresponding steps to the proper orders. (basically match the words on the left with the number of steps 1-6)
Given:
Construct a square by matching the corresponding steps to the proper orders.
Explanation:
a) The first step would be,
Draw a line segment AB.
Therefore, statement 1 itself is the first step.
b) The second step would be,
Construct a perpendicular line to AB at B.
Therefore, statement 2 itself is the second step.
c) The third step would be,
Measure the distance AB with the compass. Draw an arc on the perpendicular line from B.
Therefore, statement 3 itself is the third step.
d) The fourth step would be,
Label it as C. Draw an arc from C without changing the measurements.
Therefore, statement 4 itself is the fourth step.
e) The fifth step would be,
Place the compass at A. Draw an arc from A without changing the measurements to intersect the previous arc.
Mark it as D.
Therefore, statement 5 itself is the fifth step.
f) The sixth step would be,
Connect ABCD.
Therefore, statement 6 itself is a sixth step.
If P(6,-2). O(-2,8), R(-4, 3), and S(-9, y). find the value of y so that PO perpendicular to RS.please?
Answer:
y = - 1
Explanation:
Two lines are perpendicular if the product of their slopes is equal to -1.
Additionally, we can calculate the slope of a line with two points (x1, y1) and (x2, y2) as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]If we replace (x1, y1) by P(6, -2) and (x2, y2) by O(-2, 8), we get that the slope of PO is equal to:
[tex]m=\frac{8-(-2)}{-2-6}=\frac{8+2}{-8}=\frac{10}{-8}=-1.25[/tex]In the same way, if we replace (x1, y1) by (-4, 3) and (x2, y2) by (-9, y), we get that the slope of RS is equal to:
[tex]m_{}=\frac{y-3}{-9-(-4)}=\frac{y-3}{-9+4}=\frac{y-3}{-5}[/tex]Then, the product of these two slopes should be equal to -1, so we can write the following equation:
[tex]-1.25\cdot(\frac{y-3}{-5})=-1[/tex]So, solving for y, we get:
[tex]\begin{gathered} (-5)(-1.25)\cdot(\frac{y-3}{-5})=(-5)(-1) \\ -1.25(y-3)=5 \\ y-3=\frac{5}{-1.25} \\ y-3=-4 \\ y=-4+3 \\ y=-1 \end{gathered}[/tex]Therefore, the value of y is equal to -1
What are the coordinates of point F? 5 4 F 3 2 1 E 4 2 3 -5 -4 -3 -2 -1 0 4 -2 -3 4 -5
According to the graph, point F is on the first quadrant. Its coordinates are (1,3). Remember that the first value is x, adn the
Hence, the coordinates of point F are (1,3).-2.5 (-3 +4n + 8) how can i expand the expression
SOLUTION:
Step 1:
In this question, we are given the following:
[tex]-2.\text{ 5( -3 + 4n + 8 )}[/tex]Step 2:
Expanding the expression, we have that:
[tex]\begin{gathered} -2.\text{ 5 ( -3 + 4n + 8 )} \\ \text{solving the bracket first, we have that:} \\ -2.\text{ 5( 4n + 5)} \\ -10n\text{ - 12. 5} \end{gathered}[/tex]Two letters are chosen at random from the word MATHEMATICS, with replacement. What is the probability that the first letter is a consonant and the second letter is a vowel?
We want to know the probability of choosing two letters at random, and the first letter is a consonant and the second one is a vowel. The word we are given is
MATHEMATICS
We see that it has 7 consonants and 4 vowels. We will denote by E to the event:
[tex]E=\text{"Getting as a first letter a consonant and second letter a vowel"}[/tex]As the events: "Obtaining a consonant" and "Obtaining a vowel" are independent, we get:
[tex]P(E)=\frac{7}{11}\cdot\frac{4}{10}=\frac{28}{110}=\frac{14}{55}=0.25\bar{45}[/tex]This means that the probability that the first letter is a consonant and the second letter is a vowel is (approximately) 25.45%.
Explain how I know the vertex of m(x)=x(x+6)
Answer: a lot of 5
Step-by-step explanation:
yes
Answer:
Rewrite in vertex form and use this form to find the vertex (h,k)(h,k).(12,−254)
Step-by-step explanation:
Hope this helps ;)
Which expression below is an equivalent expression to this one: (8x- 4x^4 + 8x^3) - (6 - 2x + 6x^4) Select one: 1) -10x^4 + 13x^3+ 10x - 6 2) - 10x^4 + 13x^3 + 15x - 13) -10x^4 + 8x^3 + 10x – 6 4) -10x^4 + 13x^3 + 15x - 6
2x = 5(2-y)y = 3(-x + 5)Solve system of equation using elimination method
The given system of equations is:
[tex]2x=5(2-y);y=3(-x+5)[/tex]Simplify to get:
[tex]\begin{gathered} 2x=10-5y \\ 2x+5y=10\ldots(i) \\ y=-3x+15 \\ 3x+y=15\ldots(ii) \end{gathered}[/tex]Multiply (ii) by 5 to get:
[tex]15x+5y=75\ldots(iii)[/tex]Subtract (i) from (iii) to get:
[tex]\begin{gathered} 15x+5y=75 \\ -2x-5y=-10 \\ 13x=65 \\ x=\frac{65}{13}=5 \end{gathered}[/tex]Substitute x=5 in (ii) to get:
[tex]\begin{gathered} 3(5)+y=15 \\ y=0 \end{gathered}[/tex]Solution set {5,0}.
Can I get help on 22. I don’t understand what I did wrong
From the problem, we have an inequality :
[tex]-6x+1<7[/tex]Subtract 1 to both sides of the equation :
[tex]\begin{gathered} -6x+1-1<7-1 \\ -6x<6 \end{gathered}[/tex]Divide both sides by -6 :
[tex]\begin{gathered} -6x<6 \\ x<\frac{6}{-6} \\ x<-1 \end{gathered}[/tex]The solution is x < -1
3x – 2y= 12Find the x- and y-intercepts from the equation in standard form above. Explain how you got each intercept.
To find the y-intercept, we have to make x=0 and solve for y:
[tex]\begin{gathered} 3x-2y=12 \\ x=0 \\ \Rightarrow3\cdot0-2y=12 \\ \Rightarrow-2y=12 \\ \Rightarrow y=\frac{12}{-2}=-6 \\ y=-6 \end{gathered}[/tex]Now, to find the x-intercept, we make y=0 and do the same as the previous case:
[tex]\begin{gathered} y=0 \\ \Rightarrow3x-2\cdot0=12 \\ \Rightarrow3x=12 \\ \Rightarrow x=\frac{12}{3}=4 \\ x=4 \end{gathered}[/tex]therefore, the y-intercept is the point (0,-6) and the x-intercept is the point (4,0)
I need help with math
Answer:
w = 52
Step-by-step explanation:
We have supplementary angles.
[tex]3w - 28 + w = 180[/tex]
[tex]4w - 28 = 180[/tex]
[tex]4w = 208[/tex]
[tex]w = 52[/tex]
Allison spent $7.80 on lunch. That represents 6% of her daily net income. What is Allison's daily net income? Round your answer to the nearest penny if needed.
we get that the net income of Alison is:
[tex]\frac{7.8}{6}\cdot100=130[/tex]so her net income is $130
We estimate that the population of a certain, in t years will be given byp (t) = (2t² + 75) / (2t² + 150) million habitantsAccording to this hypothesis:What is the current population?What will it be in the long term?Sketch the population graph
Given that the population can be represented by the equation;
[tex]P(t)=\frac{2t^2+75}{2t^2+150}[/tex]The current population (Initial population) is the population at time t=0;
Substituting;
[tex]t=0[/tex][tex]\begin{gathered} P(0)=\frac{2t^2+75}{2t^2+150}=\frac{2(0)^2+75}{2(0)^2+150}=\frac{75}{150} \\ P(0)=0.5\text{ million} \end{gathered}[/tex]Therefore, the current population of the habitat is;
[tex]0.5\text{ million}[/tex]The long term population would be the population as t tends to infinity;
[tex]\begin{gathered} \lim _{t\to\infty}P(t)=\frac{2t^2+75}{2t^2+150}=\frac{2(\infty)^2+75}{2(\infty)^2+150}=\frac{\infty}{\infty} \\ \lim _{t\to\infty}P(t)=\frac{4t}{4t}=1 \end{gathered}[/tex]Therefore, the long term population of the habitat is;
[tex]P(\infty)=1\text{ million}[/tex]