Answer:
[tex](y+6)=\frac{2}{8} (x+2)[/tex]
Step-by-step explanation:
First, find the slope
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
-4+6=2
6+2=8
m=2/8
With the slop, you have everything you need to stick one of your points in point-slope form. I chose (-2,-6)
[tex](y-y1)=m(x-x1)\\(y+6)=\frac{2}{8} (x+2)[/tex]
Really, that's all you need as it is not an equation of a line. Not the most useful form, but works as an answer.
find the solution of this system of equations-7y=-34-2x2x+4y=10
we have the system
-7y=-34-2x ------> equation A
2x+4y=10 ------> equation B
In the equation A
Multiply by -1
-2x+7y=34------> new equation A
Adds new equation A and equation B
-2x+7y=34
2x+4y=10
------------------
7y+4y=34+10
11y=44
y=4
Find the value of x
Substitute the value of y in equation A or equation B
2x+4(4)=10
solve for x
2x+16=10
2x=10-16
2x=-6
x=-3
therefore
the solution is the point (-3,4)f (x) = 4x^2+2x+6find the value of the discriminate of f and how many distinct real number zeros f has.
The Solution:
Given:
Required:
To find the discriminant of f.
By formula, the discriminant (D) is:
[tex]D=b^2-4ac[/tex]Where:
[tex]\begin{gathered} a=4 \\ b=2 \\ c=6 \end{gathered}[/tex]Substitute:
[tex]\begin{gathered} D=2^2-4(4)(6)=4-96=-92 \\ No\text{ real root since D}<0 \end{gathered}[/tex]Therefore, the correct answers are:
Discriminant = -92
No distinct real root.
Hi, can you help me to solve this exercise please, it’s about Function Evaluation & Applications!
Given
[tex]f(x)=\lvert x\rvert+4[/tex]Part A
[tex]\begin{gathered} we\text{ want to find f(4)} \\ we\text{ only n}eed\text{ to substitute the value of 4 to x in the given function} \\ f(4)=\lvert4\rvert+4 \\ f(4)=4+4_{} \\ f(4)=8 \end{gathered}[/tex]Part B
[tex]\begin{gathered} we\text{ want to evaluate f(-4)} \\ \text{note that the absolute value returns postive values} \\ \text{thus, }\lvert-4\rvert=4 \\ f(-4)=\lvert-4\rvert+4 \\ f(-4)=4+4 \\ f(-4)=8 \end{gathered}[/tex]Part C
[tex]\begin{gathered} To\text{ find f(t), we only n}eed\text{ to replace t with x} \\ f(t)=\lvert t\rvert+4 \end{gathered}[/tex]Given the functions f(x) = x ^ 2 + 3x - 1 and g(x) = - 2x + 3 determine the value of (f + g)(- 2)
Start by finding (f+g)(x)
[tex](f+g)(x)=(x^2+3x-1)+(-2x+3)[/tex]simplify the equation
[tex]\begin{gathered} (f+g)(x)=x^2+(3x-2x)-1+3 \\ (f+g)(x)=x^2+x+2 \end{gathered}[/tex]then, replace x by -2
[tex]\begin{gathered} (f+g)(-2)=(-2)^2+(-2)+2 \\ (f+g)(-2)=4-2+2 \\ (f+g)(-2)=4 \end{gathered}[/tex]10. Calculate the circumference of cylinder that is 34cm tall and has a volume of560cm#9
The Solution.
By formula, the volume of the planet (sphere) is given as below:
[tex]V=\frac{4}{3}\pi r^3[/tex]In this case,
[tex]\begin{gathered} V=5.10^{18}km^3 \\ r=\text{?} \end{gathered}[/tex]Substitting these given values into the formula above, we can solve for r, the radius of the planet.
[tex]\frac{4}{3}\pi r^3=5(10^{18})[/tex]Dividing both sides by
[tex]\frac{4}{3}\pi[/tex]We get
[tex]r^3=\frac{5\times10^{18}}{\frac{4}{3}\pi}=\frac{5\times10^{18}}{4.188790205}[/tex]Taking the cube root of both sides, we have
[tex]\begin{gathered} r=\sqrt[3]{(}\frac{5\times10^{18}}{4.188790205})=(1.060784418\times10^6)km^{} \\ Or \\ r=1060784.418\text{ km} \end{gathered}[/tex]Thus, the correct answer is 1060784.418km.
Which equation could be represented by the number line? A. 3 OB.-4 5=1 OC. 1+ -5)= OD. -3+4 -1
According to the given number line, we have to go back from the second point to the first point 4 spots. In other words, the equation has to include a sum with -4.
Therefore, the answer is A since it's expressing an initial number 3, then the sum with -4.if the population of a city is 158,000 and isdecreasing by 8% every year, what will thepopulation be in 5 years?
Solution:
From the question, we use the population decay formula expressed as
[tex]\begin{gathered} P(t)=P(1-r)^t \\ where \\ P\Rightarrow initial\text{ population} \\ r\Rightarrow decay\text{ rate} \\ t\Rightarrow time \\ P(t)\Rightarrow population\text{ at time t} \end{gathered}[/tex]Given that:
[tex]\begin{gathered} P=158000 \\ r=8\%=\frac{8}{100}=0.08 \\ t=5 \end{gathered}[/tex]By substituting these values into the population decay formula, we have
[tex]\begin{gathered} P(t)=158000(1-0.08)^5 \\ =104134.88066 \end{gathered}[/tex]Hence, the population in 5 years will be
[tex]104134.88066[/tex]Pattern Exercise Mins Components Fitnes 0 5 1 9 2 25 3 89 4 ? What do you notice about the pattern of components from minute to minute? 2. State the value for the question mark. I E O BI
We can calculate how much each component increases, this is shown in the following image:
So we can see that the pattern in which the components increase from minute to mites is that starts by adding 4, then they add 4x4=16, then they add 16x4=64, and so on:
So the rule is that the next increase is the previous increase multiplied by 4.
Thus, the next increase in components (the question mark) should be:
The previous one +256, which gives:
[tex]?=89+256=345[/tex]Answer: 345
What is the value of y in the solution set of the system of linear equations shown below?y = -x + 124x - 2y = 36A.10B. 8C. 6D. 2
y = 2 (option D)
Explanation:y = -x + 12
4x - 2y = 36
rewriting the equations:
y + x = 12 ....equation 1
-2y + 4x = 36 ....equation 2
Using elimination method:
we will be eliminating y. So we need to make the coefficient of y to be the same in both equation. We will be multiplying the first equation by 2.
2y + 2x = 24 ....equation 1
-2y + 4x = 36 ....equation 2
Add both equations:
2y + (-2y) + 2x + 4x = 24 + 36
2y-2y + 6x = 60
6x = 60
x = 60/6 = 10
Insert the value of x in any of the equation. Using equation 2:
4(10) - 2y = 36
40 -2y = 36
-2y = 36 - 40
-2y = -4
y = -4/-2
y = 2 (option D)
Which number sentence can be used to find the difference between five times three and two times six?
x= 5x3-2x6
x = 5x2+3x6
x = 5(3+2x6)
x = 5x3+2x6
Which number sentence can be used to find the difference between five times three and two times six?
x= 5x3-2x6
x = 5x2+3x6
x = 5(3+2x6)
x = 5x3+2x6
If the price of bananas goes from $0.39 per pound to $1.06 per pound, what is the likely effect of quantity demanded?
When the price of bananas goes from $0.39 per pound to $1.06 per pound, the likely effect of quantity demanded is that it will reduce.
What is demand?The quantity of a commodity or service that consumers are willing and able to acquire at a particular price within a specific time period is referred to as demand. The quantity required is the amount of an item or service that customers will purchase at a certain price and period.
Quantity desired in economics refers to the total amount of an item or service that consumers demand over a given time period. It is decided by the market price of an item or service, regardless of whether or not the market is in equilibrium.
A price increase nearly invariably leads to an increase in the quantity supplied of that commodity or service, whereas a price decrease leads to a decrease in the quantity supplied. When the price of good rises, so does the quantity requested for that good. When the price of a thing declines, the demand for that good rises.
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Gina want to estimate the total of three bills she has to pay. the bills are for $125,$115,and $138. Gina wants to make sure that she has enough money. she wants the estimate to be greater than the total of the bills. should she round to the nearest ten or hundred
The bills are:
125
115
138
Since she wants an estimate that is greater than the actual total, she can round these numbers to the nearest ten.
125 will be rounded to the next tens, which is 130
115 will also be rounded to the next tens, which is 120
138 gets bumped to the next tens, that is 140
The total estimate is the sum of the 3 estimates we just made. That is:
130 + 120 + 140 = $390
Find the limit. (If an answer does not exist, enter DNE.)
Given:
[tex]\lim _{\Delta x\to0}\frac{6(x+\Delta x)-6x_{}}{\Delta x}[/tex]Solve as:
[tex]\begin{gathered} \lim _{\Delta x\to0}\frac{6x+6\Delta x-6x}{\Delta x}=\lim _{\Delta x\to0}\frac{6\Delta x}{\Delta x} \\ =6 \end{gathered}[/tex]Hence, the required answer is 6.
9. Solve the system of equations algebraically. Show your reasoning.2y = x -44x + 3y = 5
I) 2y = x - 4
II) 4x + 3y = 5
First, we put all the variables on the same side subtracting x from both sides of equation I:
I) 2y - x = -4
II) 3y + 4x = 5
Now, we multiply equation I by 4:
I) 8y - 4x = -16
II) 3y + 4x = 5
Then, we add equation I to equation II:
I) 8y - 4x = -16
II) 11y = -11
Therefore, we got from equation II:
y = -11/11 = -1
Applying this result on equation I, we got:
-8 - 4x = -16
4x = 8
x = 8/4 = 2
Final answer: (x,y) = (2,-1)
What is the average rate of change of the function f(x) = 2x^2 + 4 over the interval (-4,-1] ?
The average rate of change is:
[tex]\frac{f(-1)-f(-4)}{-1+4}=\frac{f(-1)-f(-4)}{3}[/tex][tex]f(-1)=2(-1^2)+4=6[/tex][tex]f(-4)=2(-4^2)+4=2(16)+4=36[/tex]then computing the first formula, the average rate of change of f(x) is
[tex]\frac{6-36}{3}=-10[/tex]You are taking 2 shirts(white and red) and 3 pairs of pants (black, blue, and gray) on a trip. How many different choices of outfits do you have?
A recycle bucket weighs 3.5 lb at the beginning of the school year in August. At the beginning of December it weighed 21.5 lb. Determine the weight gain per month.
Answer:
4.5 pounds
Step-by-step explanation:
21.5 - 3.5 = 18
We divide that by 4 (Aug., Sept, Oct. Nov.)
18/4 = 4.5
Answer:
6.144
Step-by-step explanation:
A system of equations is shown below:Equation A: 3c = d − 8Equation B: c = 4d + 8Which of the following steps should be performed to eliminate variable d first?Multiply equation A by −4.Multiply equation B by 3.Multiply equation A by 3.Multiply equation B by 4.
We have the following: system of equations:
A: 3c=d-8
B: c=4d+8
To eliminate variable d first, if we want to use elimination method, we need to have variable d in both equations with the same coefficient but with different signs.
As in equation B, the coefficient of d is 4, then we need to have in equation A a coefficient of -4 for variable d.
Then the answer is we need to multiply equation A by -4.
Ary is writing thank you cards to everyone who came to her wedding. It takes her of an hour to write one thank you card. If it took her 8 hours to finish writing all of the cards, how many thank you cards did she write?
From the question, It takes Ary an hour to write one thank you card.
So, the rate at which she writes the thank you card is;
[tex]\text{Rate R}=1\text{ card/hour}[/tex]To determine the number N of thank you card she would write in 8 hours.
[tex]N=R\times T[/tex]Where;
R is the rate = 1 card/hour
T is the time taken = 8 hours
Substituting the values we have;
[tex]\begin{gathered} N=1\text{ card/hour}\times8\text{ hours} \\ N=8\text{ cards} \end{gathered}[/tex]The number of thank you cards she write is 8 cards
the line that passes through point (-1,4) and point (6,y) has a slope of 5/7. find y.
Question: the line that passes through the point (-1,4) and point (6,y) has a slope of 5/7. find y.
Solution:
By definition, the slope of a line is given by the formula:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]where m is the slope of the line and (X1,Y1), (X2,Y2) are any two points on the line. In this case, we have that:
(X1,Y1) = (-1,4)
(X2,Y2) = (6,y)
m = 5/7
thus, replacing the above data into the slope equation, we get:
[tex]\frac{5}{7}\text{= }\frac{y-4}{6+1}\text{ }[/tex]
this is equivalent to:
[tex]\frac{5}{7}\text{= }\frac{y-4}{7}\text{ }[/tex]By cross-multiplication, this is equivalent to:
[tex]\text{5 = y-4}[/tex]solving for y, we get:
[tex]y\text{ = 5+ 4 = 9}[/tex]then, we can conclude that the correct answer is:
[tex]y\text{ =9}[/tex]I need help on this
To answer this question, we need to evaluate each function in x=66, this way:
[tex]\begin{gathered} y=7(66) \\ y=462 \\ y=(66)^2-12(66)+84 \\ y=3648 \\ y=1.1317^{66} \\ y=3517.76 \end{gathered}[/tex]In this case, the function that has a greater value at x=66 is the one in the second option:
[tex]y=x^2-12x+84[/tex]May I please get help finding the length to this. I tried many times.m but I couldn’t find answer for it
Both triangles are similar, so:
[tex]\frac{x}{3}=\frac{6}{4.5}[/tex]Solving for x:
4.5x = 3(6)
4.5x = 18
x = 4
ranslateSave & Exit CertifyLesson: 10.2 Parabolas11/15Question 9 of 9, Step 1 of 1CorrectFind the equationof the parabola with the following properties. Express your answer in standard form.
Given
[tex]undefined[/tex]Solution
Standard from of a parabola
[tex](x-H-h)^2=4p(y-k)[/tex](C3) In how many distinct ways can theletters of the word LILLYPILLY bearranged?A. 3.628.800B. 480C. 7.560D. 120.960.
We have:
L = 5 L's
I = 2 I's
P = 1 P
Y = 2 Y's
so:
[tex]\frac{10!}{5!2!2!}=7560[/tex]helpppppppppppppppppppppppppppppp
skill issue hahahahahhaahahhahaha
Jordan’s of Boston sold Lee Company of New York computer equipment with a $7,000 list price. Sale terms were 4/10, n/30 FOB Boston. Jordan’s agreed to pay the $400 freight. Lee pays the invoice within the discount period. What does Lee pay Jordan’s?
2x^2 +6x=-3 can you compute this?
The general formula for a quadratic equation is ax² + bx + c = 0.
To solve
[tex]2x^2+6x=-3[/tex]You can follow the steps.
Step 01: Write the equation in the general formula.
To do it, add 3 to each side of the equation.
[tex]\begin{gathered} 2x^2+6x+3=-3+3 \\ 2x^2+6x+3=0 \end{gathered}[/tex]Step 02: Use the Bhaskara formula to find the roots.
The Bhaskara formula is:
[tex]x=\frac{-b\pm\sqrt[]{\Delta}}{2\cdot a},\Delta=b^2-4\cdot a\cdot c[/tex]In this question,
a = 2
b = 6
c = 2
So, substituting the values:
[tex]\begin{gathered} \Delta=b^2-4\cdot a\cdot c \\ \Delta=6^2-4\cdot2\cdot3 \\ \Delta=36-24 \\ \Delta=12 \\ \\ x=\frac{-6\pm\sqrt[]{12}}{2\cdot2} \\ x=\frac{-6\pm\sqrt[]{2\cdot2\cdot3}}{4} \\ x=\frac{-6\pm2\cdot\sqrt[]{3}}{4} \\ x_1=\frac{-6+2\sqrt[]{3}}{4}=\frac{-3+\sqrt[]{3}}{2} \\ x_2=\frac{-6-2\sqrt[]{3}}{4}=\frac{-3-\sqrt[]{3}}{2} \end{gathered}[/tex]Answer:
Exact form:
[tex]x=\frac{-3-\sqrt[]{3}}{2},\frac{-3+\sqrt[]{3}}{2}[/tex]Decimal form:
[tex]x=-2.37,\text{ -0.63}[/tex]the following augmented matrix is in row-echelon form and represents a linear system. solve the system by using back-substitution if possible.
Given the matrix:
Given that it represents a linear system, we have the set of equations:
(1)x + 3y = 6
0x + (1)y = -1
x + 3y = 6..................equation 1
y = -1.........................equation 2.
Let's solve the system using substitution method.
Substitute -1 for y in equation 1:
x + 3(-1) = 6
x + (-3) = 6
x - 3 = 6
Add 3 to both sides:
x - 3 + 3 = 6 + 3
x = 9
From equation 2, we have the value of y:
y = -1
Therefore, the solution to the system is:
x = 9, y = -1
In point form:
(x, y) ==> (9, -1)
ANSWER:
x = 9, y = -1
what is the slope of a line perpendicular to this linewhat is the slope of a line parallel to this line
Answer:
• Slope perpendicular to the line: 8/5
,• Slope parallel to the line: –5/8
Explanation
Given
[tex]5x+8y=7[/tex]To know the result, it is better if we work with the slope-intercept form:
[tex]y=mx+b[/tex]Then, to get this kind of form we have to isolate y from the given equation:
[tex]8y=7-5x[/tex][tex]y=\frac{7-5x}{8}[/tex][tex]y=-\frac{5}{8}x+\frac{7}{8}[/tex]Thus, in this case, m = –5/8 and b = 7/8.
Perpendicular lines have negative reciprocal lines:
[tex]m_2=-\frac{1}{m_1}[/tex]where m₁ is the slope of line 1 and m₂ is the line perpendicular to line 1.
Then, replacing the values:
[tex]m_2=-\frac{1}{-\frac{5}{8}}[/tex][tex]m_2=\frac{8}{5}[/tex]Finally, the slopes of parallel lines are the same, meaning:
[tex]m_2=m_1[/tex]where m₁ is the slope of line 1 and m₂ is the line parallel to line 1.
In a class of 36 students, 25
study Chemistry, 22 study
Maths and 25 study Physics, 17
study Physics and Maths,18
study Physics and Chemistry
and 15 study only one of the
three subjects. Find the;
a) number of students who
study all three subject?
b) number of students who
study only Maths and
Chemistry?
c) Probability that a student
selected at random study only
two of the three subjects?
a) Number of students who study all three subject = 15
b) Number of students who study only Maths and Chemistry = 1
c) Probability that a student selected at random study only two of the three subjects = 1/36
Define Probability
Simply put, probability is the likelihood that something will occur.
When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.
As it is given total number of students is = 36
The subject are Physics, Maths, and Chemistry
Let, physics = p
maths = m
chemistry = c
The possible combination are,
p, c, m, pm, cp, cm, pcm (means 7 combination total)
Let x be the number of student who study all three subjects.
The students who study physics and maths = 17 - x
The students who study physics and chemistry = 18 - x
The number of student who study physics = 25
Now, with the expression we can find the students who study only physics
25 - ((x) + (18 -x) + (17- x))
⇒25 - (x + 18 - x + 17 - x)
⇒25 - (35 - x)
⇒25 - 35 + x
⇒x - 10
Let y be the number of student only chemistry and mathematics.
Now, with the expression we can find the students who study only chemistry
25-(x + (18- x)) + y
⇒25 - 18 + y
⇒ 7 - y
Now, with the expression we can find the students who study only maths
22 - (x + (17 - x)) + y
⇒ 22 - 17 + y
⇒ 5 - y
The possible combination and expression for each
pcm → x
cm → y
pc → 18 - x
pm → 17 - x
p → x - 10
c → 7 - y
m → 5 - y
____________
Total → 37 - y
But the number of students is 36 , so y = 1
That means,
The number of student who take only chemistry = 7 - y
= 7 - 1 = 6
The number of student who take only maths = 5 - y
= 5 - 1 = 4
The 15 students takes only one of the three subject
the number that take only physics is 5
so, x - 10 = 5
x = 15 (the student who takes all 3 subjects)
The student who takes only physics and chemistry = 18 - x
= 18 - 10 = 3
The student who takes only physics and Maths = 17 - x
= 17 - 15 = 2
To cross check put the values of x and y,
pcm → 15
cm → 1
pc → 3
pm → 2
p → 5
c → 6
m → 4
____________
Total → 36
Therefore, the answers :
a) Number of students who study all three subject = 15
b) Number of students who study only Maths and Chemistry = 1
c) Probability that a student selected at random study only two of the three subjects = ( 3 + 1 + 2) / 36 = 1/36
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