The required equation for the line is y = x + 4 that perpendicular to y = -x + 4 and passes through the point (1, 5).
The required equation is y = 2x + 7 that parallel to y = -3x+7 passes through the point (0, 7).
What is the slope of the line?The slope of a line is defined as the angle of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
The equation of the line which is given as
2x + 3y = 18
3y = -2x + 18
y = -2x/3 + 6
Here the slope of the line, m = -1/3
Let the required line would be as
⇒ y₀ - y₁ = m₀ (x₀ - x₁ )
The required line passes through the point (1, 5)
Here x₁ = 1 and y₁ = 5 and m₀ = 1/3 (Since required line perpendicular)
The equation of the line is obtained by substituting these values into the above equation;
⇒ y - 5 = 1 (x - 1)
⇒ y = x - 1 + 5
⇒ y = x + 4
Therefore, the required equation for the line is y = x + 4 that perpendicular to y = -x + 4 and passes through the point (1, 5).
The equation of the line which is given as
y = 2x + 6
Here the slope of the line, m = 2
The given coordinates of the line;
points on the line (0, 7)
Let the required line would be as
⇒ y - y₁ = m (x - x₁ )
Here x₁ = 0 and y₁ = 7 and m = 2
The equation of the line is obtained by substituting these values into the above equation;
⇒ y - 7 = 2 (x - 0)
⇒ y - 7 = 2x
⇒ y = 2x + 7
Therefore, the required equation is y = 2x + 7 that parallel to y = -3x+7 passes through the point (0, 7).
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I'll send a picture! please answer fast!
Given data:
The given expression for the points is,
[tex]10w-3t+5[/tex]Thus, the expression or
Fine the end behavior and x-value of holeEquation is to the right
Given the function:
[tex]\: f\mleft(x\mright)=\frac{x+1}{\left(x-3\right)\left(x^2-1\right)}[/tex]The end behaviour of the function f(x) describes the behaviour of the function as x approaches +∞ and -∞.
When x approaches +∞,
[tex]\lim _{x\rightarrow\infty}f(x)=\text{ }\lim _{x\rightarrow\infty}\frac{x+1}{(x-3)(x^2-1)}=0[/tex]Thus, as x approaches +∞, the function f(x) approaches zero.
When x approaches -∞,
[tex]\lim _{x\rightarrow-\infty}f(x)=\text{ }\lim _{x\rightarrow-\infty}\frac{x+1}{(x-3)(x^2-1)}=0[/tex]Thus, as x approaches -∞, the function f(x) approaches zero.
x-value of the hole:
For a rational function f(x) given as
[tex]f(x)=\frac{p(x)}{q(x)}[/tex]Provided that p(x) and q(x) have a common factor (x-a), the function f(x) will have a hole at x=a.
Thus, from the function f(x)
[tex]f(x)=\frac{x+1}{(x-3)(x^2-1)}[/tex]by expansion, we have
[tex]f(x)=\frac{x+1}{(x-3)(x^{}-1)(x+1)}[/tex]The expression (x-1) is a common factor of the numerator and the denominator.
Thus,
[tex]\begin{gathered} x-1=0 \\ \Rightarrow x=1 \end{gathered}[/tex]Hence, the x-value of the hole is 1.
Working 5 hours a day, A can Complete a work in 8 days and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in how many days?
After solving the equation, If both A and B of them worked together, then Working 8 hours a day, they can jointly complete the work in 6 days.
What is an equation?Two mathematical expressions' values are said to be equal in an equation, which is a statement of this fact. A mathematical formula declares that two things are equal.
The equals sign ('=') is used to indicate it.
Let the work completed be W
For A
W = 5hours = 1/8 days
1 hour = 1/8 days ÷ 5
1 hour = 1/40 days
For B
W = 6 hours = 1/10 days
1 hour = 1/60 days
Add both the equation
1 hours + 1 hours = 1/40 days + 1/60 days
2 hours = 5/120 days
2 hours = 1/24days
If both of them worked for 1 hour a day
1 hour = 1/48 days
If both of them worked for 8hour a day
8 hours = 1/48 × 8
= 1/6 days
Thus, if both of them worked together, then Working 8 hours a day, they can jointly complete the work in 6 days.
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In how many ways can a committee of 5 be chosen from 9 people given that Jones must be one of them?
There are 126 ways to choose a committee of five from a group of nine people using combinations; one of them must include JONES.
What do we mean by COMBINATIONS?Combinations are a mathematical method for calculating the number of alternative arrangements. In a collection of objects where the order of the selection is irrelevant. You are free to choose any combination of the available things.Mathematically it can be expressed as : nCr = n! / r!(n-r)!So, we have a comiitte of 5 be chosen from 9 people and JONES must be one of them -
Using the rule of combinantion - nCr = n! / r!(n-r)!We have n = 9 and r= 59C5 = 9! / 5!(9-5)!C(9,5) = 3024/24C(9,5) = 126Therefore, there are a total of 126 ways in which we can decide that JONES must be on it.
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HELP PLEASEEEEE!!!!!!
One rational number between -0.45 and -0.46 is -0.451, such that:
-0.45 > -0.451 > -0.46
How to find a rational number in the given interval?
So we want to find a rational number between -0.45 and -0.46. Remember that any decimal number with a finite number of digits after the decimal point (like the above numbers) is a rational number.
So:
3.16436
2.21412
1.4
All of these are rational numbers.
Then a rational number on the interval -0.45 and -0.46 could be -0.451, which is smaller than -0.45 and larger than -0.46
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What is the slope of a line that passes the points (-1,4 ) and ( 3,9 ) ?
Answer:
slope = 5/4
Step-by-step explanation:
What is the slope of a line that passes the points (-1,4 ) and ( 3,9 ) ?
slope = change in y ÷ change in x
slope = (9-4) ÷ (3 - (-1))
slope = 5/4
Find the equation for the circle with a diameter whose endpoints are (8,17) and (4, - 15).
Answer:
Given that,
Circle with a diameter whose endpoints are (8,17) and (4, - 15).
To find the equation for the circle
we know that,
Equation of the circle is of the form,
[tex](x-h)^2+(y-k)^2=r^2[/tex]where r is the radius and (h,k) is the center of the circle.
If the end points of the diameter is given, then the equation of the circle is,
[tex](x-x1)(x-x2)+(y-y1)(y-y2)=0[/tex]Substitute the points we get,
[tex](x-8)(x-4)+(y-17)(y+15)=0[/tex]On simplifying this we get,
[tex]x^2-8x-4x+32+y^2-17y+15y-255=0[/tex][tex]x^2+y^2-12x-2y-223=0[/tex]What is Qualitative Data and what is the discreate and Continuous in qualitative data?
Answer:
Qualitative data is the data that is not represented by numbers, for example, favorite food or country.
On the other hand, the quantitative data is represented by numbers and it is classified as discrete and continuous. The discrete data is the data that only can take specific values, for example, the number of people is always a whole number, there can't be 5.5 people. The continuous data is the data that can take decimal values, for example, the mass of an object can be 4.06 kg.
Given the general form: F( x )= a(x^2)+bx+cConvert it to vertex form (also known as standard form) by putting the values for a,h and k into the correct boxes.F(x)=a(x-h)^2+kIdentify the vertex(x,y)General form: F( x )=1 x^2+6 x +-1 Vertex form: F( x )= Answer for part 1 and coordinate 1 (x- Answer for part 1 and coordinate 2 )^2 +Answer for part 1 and coordinate 3Vertex: (Answer for part 2 and coordinate 1,Answer for part 2 and coordinate 2)
1) In order to convert from the standard version to the vertex form we'll need to find the vertex of that parabola:
[tex]f(x)=x^2+6x-1[/tex]We can find the vertex, using these formulas:
[tex]\begin{gathered} x=h=-\frac{b}{2a}=\frac{-6}{2}=-3 \\ k=(-3)^2+6(-3)-1=9-18-1=9-19=-10 \\ V(-3,-10) \end{gathered}[/tex]So this is the vertex of that parabola at point (-3,-10)
2) Now, note that the coefficient a = 1, and with the vertex, we can now rewrite that equation into the vertex form:
[tex]\begin{gathered} y=a(x-h)^2+k \\ y=(x-(-3))^2+(-10) \\ y=(x+3)^2-10 \end{gathered}[/tex]
I need help with this practice,I will send you an additional pic that goes along with this problem Freya went to her local park to find 5 organisms/species She found 5 and wrote down the name of these organisms and the quantity of each she seen:Eastern gray squirrels/14 individualsWolf spiders/2 individualsPaper wasps/9 individualsBlack vulture/1 individualNorthern cardinals/7 individuals
ANSWER :
The answer is 5/33 or 0.15
EXPLANATION :
From the problem, we have a total of 5 number of species.
Using the given Biodiversity Index formula :
[tex]\frac{\text{ total number of species}}{\text{ total number of individuals}}=\frac{5}{14+2+9+1+7}=\frac{5}{33}\quad or\quad0.1515[/tex]The total cost, in dollars of a membership in a fitness center is given by the function c(m) = 40m +10, where m is the number of months a person is a member. In dollars, how much is the cost of a membership for 1 year?
The cost of a membership for 1 year is 490
How to determine the cost of a membership for 1 year?The equation of the membership is given as
c(m) = 40m + 10
From the question, we understand that:
m represents the number of months
For the cost of a membership for 1 year, the number of months is 12
i.e. m = 12
Substitute the known values in the above equation
So, we have
c(12) = 40 * 12 + 10
Evaluate
c(12) = 490
Hence, the cost is 490
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Granny Smith is making strawberry jelly. She places 6.3 ounces in each jar to give as gifts.granny was able to fill 9.5 jars. How many ounces of strawberry jelly did granny make
1)EF=JHFEG = HJGXProve FEG = HJGStatement1) EF = JHReason1) given2)2) given3) Vertical angles are conguent3)4)4)Theorem
2.
[tex]\angle FEG\cong\angle HJG[/tex]3.
[tex]\angle HGJ\cong\angle EGF[/tex]After a 35% reduction, you purchase a new bike for $282.75. What was the price of the bike before the reduction?
A) First write an equation you can use to answer this question. Use x as your variable and express any percents in decimal form in the equation.
B) Solve your equation in part [A] to find the original price of the bike.
The equation to represent this situation is given by 0.65x = 282.75 .
In the various mathematical formulas that are used, the equals sign is used to show that two expressions on either side of the equal sign are equal. The meaning of the word equation and its cognates might vary slightly depending on the language.
Finding the exact values of the unknown variables that result in the given equality is the very first step in the solving of a variable equation. The values of the unknown variables that fulfil the equality are the equation's solutions, also known as the variables for which the equation must be solved. There are two sorts of equations.
Le t the original cost of the bike be x dollars.
After 35% reduction the new cost is x - (35% of x) = 0.65 x
Therefore 0.65 x = 282.75
or, x = 435
Therefore the cost of the bike is $435.
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i need help with this problem
Answer:
whats the problme?
Step-by-step explanation:
The figure shows a quarter circle and an equilateral triangle. What is thearea of the shaded part? Give your answer to 3 significant figures. (Take it= 3.14.)7 cm
Since the triangle is equilateral, all of its interior angles have a measure of 60º.
Substract the area of the triangle from the area of a circular sector with radius 7cm enclosed by an angle of 60º to find the area of the shaded region.
The area of an equilateral triangle with side length L is:
[tex]A=\frac{\sqrt[]{3}}{4}L^2[/tex]The area of a circular sector of radius r enclosed by an angle of θ degrees is:
[tex]A=\frac{\theta}{360}\times\pi r^2[/tex]Replace θ=60 and r=7cm to find the area of the circular sector:
[tex]A_c=\frac{60}{360}\times3.14\times(7\operatorname{cm})^2=25.643\ldots cm^2[/tex]Replace L=7cm to find the area of the triangle:
[tex]A_T=\frac{\sqrt[]{3}}{4}\times(7\operatorname{cm})^2=21.2176\ldots cm^2[/tex]Then, the area of the shaded region is:
[tex]\begin{gathered} A_C-A_T=25.6433\ldots cm^2-21.2176\ldots cm^2 \\ =4.4257\ldots cm^2 \\ \approx4.43\operatorname{cm}^2 \end{gathered}[/tex]Therefore, the area of the shaded region to 3 significant figures, is:
[tex]4.43\operatorname{cm}^2[/tex]URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
The correct option b: 49° because the angles are supplementary to angle d.
What is defined as supplementary angles?The definition of supplementary is linked to angles that form a straight angle when joined together. When two angles add up to 180 degrees, they are referred to as supplementary angles. If two angles are supplementary. One of its angles is just an acute angle, while another is an obtuse angle.For the given question.
∠d = 131 degrees.
∠d + ∠f = 180 (supplementary angle)
∠f = 180 - 131
∠f = 49 degrees
Now,
∠f = ∠g = 49 degrees (vertically opposite angles)
∠f = ∠c = 49 degrees (alternate interior angles)
Thus, the angle d is supplementary to angle f, c and g.
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Use the ALEKS calculator to write as a percentage.
31
32
Round your answer to the nearest tenth of a percent.
0%
X 5
?
Divide 31 into 32 and then multiply the result by 100 to get the percent:
[tex]\begin{gathered} \frac{31}{32}=0.96875 \\ \\ 0.96875*100=96.875 \end{gathered}[/tex]Then, to the nearest tenth of a percent the given fraction is 96.9%While solving an equation 2x^2+32=0 the answer calculated is x=+-4i I understand the +- means the answer can be positive or negative but what does the i mean
Answer:
Explanation:
Given:
[tex]\begin{gathered} 2x^2+32=0 \\ \text{The answer is x=}+-4i \end{gathered}[/tex]To fully understand how we get the given answer, we simplify the equation first:
[tex]\begin{gathered} 2x^2+32=0 \\ \text{Simplify and rearrange} \\ 2x^2=-32 \\ x^2=-\frac{32}{2} \\ x^2=-16 \\ \end{gathered}[/tex]Next, we apply the rule:
[tex]\begin{gathered} \text{For x}^2=f(a),\text{ the solutions are } \\ x=\sqrt[]{f(a)} \\ x=-\sqrt[]{f(a)} \end{gathered}[/tex]So,
[tex]\begin{gathered} x^2=-16 \\ x=\sqrt[]{-16},x=-\sqrt[]{-16} \end{gathered}[/tex]Then, we also apply the radical rule:
[tex]\begin{gathered} \sqrt[]{-a}=\sqrt[]{-1}\sqrt[]{a} \\ So, \\ x=\sqrt[]{-16} \\ =\sqrt[]{-1}\sqrt[]{16} \\ \text{Then, apply the imaginary number rule:} \\ \sqrt[]{-1}=i \\ \text{Hence,} \\ x=4i \end{gathered}[/tex]For
[tex]\begin{gathered} x=-\sqrt[]{-16} \\ Use\text{ the same steps} \\ x=-4i \end{gathered}[/tex]Therefore the x-values are: x=4i, x=-4i. The i on the answer means imaginary number. It is a number that, when squared, has a negative result.
If sin 0= -3/5 in quadrant 3, what is cos 0?
Given
[tex]sin\theta=-\frac{3}{4}[/tex]Solution
Recall : SOHCAHTOA
The final answer
Option A
[tex]Cos\text{ }\theta=-\frac{4}{5}[/tex]use the two given points and calculate the slope.(6,4),(4,-1)
EXPLANATION:
Given;
We are given two points which are shown below;
[tex]\begin{gathered} (6,4) \\ (4,-1) \end{gathered}[/tex]Required;
We are required to calculate the slope.
Step-by-step solution;
To calculate the slope given two points, we shall use the following formula;
[tex]\begin{gathered} Slope: \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Where the variables are;
[tex]\begin{gathered} (x_1,y_1)=(6,4) \\ (x_2,y_2)=(4,-1) \end{gathered}[/tex]We can now substitute these values and solve;
[tex]m=\frac{-1-4}{4-6}[/tex][tex]m=\frac{-5}{-2}[/tex][tex]m=\frac{5}{2}[/tex]Therefore.
ANSWER:
[tex]m=\frac{5}{2}[/tex]Travelers arriving at Cape Town International Airport 70% of the travelers fly on major airlines, 20% by on privately owned planes and the remainder by on commercially owned planes not belonging to a major airline. Of those traveling on major airlines, 40 degrees are traveling for business reasons, whereas 70% of those arriving on private planes and 80% of those arriving on other commercially owned planes are traveling for business reasons Suppose that we randomly select one person arriving at this airport. What is the probability that the traveler is flying privately for business reasons?
Step 1
Given;
[tex]\begin{gathered} 20\text{\% fly privately owned jets} \\ 70\text{\% of those arriving on the plane are travelling for business reason} \end{gathered}[/tex]Given the formula FV = P + Prt, what is the future value of a savings account that had an initial deposit of $7,900 earning 6.5% simple interest for 4 years?$10,074.23$9,954.00$9,376.85$10.756.43None of these choices are correct.
Step 1: Use the formula below to find the future value:
Fv = P + Prt
P = present value or initial deposit
r = rate in %
t = time in years
Step 2: List the given data
P = $7900
r = 6.5% = 0.065
t = 4 years
Step 3: Substitute the values of P, r and t to find the future value.
FV = P + Prt
= 7900 + 7900 x 0.065 x 4
= 7900 + 2054
= $9954.00
Stop 4: Final answer
Future value = $9954.00
What’s the correct answer answer asap for brainlist
Answer:
A. a chorus
Step-by-step explanation:
Select the correct answer. What is the solution to the equation? (x - 2)^1/2 + 4 = x A. -3 and -6 B. 3 and 6 C. -3 D. 6
Answer:
D. x = 6
Step-by-step explanation:
Given equation:
[tex](x-2)^{\frac{1}{2}}+4=x[/tex]
Subtract 4 from both sides:
[tex]\implies (x-2)^{\frac{1}{2}}+4-4=x-4[/tex]
[tex]\implies (x-2)^{\frac{1}{2}}=x-4[/tex]
Square both sides:
[tex]\implies \left( (x-2)^{\frac{1}{2}}\right)^2=(x-4)^2[/tex]
[tex]\implies x-2=(x-4)^2[/tex]
Expand the brackets on the right side:
[tex]\implies x-2=(x-4)(x-4)[/tex]
[tex]\implies x-2=x^2-8x+16[/tex]
Subtract x from both sides:
[tex]\implies x-2-x=x^2-8x+16-x[/tex]
[tex]\implies -2=x^2-9x+16[/tex]
Add 2 to both sides:
[tex]\implies -2+2=x^2-9x+16+2[/tex]
[tex]\implies 0=x^2-9x+18[/tex]
[tex]\implies x^2-9x+18=0[/tex]
Factor the left side of the equation:
[tex]\implies x^2-6x-3x+18=0[/tex]
[tex]\implies x(x-6)-3(x-6)=0[/tex]
[tex]\implies (x-3)(x-6)=0[/tex]
Apply the zero-product property:
[tex]\implies x-3=0 \implies x=3[/tex]
[tex]\implies x-6=0\implies x=6[/tex]
Therefore, the solutions of the quadratic equation are:
[tex]x=3, \quad x=6[/tex]
Input both solutions into the original equation to check their validity:
[tex]\begin{aligned}x=3 \implies (3-2)^{\frac{1}{2}}+4&=3\\(1)^{\frac{1}{2}}+4&=3\\1+4&=3\\5&=3\end{aligned}[/tex]
[tex]\begin{aligned}x=6 \implies (6-2)^{\frac{1}{2}}+4&=6\\(4)^{\frac{1}{2}}+4&=6\\2+4&=6\\6&=6\end{aligned}[/tex]
Therefore, the only valid solution to the given equation is x = 6.
Answer:
The answer is D. 6
Step-by-step explanation:
Add both sides:
(x - 2)^1/2 + 4 + (-4) = x + (-4)
(x - 2)^1/2 = -4
Solve exponent:
(x - 2)^1/2 = x - 4
((x - 2)^1/2)^2 = (x - 4)^2
x − 2 = x^2 − 8x + 16
x − 2 − (x^2 − 8x + 16) = x^2 − 8x + 16 − (x^2 − 8x + 16)
−x^2 + 9x − 18 = 0
(−x + 3)(x − 6) = 0
−x + 3 = 0 or x − 6 = 0
x = 3 or x = 6
Check the answers: (Plug them in to see what will work.)
x = 3 (won't work)
x = 6 (does work)
Therefore,
x = 6
while digging in his garden , will pushes a shovel into the ground at an 80 degree angle with 585 newtons of force . show the resolution of the force into its retangular components
Solution
Part a
Part b
For this case we can do this:
Fx= 585 N* cos 80= 101.58 N
Fy= 585N * sin 80= 576.11 N
Then the best answer is:
B. (102, 576) N
Identifying the Type of Series
3+6+12+ 24 + ...
5+7+10+14+
1+2+3+4+
2+4+2+4+
Answer:
geometric, neither, arithmetic, and neither
Step-by-step explanation:
right on edg 2023
Jamar finds some nickels and quarters in his change purse. How much money (in cents) does he have if he has 4 nickels and 11 quarters? How much money (in cents) does he have if he has n nickels and q quarters?
1 nickel is worth 5 cents and 1 quarter is worth 25 cents.
So, if he has 4 nickels, this is worth 4 times 5 cents and if he has 11 quarters, this is worth 11 times 25 cents.
Both are worth the sum of these, so:
[tex]4\cdot5+11\cdot25=20+275=295[/tex]So, he has 295 cents.
If he has n nickels and q quarters, he has 5 times n plus 25 times q worth, so he has:
[tex]5n+25q[/tex]10. The product of 6 and a number when added to 5 is equal to 1 less than 9 times the number.
Answer:
x = 2
Step-by-step explanation:
Hello!
Let the unknown number be x. The product of 6 and that number can be represented by 6x. And since we are adding 5, we can use 6x + 5 to represent that expression.
This equation is equal to the difference of 9x and 1, or 9x - 1.
Solve for x6x + 5 = 9x - 15 = 3x - 16 = 2x2 = xThe value of x is 2.
Solve the following. List all possible possible solutions for the ambiguous case. #7
The sum of the interior angles of any triangle is always 180º:
[tex]A+B+C=180[/tex]Use the equation above and the given data to find C:
[tex]\begin{gathered} C=180º-A-B \\ C=180º-38º-72º \\ C=70º \end{gathered}[/tex]Law of sines:
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]Use the pair of ratios for a and b to solve a:
[tex]\begin{gathered} \frac{a}{sinA}=\frac{b}{sinB} \\ \\ a=sinA*\frac{b}{sinB} \\ \\ a=sin38º*\frac{12}{sin72º} \\ \\ a=7.8 \end{gathered}[/tex]Use the pair of ratios for b and c to solve c:
[tex]\begin{gathered} \frac{c}{sinC}=\frac{b}{sinB} \\ \\ c=sinC*\frac{b}{sinB} \\ \\ c=sin70º*\frac{12}{sin72º} \\ \\ c=11.9 \end{gathered}[/tex]Thenm, the solution for the given triangle is:A=38ºB=72ºC=70ºa=7.8b=12c=11.9