The equation of a line that passes through the point (8, -4) and is parallel to the line 6x + 2y = 9 is 3x+y-20=0.
6x + 2y - 9 = 0
2y = -6x + 9
divide by 2 on both sides
y = -3x + 9/2
slope m = -3 and c = 9/2.
Line equation through point(8, -4) is y-y1 = m(x-x1)
y - (-4) = -3(x-8)
y+4=-3x+24
3x+y-20=0.
Therefore the equation of a line that passes through the point (8, -4) and is parallel to the line 6x + 2y = 9 is 3x+y-20=0.
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For each equation chose the statement that describes its solution
GIven:
The equations
[tex]\begin{gathered} -6(u+1)+8u=2(u-3) \\ 2(v+1)+7=3(v-2)+2v \end{gathered}[/tex]Required:
Find the correct solution.
Explanation:
The equations,
[tex]\begin{gathered} -6(u+1)+8u=2(u-3) \\ -6u-6+8u=2u-6 \\ -6u+8u=2u \\ -8u+8u=0 \\ 0=0 \\ Hence,\text{ true for all }u. \end{gathered}[/tex]And
[tex]\begin{gathered} 2(v+1)+7=3(v-2)+2v \\ 2v+2+7=3v-6+2v \\ 9=3v-6 \\ 3v=15 \\ v=5 \end{gathered}[/tex]Answer:
[tex]\text{ In equation 1, equation is true for all }u\text{ and equation 2 is true for }v=5.[/tex]A town has a population of 10000 and grows at 2% every year. To the nearest year, how long will it be until the population will reach 12700?
A town has a population of 10000 and grows at 2% every year. To the nearest year, how long will it be until the population will reach 12700
Given the data as
Population = P_0 = 10,000
Growth rate = r = 2%
Let us assume the time would be 12 years, so
Time = t = 12
The formula for calculating the population after given time at given rate is:
[tex]P = P_{0}(1+r)^{t}[/tex]
Inserting the given values in the above formula:
[tex]P = (10,000)(1+0.02)^{12}[/tex]
[tex]= (10,000)(1.02)^{12}[/tex]
[tex]= 10,000+1.268\\\\= 12682[/tex]
Hence the answer is 12 years to be until the population to reach 12700
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Find the length of the Latus Rectum with the following equation: y= x^2 +6
We have the next equation
[tex]y=x^2+6[/tex]First, we need to find the focus of this parabola the vertice is in (0,6)
[tex]4p\mleft(y-k\mright)=\mleft(x-h\mright)^2[/tex]where in our case h =0, k=6
[tex]4\cdot\frac{1}{4}(y-6)=x^2[/tex]Therefore the focus will be
[tex](0,6+\frac{1}{4})=(0,\frac{25}{4})[/tex]Then for Latus Rectum is located between the next points
[tex](-0.5,\frac{25}{4})\text{ and (}0.5,\frac{24}{5}\text{)}[/tex]the latus Rectum
[tex]4p=4(\frac{1}{4})=1[/tex]the length of the latus rectum is 1
Can you please write the basic equation forConstant parent functionInverse sine parent functionInverse cosine parent function Inverse tangent parent function
• In order to understand this, we need to know that an inverse trigonometric function “undo” what the original trigonometric function
• e.g Trig function : inverse of trig. function .
Explanations :(a) Inverse sine parent function:The inverse y = six x parent function will be
[tex]\begin{gathered} y=sinx^{-1}\text{ ; meaning } \\ x\text{ = sin y } \end{gathered}[/tex]• y = sinx ^-1 , has domain at [-1;1] and range at (-/2; /2)
(b)Inverse cosine parent functionthe inverse of y = cos x parent function will be :
[tex]\begin{gathered} y=cosx^{-1};\text{ meaning } \\ x\text{ = cos y } \end{gathered}[/tex]• y = cosx^-1 , has domain at [-1;1] and range at (0;)
(c)Inverse tangent parent function
The inverse of y = tan x parent function will be :
[tex]\begin{gathered} y=tanx^{-1\text{ }},\text{ meaning } \\ x\text{ = tan y } \end{gathered}[/tex]• y = tanx^-1 has domain at (-∞;∞) and range at (- /2 ; /2)
see the graphs below that shows the asympotes of the trigonometric function.Are the triangles similar?.. help me with this problem! Thank you :)
In similar triangles, corresponding sides are always in the same ratio.
Find the ratio of corresponding sides in the given triangles, to identify corresponding sides the greater side in one triangle is corresponding with the greater side of the other triangle.
[tex]\begin{gathered} \frac{QR}{TU}=\frac{28}{8}=\frac{7}{2} \\ \\ \frac{RP}{US}=\frac{21}{6}=\frac{7}{2} \\ \\ \frac{PQ}{ST}=\frac{14}{4}=\frac{7}{2} \end{gathered}[/tex]As the ratio of corresponding sides is the same, triangle PQR is similar to triangle STUFor similar triangles the corresponding angles are equal.
Corresponding angles for triangles PQR and STU:
P and S
Q and T
R and U
[tex]\begin{gathered} \angle P=\angle S=70º \\ \angle Q=\angle T \\ \angle R=\angle U=46º \end{gathered}[/tex]The sum of the interior angles in any triangle is always 180º:
[tex]\begin{gathered} \angle P+\angle Q+\angle R=180º \\ \angle Q=180º-\angle P-\angle R \\ \angle Q=180º-70º-46º \\ \angle Q=64º \\ \\ \angle Q=\angle T=64º \end{gathered}[/tex]if you travel 35 miles per hour for 4.5 hours hovú far will you travle
We need to multiply 4.5 hours by 35 miles per hour, as follows:
[tex]4.5\text{ hours}\cdot35\frac{miles}{hour}=157.5\text{ miles}[/tex]You will travel 157.5 miles
Evaluate the function.
f(x)=(x−7)2+4
for f(−6)
f(−6)
Answer:
F(-6) = 173
Hope this helps!
write the thirteen million, three hundred two thousand, fifty in expanded form.
Let's begin by listing out the information given to us:
[tex]13,302,050=13,000,000+300,000+2,000+0+50[/tex]thirteen million = 13,000,000
three hundred and two thousands = 300,000 + 2,000
fifty = 50
13,302,050 = 13,000,000 + 300,000 + 2,000 + 50
Game System C Last month, you sold 21 systems. The total for the last two months is 37. Write and solve an equation to find how many systems you sold this month. Let c = number of systems sold this month Equation: Systems Sold:
You sold 21 systems last month.
The total systems sold in the last two months is 37 (that means this month and last month)
How many systems have you sold this month?
Let c = number of systems sold this month
Then we may write the following equation
[tex]c+21=37[/tex]Where c represents the number of systems sold this month
21 represents the number of systems sold last month
Then the sum of these two months must be equal to 37 (total systems sold in two months)
Now let us solve the equation for c
[tex]\begin{gathered} c+21=37 \\ c=37-21 \\ c=16 \end{gathered}[/tex]Therefore, you have sold 16 systems this month
The steps to derive the quadratic formula are shown below:Step 1 ax2 + bx + c = 0Step 2 ax2 + bx = - CStep 3Provide the next step to derive the quadratic formula.
Here, we are given the first two steps to derive the quadratic formula:
Step 1: ax² + bx + c = 0
Step 2: ax² + bx = -c
Let's determine the next step to derive the quadratic formula.
To provide the next step, let's divide all terms by a:
We have:
Step 3.
[tex]\begin{gathered} \frac{ax^2}{a}+\frac{bx}{a}=-\frac{c}{a} \\ \\ \frac{x^2}{a}+\frac{b}{a}x=-\frac{c}{a} \end{gathered}[/tex]Therefore, the next step to derive the quadratic formula is:
[tex]\frac{x^2}{a}+\frac{b}{a}x=-\frac{c}{a}[/tex]ANSWER:
[tex]\frac{x^2^{}}{a}+\frac{b}{a}x=-\frac{c}{a}[/tex]The perimeter of the rectangle below is units. Find the length of side .Write your answer without variables.
SOLUTION
From the question, the perimeter of the rectangle is 102 units, we want to find XY. Note that side XY = side WV, so XY = 4z.
But we need to find z. To do this we add all the sides and equate it to 102, we have
[tex]\begin{gathered} 2(3z+2)+2(4z)=102 \\ 6z+4+8z=102 \\ 6z+8z+4=102 \\ 14z=102-4 \\ 14z=98 \\ z=\frac{98}{14} \\ z=7 \end{gathered}[/tex]So z is 7, and XY becomes
[tex]\begin{gathered} XY=4z \\ XY=4\times7 \\ =28 \end{gathered}[/tex]Hence the answer is 28
Use the given row transformation to transform the following matrix.
The 2 x 2 matrix is given
[tex]\begin{bmatrix}{2} & {8} \\ {10} & {7} \\ {} & {}\end{bmatrix}[/tex]The row transformation given is:
[tex]\frac{1}{2}R_1[/tex]this means we take half of all the elements of Row 1
The process is shown below:
[tex]\begin{gathered} \begin{bmatrix}{\frac{1}{2}\times2} & {\frac{1}{2}\times8} & \\ {10} & {7} & {} \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{1} & {4} & \\ {10} & {7} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex]Hence, the final matrix Row 2 is same as previous matrix, but Row 1 is half of the elements of previous matrix.
Answer:
[tex]\begin{bmatrix}{1} & {4} & \\ {10} & {7} & {} \\ {} & {} & {}\end{bmatrix}[/tex]A group of five will rent a car for a spring break trip and divide the costs associated with the car among them. The rental costs $480 for the week. Insurance is an additional $175, they estimated they’ll use 120 gallons of gas, and gas costs around $2.80 per gallon. Estimate how much each friend will pay for the cost associated with the car
Solution:
Given:
[tex]\begin{gathered} car\text{ rental cost}=\text{ \$}480 \\ Insurance=\text{ \$}175 \\ Gas=120\times2.80=\text{ \$}336 \end{gathered}[/tex]Thus, the total cost associated with the car is;
[tex]480+175+336=\text{ \$}991[/tex]Each friend will pay;
[tex]\frac{991}{5}=\text{ \$}198.20[/tex]Therefore, each friend will pay $198.20
the value of x in the equation below represents the number of siblings i have, solve the equation and tell me how many siblings do i have?3(×+4)=3×+10-2×+23-×
to solve for x, we'll first of all open the bracket and the collect like terms
[tex]3(x\text{ + 4) = 3x + 10 - 2x + 23 - x}[/tex][tex]\begin{gathered} 3x\text{ + 12 = 3x + 10 - 2x + 23 - x} \\ 3x\text{ - 3x + 2x + x = 10 - 12 + 23} \\ 3x\text{ = 21} \\ \end{gathered}[/tex]divide both sides by 3
[tex]\begin{gathered} 3x\text{ = 21} \\ \frac{3x}{3}\text{ = }\frac{21}{3} \\ x\text{ = 7} \end{gathered}[/tex]x = 7
How many ways can 6 different students be arranged in a line?
It is required to find the number of ways 6 different students can be arranged.
Since the students are different and they are required to be arranged in a line, the number of ways is:
[tex]n![/tex]Where n is the number of items.
Hence, for 6 students the number of ways of arranging them on a line is:
[tex]6!=6\cdot5\operatorname{\cdot}4\operatorname{\cdot}3\operatorname{\cdot}2\operatorname{\cdot}1=720\text{ ways}[/tex]The answer is 720 ways.
Answer:720 ways
Step-by-step explanation:
The total number of ways 6 students can be arranged in a line is = n!
= 6!
=720 ways
The cost of any soda from a soda machine is $0.50. The graph representing this relationship is shown below. Soda Machine Total Cost 3 2 Number & Sodas 6 6 What is the slope of the line that models this relationship?
Answer:
The slope of the line is;
[tex]m=\frac{1}{2}=0.5[/tex]Explanation:
Given the attached graph.
Recall that the formula for calculating the slope m of a line is;
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]From the graph, let us select two points on the line;
We have;
[tex]\begin{gathered} (2,1)\text{ } \\ \text{and} \\ (4,2) \end{gathered}[/tex]The slope can then be calculated by substituting this points into the formula;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{4-2} \\ m=\frac{1}{2}=0.5 \end{gathered}[/tex]Therefore, the slope of the line is;
[tex]m=\frac{1}{2}=0.5[/tex]Solve algebraicallyX+4=-2
SOLUTION:
Step 1:
In this question, we are given the following:
Solve algebraically
[tex]x\text{ + 4 = -2}[/tex]Step 2:
The details of the solutio are as follows:
[tex]\begin{gathered} x\text{ + 4 = -2} \\ collecting\text{ like terms, we have that:} \\ x\text{ = - 2 - 4} \\ x\text{ = - 6} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]x\text{ = - 6}[/tex]Using f(x) = 3x - 3 and g(x) = -x, find g(f(x)).3x+33-3x-3-3x2x-3I am not sure if my answer is right please help me
Given
[tex]\begin{gathered} f(x)=3x-3 \\ g(x)=-x \end{gathered}[/tex]Then,
[tex]\begin{gathered} g(f(x))=g(3x-3) \\ =-(3x-3) \\ =3-3x \end{gathered}[/tex]Hence, the correct option is (B)
Please see picture. I am looking for help on part b of #5
5.a).
GIven:
Principal P= $ 5000.
Interest rate R = 7 % =0.07.
The number of years T=x.
Consider the following formula to find the amount.
[tex]A=P(1+r)^t[/tex]Substitute A=y P=5000, R=0.07, and T=x in the equation, we get
[tex]y=5000(1+0.07)^x[/tex][tex]y=5000(1.07)^x[/tex]Which is of the form
[tex]y=a(b)^x[/tex]We know that this is the exponential growth function.
Hence the exponential function is
[tex]y=5000(1.07)^x[/tex]b)
Consider the y values from the table.
5,10,15,20,25,30,...
The difference between 5 and 10 = 10-5 =5.
The difference between 10 and 15 = 15-10 =5.
Proceed this way to find the common difference.
The common difference is 5.
The y value is increasing by the common value of 5.
The slope =5 and the y-intercept is 5 from point (0,5).
The equation is
[tex]y=5+5x[/tex]This is a linear equation.
Tickets for the school football game cost $10 for students and $12 for non-students. A total of 150 ticketswere sold and $1440 was collected.Let x = the # of student tickets soldLet y = the # of non-student tickets sold
x = students = $10
y = non students = $12
total tickets = 150
Equations
x + y = 150
10x + 12y = 1440
x = 150 - y
10(150 - y) + 12y = 1440
1500 - 10y + 12y = 1440
2y = 1440 - 1500
2y = -60
y = -60/2
y = 30
x = 150 -
Fill in the blanks (B1, B2, B3) in the equation based on the graph.(a-B1)2 + (y-B2)² = (B3)²8182=83=Blank 1:
Given: a circle is given with center (3,-3) and equation
[tex](x-B_1)^2+(y-B_2)^2=(B_3)^2[/tex]Find:
[tex]B_{1,\text{ }}B_{2,}B_3[/tex]Explanation: the general equation of the circle with center (a,b) and radius r is
[tex](x-a)^2+(y-b)^2=r^2[/tex]in the given figure the center of the circle is at (3,-3)
so the equatio of the circle becomes
[tex](x-3)^2+(y+3)^2=(3)^2[/tex]on comparing eith the given equation we get
[tex]B_1=3,\text{ B}_2=-3\text{ and B}_3=3[/tex]Lucy's mom started a 529 college fund for her when she was 4 years old inorder to save money for college. She put $9,000 into an account that earnsa 5% compounded annually. Lucy wants to know how much money she willhave when she is 18. Look at her work below.Is her solution correct? If not, describe the mistake(s) in her work.y = 900011+ 9(e)y = 9000 (1.5) 18y = 8133010 26.92
Explanation:
P = $9000
i = 5% 0.05
We nee to apply the formula:
[tex]\begin{gathered} \frac{FV}{(i+i)^n}=\text{ PV} \\ FV\text{ = }PV\text{ }(1+i)^n \\ FV=9000(1+0.05)^{18}\text{ } \end{gathered}[/tex][tex]undefined[/tex]Write the following parametric equations as a polar equation.x = 2ty=t²
ANSWER:
2nd option: r = 4 tan θ sec θ
STEP-BY-STEP EXPLANATION:
We have the following:
[tex]\begin{gathered} x=2t\rightarrow t=\frac{x}{2} \\ \\ y=t^2 \end{gathered}[/tex]We substitute the first equation in the second and we are left with the following:
[tex]\begin{gathered} y=\left(\frac{x}{2}\right)^2 \\ \\ y=\frac{x^2}{2^2}=\frac{x^2}{4} \end{gathered}[/tex]Now, we convert this to polar coordinates, just like this:
[tex]\begin{gathered} x=r\cos\theta,y=r\sin\theta \\ \\ \text{ We replacing:} \\ \\ r\sin\theta=\frac{(r\cos\theta)^2}{4} \\ \\ r\sin\theta=\frac{r^2\cos^2\theta^{}}{4} \\ \\ r\sin\theta=\frac{r^2\cos\theta\cdot\cos\theta{}}{4} \\ \\ \frac{r^2\cos\theta\cdot\cos\theta}{4}=r\sin\theta \\ \\ r=4\frac{\sin\theta}{\cos\theta}\cdot\frac{1}{\cos\theta} \\ \\ r=4\tan\theta\cdot\sec\theta \end{gathered}[/tex]So the correct answer is the 2nd option: r = 4 tan θ sec θ
6. Write the equation of the line below. 1-10 7 6 5 3 2 का 2 3 4 5 6 7 8 9 10
Let the two points in the graph are (0,7) and (1,3).
Then, the slope of the line is,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{3-7}{1-0} \\ m=-4 \end{gathered}[/tex]Use the equation y=y1=m(x-x1) to find the equation of the line.
[tex]\begin{gathered} y-7=-4(x-0)\text{.} \\ y-7=-4x \\ y=-4x+7 \end{gathered}[/tex]Therefore, the equation of the line is y=-4x+7.
If D and R denote the degree and radian measure of an angle, then prove that D/180=R/pie
Given: D and R denote the degree and radian measure of an angle
To Determine: The prove that D/180=R/pie
Solution
Please note that
[tex]180^0=\pi radians[/tex]So
[tex]1^0=\frac{\pi}{180^}radian[/tex]Then
[tex]\begin{gathered} D^0=D\times\frac{\pi}{180}radian \\ D^0=\frac{D\pi}{180}radians \end{gathered}[/tex]Therefore
[tex]\frac{D\pi}{180}=R[/tex]Let us divide both sides by pie
[tex]\frac{D\pi}{180}\div\pi=R\div\pi[/tex][tex]\begin{gathered} \frac{D\pi}{180}\times\frac{1}{\pi}=R\times\frac{1}{\pi} \\ \frac{D}{180}=\frac{R}{\pi} \end{gathered}[/tex]Hence, the above help to prove that D/180 = R/pie
Ms. Tui is having new floors installed in her house. Floor Company A charges $90for installation and $9 per square yard of flooring. Floor Company B charges $50for installation and $13 for each square yard.
We have two cost functions.
Company A charges a fixed value of $90 and a variable cost of $9 per sq yd.
[tex]C_A=90+9x[/tex]Company B chargesa fixed value of $50 and a variable cost of $13 per sq yd.
[tex]C_B=50+13x[/tex]The breakeven point for the square yard of the floor, when both cost are the same, can be calculated as:
[tex]\begin{gathered} C_A=C_B \\ 90+9x=50+13x \\ 90-50=13x-9x \\ 40=4x \\ x=\frac{40}{4} \\ x=10 \end{gathered}[/tex]The breakeven point is x=10 sq yd.
If x>10, company B is more expensive that company A.
What is the 13th term of the geometric sequence with this explicit formula?an-3-(-2)(n-1)
Answer:
C. 12,288
Explanation:
Given the explicit formula of a given geometric sequence:
[tex]a_n=3(-2)^{n-1}[/tex]To find the 13th term, substitute n for 13:
[tex]\begin{gathered} a_{13}=3\times(-2)^{13-1} \\ =3\times(-2)^{12} \\ =3\times4096 \\ =12,288 \end{gathered}[/tex]The 13th term of the geometric sequence is 12,288.
Option C is correct.
Help with Algebra 2 question.14) An angle is in standard position and is terminal side pauses through point (-2,5), find sec.
Given:
An angle is in standard position and is terminal side passes through the point (-2,5),
Required:
To find the value of the secant function.
Explanation:
The value of the secant function is given as:
[tex]sec\theta=\frac{r}{x}[/tex]Where
[tex]r=\sqrt{x^2+y^2}[/tex]Consider x= -2 and y = 5
Now calculate the value of r by using the formula:
[tex]\begin{gathered} r=\sqrt{(-2)^2+(5)^2} \\ r=\sqrt{4+25} \\ r=\sqrt{29} \end{gathered}[/tex]Thus the required value is:
[tex]sec\theta=\frac{\sqrt{29}}{-2}[/tex]Final Answer:
[tex]sec\theta=-\frac{\sqrt{29}}{2}[/tex]what is the factor of the expression of 39-13 using gcf
We are asked to find out the GCF of the given expression
[tex]39-13[/tex]GCF (greatest common factor) is the greatest common factor between two or more numbers.
To find the GCF, let us first list out the common factors of both numbers
Factors of 13 = 1, 13
Factors of 39 = 1, 3, 13, 39
Now which factor is common to both and is greatest?
Yes, it is 13
Therefore, the GCF of the given expression is 13
[tex]39-13=13(3-1)[/tex]11/8 Percent / Valuehow can I find it please help me understand it
20 candies represent 3%
Explanation:Sincne 15% = 100
Let x% = 20, then
100x = 20 * 15
100x = 300
x = 300/100 = 3
Therefore, 20 candies represent 3%