Answers
The graph of y = 5/(x + 6) is a vertical stretching of y = 1/x by a factor of 5 and a horizontal translation to the left by 6 units.
A function y = kf(x) is a vertical stretch of y = f(x), if:
[tex]k\gt1[/tex]y = kf(x) is a vertical compression of y = f(x), if:
[tex]0\lt k\lt1[/tex]A function f(x + k) is a horizontal translation to the left of f(x), if:
[tex]k\gt0[/tex]f(x + k) is a horizontal translation to the right of f(x), if:
[tex]k\lt0[/tex]Related Questions
X=4Domain=RangeFunction?
Answers
For this case we have the following function:
[tex]x=4[/tex]The domain for this case would be x=4
And the range would be all the real numbers:
[tex]\text{Range =R}[/tex]And then we can conclude that we have a function.
the rotation are is a 60 degree rotation about the center of the regular hexagon State the image of B for the following r1=
Answers
They are asking to us, in other words, What is the position on B after a rotation of 60 degrees? remember that if it is not said something different we always rotate clockwise, and because all the triangles sum 360 degrees we can infer that each triangle has each of its angles of 60 degrees... so answering your question the final position to B is the point (or vertix) A.
SoIve each equation. TWO of these are special cases ("no solution" and " all real numbers ".)4 (j-7) =127(2p +3 - 8 =6p +292 ( x-1) = 4+2x3(4c+5)=274(2k-6) +11 =8k -13
Answers
1.
[tex]\begin{gathered} 4\mleft(j-7\mright)=12 \\ 4j-28=12 \\ 4j=12+28 \\ 4j=40 \\ j=\frac{40}{4} \\ j=10 \end{gathered}[/tex]2.
[tex]\begin{gathered} 7(2p+3)-8=6p+29 \\ 14p+21-8=6p+29 \\ 14p-6p=29-21+8 \\ 8p=16 \\ p=\frac{16}{8} \\ p=2 \end{gathered}[/tex]3.
[tex]\begin{gathered} 2(x-1)=4+2x \\ 2x-2=4+2x \\ 2x-2x=4+2 \\ 0x=6 \\ no\text{ solution} \end{gathered}[/tex]4.
[tex]\begin{gathered} 3(4c+5)=27 \\ 12c+15=27 \\ 12c=27-15 \\ 12c=12 \\ c=1 \end{gathered}[/tex]5.
[tex]\begin{gathered} 4(2k-6)+11=8k-13 \\ 8k-24+11=8k-13 \\ 8k-8k=-13+24-11 \\ no\text{ solution} \end{gathered}[/tex]A sequence is defined by the term-to-term rule
Un+1 = U₂ - 3u + 1
Given that u₁ = 3,
a) find u₂
b) find us
c) find u₁
Answers
Answer:
a) u₂ = 1
b) u₃ = -1
c) u₄ = 5
Step-by-step explanation:
A recursive formula for an arithmetic sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.
Given recursive rule:
[tex]\begin{cases}u_{n+1}=u{_n}^2-3u_n+1\\u_1=3\end{cases}[/tex]
Part a
To find u₂, substitute n = 1 into the formula:
[tex]\begin{aligned}\implies u_{2}=u_{1+1}&=u{_1}^2-3u_1+1\\&=(3)^2-3(3)+1\\&=9-9+1\\&=0+1\\&=1\end{aligned}[/tex]
Part b
To find u₃, substitute n = 2 into the formula:
[tex]\begin{aligned}\implies u_{3}=u_{2+1}&=u{_2}^2-3u_2+1\\&=(1)^2-3(1)+1\\&=1-3+1\\&=-2+1\\&=-1\end{aligned}[/tex]
Part c
To find u₄, substitute n = 3 into the formula:
[tex]\begin{aligned}\implies u_{4}=u_{3+1}&=u{_3}^2-3u_3+1\\&=(-1)^2-3(-1)+1\\&=1+3+1\\&=4+1\\&=5\end{aligned}[/tex]
Jacob and his family make their first stop on their vacation.. The beach! Jacob and his little brother enter a sand castle competition. The rules of the competition are 1. You can use any object that you bring yourself 2. You must use between 4000 and 14500 cubic inches of sand Below are all of the items that jacob and his brother will use to build their castle. For each item, calculate the volume of sand that each will hold
Answers
Answer with Explanation:
We have to find the volume of the (i) can and (ii) a cone, the volumes of the two shapes are as follows:
(i) Can:
The fomula for the volume of a cylinder (can) as well as the calculations for the volume are as follows:
[tex]\begin{gathered} V=\pi r^2h \\ r=\frac{3}{2}in \\ h=5in \\ \therefore\rightarrow \\ V=\pi(\frac{3}{2}in)^2(5in) \\ V=\frac{45\pi}{4}in^3 \\ V=35.343in^3 \end{gathered}[/tex](ii) Cone:
The formula for the cone as well as the calculations for the volume are as follows:
[tex]\begin{gathered} V=\pi r^2\frac{h}{3} \\ r=3in \\ h=5in \\ \therefore\rightarrow \\ V=\pi(\frac{3}{2}in)^2\times\frac{(5in)}{3} \\ V=\frac{45}{12}\pi in^3 \\ V=11.789in^3 \end{gathered}[/tex]in the diagram of HLK below, MJ||LK,HM=6,ML=36, and HJ=2 what isntje length of HK ?
Answers
This is a case of similar triangles. The ratio of the corresponding sides of the triangle are in proportion .
[tex]\frac{HJ}{HK}=\frac{HM}{HL}[/tex]It is true for all combination of the corresponding sides. The one above is the one we will use to answer this problem. Now, let's substitute the known legths of the segments in the given proportion.
[tex]\begin{gathered} \frac{HJ}{HK}=\frac{HM}{HL} \\ HL=HM+ML \\ \frac{2}{HK}=\frac{6}{6+36} \\ \frac{2}{HK}=\frac{6}{42} \end{gathered}[/tex]By cross multiplication, we can solve for HK
[tex]\begin{gathered} \frac{2}{HK}=\frac{6}{42} \\ 2\cdot42=6\cdot HK \\ 84=6\cdot HK \\ \frac{84}{6}=\frac{6\cdot HK}{6} \\ 14=HK \\ HK=14 \end{gathered}[/tex]Answer: HK = 14
Solve each system by the substitution method. If there is no solution or an infinite number of solution, so state. Use set notation to express solution sets.
Answers
(b) x = 43/5, y = -1/5
Explanation:(b)
x = 2y + 9 ......................................(1)
x = 7y + 10 .....................................(2)
From these equations, we can write
2y + 9 = 7y + 10
7y - 2y = 9 - 10
5y = -1
y = -1/5
Using y = -1/5 in (1)
x = 2(-1/5) + 9
= 9 - 2/5
= 43/5
A local community college has announced that they will be raising tuition cost from $46 per unit to $56 per unit. Determine the percent increase intuition cause round your answer to the nearest tenth of a percent
Answers
The percent increase is given by:
[tex]\frac{final-initial}{initial}*100[/tex]In this case the final price is $56 and the initial price is $46; then we have:
[tex]\frac{56-46}{46}*100=21.7[/tex]Therefore, the percent increase is 21.7%
Find the roots of the quadratic equation x2 + 121 = 0.11 and -1111i and -11i11i and -11-11i and 11
Answers
Given:
There is a quadratic equation given as
[tex]x^2+121=0[/tex]Required:
We need to find the roots of given equation
Explanation:
To find roots
[tex]\begin{gathered} x^2+121=0 \\ x^2=-121 \\ x=\sqrt{-121} \\ x=\pm11i \end{gathered}[/tex]Final answer:
x=11i and x=-11i
In a convex octagon, three of the exterior angles each have a measure of x°. The other five exteriorangles each have a measure of (2x + 7)'. Find the measure of each exterior angle.x =(2x+7) =
Answers
Since we have that the sum of all exterior angles of any convex polygon adds 360°, we will have the following:
[tex]3(x)+5(2x+7)=360[/tex]Now, we operate like terms and solve for x:
[tex]3x+10x+35=360\Rightarrow13x+35=360[/tex][tex]\Rightarrow13x=325\Rightarrow x=25[/tex]So, the value of x is 25.
And, the value of (2x + 7) is 57.
I learned that to solve a division problem with reminders, I need to
Answers
In order to solve a division problem with reminders, we need to find the number that will multiply the divisor and get the closest to the dividend. That number will be the quotient.
Then, to find the reminder, we need to calculate it in the formula:
[tex]\text{Dividend}=\text{quotient}\cdot\text{divisor}+\text{remider}[/tex]For example, in the division of 15 by 6, the quotient we should use is 2, because 2 *6 = 12 will be the closest to 15 (if we choose the quotient 3, we will have 3 * 6 = 18, which is bigger than 15).
Then, to find the reminder, we have:
[tex]\begin{gathered} reminder=\text{Dividend}-\text{quotient}\cdot\text{divisor} \\ reminder=15-2\cdot6=15-12=3 \end{gathered}[/tex]the scientific form of 792 to the power pls helpT-T
Answers
Given that
There is a number 792 and we have to convert it to scientific form.
Explanation -
To convert it into the scientific form we have to write it into powers of 10.
Scientific notation is always represented as
a x 10^b
The following steps will be followed as
Step 1
To find a, take the number and move a decimal place to the right one position.
Original Number: 792
New Number: 7.92
Step 2
Now, to find b, count how many places to the right of the decimal.
New Number:7.92
Decimal Count: 1 2
There are 2 places to the right of the decimal place.
Step 3
Building upon what we know above, we can now reconstruct the number into scientific notation.
Remember, the notation is: a x 10^b
a = 7.92
b = 2
Now the whole thing:
7.92 x 10^2
Step 4
The required answer
7.92 x 10^2 = 100 x 7.92 = 792
Final answer -
Therefore the final answer is 7.92 x 10^2m (2x + 30) Lines I and m are cut by a transversal. Solve for the value of x that proves l | m? (4x – 90) 25 30 40 60 sic off Zoom In Doucle Jeop-
Answers
x = 60 (option B)
Explanation:
I will be using an illustration to make it easy to comprehend
l parallel to m:
From the diagram above, the angles opposite each other are called vertical lines.
Vertical lines are equal.
When two lines intersect, the angles opposite each other are equal.
The angles with same collours are corresponding angles. And corresponding angles are equal.
We can see the top (2x + 30)° is equal to the down part with the second brown colour.
And the second brown is equal to the green opposite it (4x-90)°.
2x + 30 = 4x - 90
collect like terms:
2x - 4x = - 90 - 30
-2x = -120
divide both sides by -2:
-2x/-2 = -120/-2
x = 60 (option B)
34. A virus decays on a steelsurface at a rate of -15% perhour. There are 5,000,000viruses present on a steelcountertop. Write an equationmodeling the situation andpredict the amount of viruspresent in 24 hours.
Answers
In this problem
we have an exponential decay function of the form
[tex]y=a(1-r)^t[/tex]where
a is the initial value --------> a=5,000,000 virus
t is the time in hours
r is the rate -------> r=15%=0.15
y is the amount of virus
substitute given values
[tex]\begin{gathered} y=5,000,000(1-0.15)^t \\ y=5,000,000(0.85)^t \end{gathered}[/tex]For t=24 hours
substitute
[tex]\begin{gathered} y=5,000,000(0.85)^{24} \\ y=101,164\text{ virus} \end{gathered}[/tex]Courtney and Joe are power washing the patio. Courtney can power wash the entirepatio in 7 hours while it takes Joe just 5 hours to power wash the patio. How long willit take Courtney and Joe to power wash the patio together? Choose the equation thatshould be used to solve this problem and state the solution
Answers
Solution:
Given:
Courtney can power wash the entire patio in 7 hours while
it takes Joe just 5 hours to power wash the patio
Based on the given information,
Courtney work rate = 1/7
Joe work rate = 1/5
let x represent the number of hours it take Courtney and Joe to power wash the patio together
Thus,
[tex]\begin{gathered} \frac{1}{x}=\frac{1}{7}+\frac{1}{5} \\ \\ \frac{1}{x}=\frac{5+7}{35} \\ \\ \frac{1}{x}=\frac{12}{35} \\ \\ x\text{ =}\frac{35}{12}\text{ hours} \\ \\ x=2\frac{11}{12}\text{ hours} \\ \\ The\text{ answer is 2}\frac{11}{12}hours \end{gathered}[/tex]Convert from Barrels to (Feet, inches andquarter inch.Tank # 01 capacity:Barrels per feet: 62.52Barrels per inch: 5.21Barrels per quarter inch: 1.3If you deposited 170 barrels into tank # 01 What would be the total deposited into the tank in feet/inch/ and quarter inch?
Answers
ANSWER:
Total capacity in feet = 2.72 feet
Total capacity in inches = 32.63 inches
Total capacity in quarter inches = 130.77 quarter inches
EXPLANATION:
Given the capacity of the tank as;
62.52 barrels per feet
5.21 barrels per inch
1.3 barrels per quarter inch
If 170 barrels was deposited into the tank, we can go ahead and determine the total deposited into the tank in feet/inch/ and quarter inch as seen below;
Total capacity in feet:
[tex]\begin{gathered} \frac{62.52}{1}=\frac{170}{x} \\ \\ 62.52x=170 \\ \\ x=\frac{170}{62.52} \\ \\ x=2.72\text{ feet} \end{gathered}[/tex]Total capacity in inches:
[tex]\begin{gathered} \frac{5.21}{1}=\frac{170}{y} \\ \\ 5.21y=170 \\ \\ y=\frac{170}{5.21} \\ \\ y=32.63\text{ inches} \end{gathered}[/tex]Total capacity in quarter inches:
[tex]\begin{gathered} \frac{1.3}{1}=\frac{170}{z} \\ \\ 1.3z=170 \\ \\ z=\frac{170}{1.3} \\ \\ z=130.77\text{ quarter inches} \end{gathered}[/tex]Find the value of the Riemann sumV = sum k = 1 to n f(c_{k}) * Delta*x_{k}
Answers
The values for Δx_k are:
[tex]\begin{gathered} (2-0)=2 \\ (3-2)=1 \\ (5-3)=2 \end{gathered}[/tex]So, now we will use the right endpoints of each interval to find the c_k values: 2,3 and 5.
And f(c_k):
[tex]\begin{gathered} 2^2+2=4+2=6 \\ 3^2+2=9+2=11 \\ 5^2+2=25+2=27 \end{gathered}[/tex]So each term in the Riemann sum is:
[tex]\begin{gathered} (6\times2)=12 \\ (11\times1)=11 \\ (27\times2)=54 \end{gathered}[/tex]Adding them together:
[tex]V=12+11+54=77[/tex]The value V is 77.
Two friends visited Washington D.C. for the weekend. Person 1 rode the subway three times at the peak fare price and five times at the off-peak fare price for a total cost of $19.50. Person 2 rode two times at the peak fare price and four times at the off-peak fare price for a total cost of $14.50. How much was the peak fare price?
Answers
We are given the following information.
Person 1 rode the subway three times at the peak fare price and five times at the off-peak fare price for a total cost of $19.50.
Person 2 rode two times at the peak fare price and four times at the off-peak fare price for a total cost of $14.50.
We are asked to find the peak fare price.
Let x represent the peak fare price.
Let y represent the off-peak fare price.
Then we can set up the following two equations for persona 1 and person 2.
[tex]\begin{gathered} 3x+5y=19.50\;\;eq.1 \\ 2x+4y=14.50\;\;eq.2 \end{gathered}[/tex]Separate out the y variable in eq.1
[tex]\begin{gathered} 3x+5y=19.50 \\ 5y=19.50-3x \\ y=\frac{19.50-3x}{5} \end{gathered}[/tex]Now, substitute it into eq.2
[tex]\begin{gathered} 2x+4y=14.50 \\ 2x+4(\frac{19.50-3x}{5})=14.50 \\ 2x+\frac{78-12x}{5}=14.50 \\ \frac{5\cdot2x+78-12x}{5}=14.50 \\ \frac{10x+78-12x}{5}=14.50 \\ 10x-12x+78=14.50\cdot5 \\ -2x+78=72.5 \\ -2x=72.5-78 \\ -2x=-5.5 \\ 2x=5.5 \\ x=\frac{5.5}{2} \\ x=\$2.75 \end{gathered}[/tex]Therefore, the peak fare price is $2.75
Thomas has 40 cups of flour that he wants to share equally with 5 friends. How many quarts of flour will each friend get?
Answers
From the statement of the problem, we know that:
• Thomas has 40 cups of flour,
,• he wants to share equally with 5 friends.
If Thomas wants to share equally the cups of flour with his friends, he must give the same number of cups to each friend, that number is given by the quotient:
[tex]\frac{\text{total \# of cups of flour}}{\text{total \# of friends}}=\frac{40\text{ cups}}{5\text{ friends}}=8\cdot\frac{\text{cups}}{\text{friend}}\text{.}[/tex]So each friend will receive 8 cups of flour. Now, because each cup has 4 quarts, each friend will receive:
[tex]8\cdot\frac{\text{cups}}{\text{friend}}\cdot4\cdot\frac{\text{quarts}}{\text{cup}}=32\cdot\frac{\text{quarts}}{\text{friend}}\text{.}[/tex]Answer
Each friend will receive 32 quarts of flour.
Melvin is pushing a tire during a workout with the dimension shown.How many square inches of space has the tire covered after Melvin pushes the tire 5 times around. Round to the nearest tenths
Answers
We are given the diameter and height of the tire.
Diameter = 29 in
Height = 8 in
Recall that the surface area of a cylindrical shape is given by
[tex]SA=2\pi r^2+2\pi rh[/tex]Where r is the radius.
We know that the radius is half of the diameter.
So the surface area becomes
[tex]SA=2\pi(\frac{D}{2})^2+2\pi(\frac{D}{2})h[/tex]Substitute the values of diameter and height.
[tex]\begin{gathered} SA=2\pi(\frac{29}{2})^2+2\pi(\frac{29}{2})\cdot8 \\ SA=2\pi(14.5)^2+2\pi(14.5)\cdot8 \\ SA=2\pi\cdot210.25^{}+2\pi\cdot116 \\ SA=1321.04^{}+728.85 \\ SA=2049.89\: in^2 \end{gathered}[/tex]Finally, multiply the surface area by 5 times
[tex]\begin{gathered} SA=2049.89\cdot5 \\ SA=10249.4\: in^2 \end{gathered}[/tex]Therefore, the tire has covered 10249.4 square inches of space.
will send image of problem
Answers
We are given the graph of a function and we are asked to determine the following:
VA (vertical asymptote). This is the value of "x" that the graph of the function doesn't touch. In this case, the VA is approximately x = -3.5
HA (horizontal asymptote) is the value of "y" that the graph of the function doesn't touch, in this case, the HA is y = 2.
The Domain of the function is the values of "x" that the function takes as input. Since the function takes all the values of "x" except the VA, the domain is:
[tex]D=\mleft\lbrace x\in\R\parallel x\ne-3.5\mright\rbrace[/tex]The range of the function is the values of "y" that the function yields. Since the function produces values for every "y" except the HA, the range is:
[tex]R=\mleft\lbrace y\in\R\parallel y\ne2\mright\rbrace[/tex]
use the equation to draw a line in the graph -x+5y>-5
Answers
ok
-x + 5y > -5
-x + 5y = -5
x y
-2 -7/5
-1 -6/5
0 1
1 -4/5
2 -3/5
I'll graph it
write the appropriate number for each product or quotient
Answers
Ok
Question 8
1
[tex]\begin{gathered} 1\frac{1}{4}\frac{.}{.}\text{ 7}\frac{1}{2} \\ \frac{5}{4}\text{ }\frac{.}{.}\text{ }\frac{15}{2} \\ =\text{ }\frac{5}{4}\text{ }\times\text{ }\frac{2}{15} \\ =\text{ }\frac{10}{60} \\ =\text{ }\frac{1}{6} \end{gathered}[/tex]2.
[tex]\begin{gathered} \frac{4}{5}\text{ }\frac{.}{.}\text{ }\frac{2}{15} \\ =\text{ }\frac{4}{5}\text{ }\times\text{ }\frac{15}{2} \\ =\text{ }\frac{60}{10} \\ =\text{ 6} \end{gathered}[/tex]3.
[tex]\begin{gathered} 6\frac{1}{4}\text{ }\times\text{ }\frac{2}{3} \\ =\text{ }\frac{25}{4}\text{ }\times\text{ }\frac{2}{3} \\ =\text{ }\frac{50}{12} \\ =\text{ }\frac{25}{6} \\ =\text{ 4}\frac{1}{6} \end{gathered}[/tex]4.
[tex]\begin{gathered} 1\frac{1}{2}\text{ }\frac{.}{.}\text{ }\frac{4}{25} \\ =\text{ }\frac{3}{2}\text{ }\frac{.}{.}\text{ }\frac{4}{25} \\ =\text{ }\frac{3}{2}\text{ }\times\text{ }\frac{25}{4} \\ =\text{ }\frac{75}{8} \\ =\text{ 9}\frac{3}{8} \end{gathered}[/tex]5.
[tex]\begin{gathered} \frac{2}{3}\text{ }\frac{.}{.}\text{ 6}\frac{1}{4} \\ =\text{ }\frac{2}{3}\text{ }\frac{.}{.}\text{ }\frac{25}{4} \\ =\text{ }\frac{2}{3}\text{ }\times\text{ }\frac{4}{25} \\ =\text{ }\frac{8}{75} \end{gathered}[/tex]6.
[tex]\begin{gathered} 1\frac{1}{4}\text{ }\times\text{ 7}\frac{1}{2} \\ =\text{ }\frac{5}{4}\text{ }\times\text{ }\frac{15}{2} \\ =\text{ }\frac{75}{8} \\ =\text{ 9}\frac{3}{8} \end{gathered}[/tex]7.
[tex]\begin{gathered} 1\frac{1}{2}\text{ }\frac{.}{.}\text{ 6}\frac{1}{4} \\ =\text{ }\frac{3}{2}\text{ }\frac{.}{.}\text{ }\frac{25}{4} \\ =\text{ }\frac{3}{2}\text{ }\times\text{ }\frac{4}{25} \\ =\text{ }\frac{12}{50} \\ =\text{ }\frac{6}{25} \end{gathered}[/tex]8.
[tex]\begin{gathered} \frac{4}{5}\text{ }\times\text{ }\frac{2}{15} \\ =\text{ }\frac{4\text{ x 2}}{5\text{ x 15}} \\ =\text{ }\frac{8}{75} \end{gathered}[/tex](6.25 x 10^9) − (3.44 x 10^8)
Answers
To solve this operation we first factorize with the number that has the lowest value in the exponential. In this case:
[tex]\begin{gathered} 6.25\cdot10^9-3.44\cdot10^8 \\ 10^8\cdot(6.25\cdot10^1-3.44) \end{gathered}[/tex]Now, we can multiply the number 6.25 by 10 and solve the operation!
[tex]\begin{gathered} 10^8\cdot(62.5-3.44) \\ 59.06\cdot10^8 \\ 5.906\cdot10^9 \end{gathered}[/tex]Therefore, the answer is 5.906*10^9
does the equation below represent a direct proportion? If yes, identify the constant of proportionality 1/2y = 5x
Answers
The equation [(1/2)y = 5x] represents a direct proportion and it's constant of proportionality is (1/10)
As per the question statement, we are provided with an equation,
[(1/2)y = 5x]
We are required to determine if the above mentioned equation represents a direct proportion or not, and if it does, we have to also mention it's constant of proportionality.
Now to solve this question, first we need to know what a direct proportion and it's constant of proportionality are.
A direct proportion or a direct variation is the relation between two quantities (numbers or variables) where the ratio of the two is equal to a constant value, and this constant value is known as the constant of proportionality for that direct proportion.Here, our concerned equation is [(1/2)y = 5x], which can be altered to,
[(y/2) = 5x]
Or, [(x/y) = 10]
Or, [(x : y) = 10]
Hence, the relation between the variables "x" and "y" of the equation
[(y/2) = 5x] is direct, as their ratio (x : y) is equal to a constant term (10), and 10 is therefore, the constant of proportionality of the equation
[(y/2) = 5x].
Equation: In Mathematics, an equation is a mathematical statement that determine the relation of equality between two separate expressions, by connecting them with an "Equal to" sign.To learn more about Equations and Direction proportions, click on the link below.
https://brainly.com/question/23268818
#SPJ9
The point A(4,1) is reflected over the point (0, -3) and its image is point B. Whatare the coordinates of point B?
Answers
Step 1: Concept
Given point A (4, 1) reflect over (0, -3). The image is at point B.
Step 2:
Let the coordinate of B = (x,y)
Step 3:
To find image B, apply the formulas below.
[tex]\begin{gathered} 0\text{ = }\frac{\text{x + 4}}{2} \\ \text{Cross multiply} \\ x\text{ + 4 = 2 }\times0 \\ \text{x + 4 = 2} \\ \text{x = -4} \\ \\ -3\text{ = }\frac{y\text{ + 1}}{2} \\ \text{Cross multiply} \\ \text{y + 1 = -3 }\times\text{ 2} \\ y\text{ + 1 = -6} \\ \text{y = -6 - 1} \\ y\text{ = -7} \end{gathered}[/tex]Step 4: Final answer
The coordinates of the image B = (x,y) = (-4,-7)
2. Rewrite by factoring the GCF from each expression.b) 6y - 12Show your work here:Answer:
Answers
First, we find the Greatest Common Factor (GCF) between 6 and 12. It's important to remember that the GCF refers to the greatest number that can divide by each number. In this case, we can easily deduct that 6 is the greatest number that divides each of them.
[tex]\begin{gathered} \frac{6}{6}=1 \\ \frac{12}{6}=2 \end{gathered}[/tex]So, the GCF is 6. Once we know the GCF, we use the result of each division to express the factored expression.
[tex]6y-12=6(y-2)[/tex]Observe that the GCF is the coefficient of the binomial and the result of each division it represents each new term.
Therefore, the factored expression is 6(y - 2).Given f(x) = - = -X 5, solve for x when f (x) = -3.
Answers
The given expression : f(x) = - x - 5
to find the value of f(x) at x = (-3)
Substitute the value of x = (-3)
[tex]\begin{gathered} f(x)=-x-5 \\ at\text{ x = (-3)} \\ f(-3)=-(-3)-5 \\ f(-3)=3-5 \\ f(-3)=(-2) \end{gathered}[/tex]So, at x = (-3), f(x) = (-2)
Answer : f(x) = (-2)
Reference attached image for the problem.Please show your work for finding the partial area.
Answers
To find the area of a sector of a circle use the next formula:
[tex]A=\frac{\theta}{360º}*\pi *r^2[/tex]As the given circle has a outside angle 90º (it is not part of the sector of the circle) subtract the 90º from 360º (total angle of a circle) to find the angle of the sector:
[tex]\theta=360º-90º=270º[/tex]Find the area of the sector with angle 270º:
[tex]\begin{gathered} A=\frac{270º}{360º}*3.14*(11in)\placeholder{⬚}^2 \\ \\ A=0.75*3.14*121in^2 \\ \\ A=284.955in^2 \end{gathered}[/tex]Then, the approximate area of the given sector of a circle is 284.955 square incheshey I need help with math because I don't know so what is 5 divided by 536
Answers
we are asked to divide 5 over 536. Since the number we are diving by is larger than 5, the answer is a decimal number, the division can be done like this:
[tex]5\parallel536[/tex]We need to add zeroes to the 5 until we get a number that is largest than 536, every time we do that we also add a zero to the answer, like this:
Now, if we multiply 536 by 9 we get 4824, we subtract that from 5000, like this:
Therefore, the answer is 0.009 with a remainder of 176
