Given
[tex]-2y\ge10[/tex]Solution
Recall: Dividing by a negative number means you reverse the inequality symbol
[tex]\begin{gathered} -2y\ge10 \\ divide\text{ both sides by -2} \\ -\frac{2y}{-2}\ge\frac{10}{-2} \\ \\ y\leq-5 \end{gathered}[/tex]The final answer
[tex]y\leq-5[/tex]The perimeter of a rectangular pool is 44 feet. The length is 8ft longer than the width. Find the dimensions.
Given:
A rectangular pool with the following measures,
Perimeter
Length = x + 8
Width = x
Let's determine the measure of its dimensions:
[tex]\text{ Perimeter = 2L + 2W}[/tex][tex]\text{ = 2(x + 8) + 2(x)}[/tex][tex]\text{ 44 = 2x + 16 + 2x}[/tex][tex]\text{ 44 = 4x + 16}[/tex][tex]\text{ 44 - 16 = 4x}[/tex][tex]\text{ 28 = 4x}[/tex][tex]\text{ }\frac{28}{4}\text{ = }\frac{4x\text{ }}{4}[/tex][tex]\text{ 7 = x}[/tex]Let's now determine its dimensions,
Length = x + 8 = 7 + 8 = 15 ft.
Width = x = 7 ft.
Therefore, the dimension of the rectangular pool is Length = 15 ft. and Width =7 ft.
Which kind of symmetry does the letter D have?A. point symmetry, onlyB. line symmetry, onlyC. neither point nor line symmetryD. both point and line symmetry
Analysing the letter D, we can find the following symmetry (in red):
There is no point of symmetry. Therefore, the correct option is B.
Use the system of equations below to solve for z.7x+3y+2z-4w=184w+5x-3y-2z=6-2w-3x+y+z=-52z+3w+4y-8x=11253
Equations:
[tex]\begin{gathered} 7x+3y+2z-4w=18\text{ \lparen1\rparen} \\ 5x-3y-2z+4w=6\text{ \lparen2\rparen} \\ -3x+y+z-2w=-5\text{ \lparen3\rparen} \\ -8x+4y+2z+3w=11\text{ \lparen4\rparen} \end{gathered}[/tex]Sum (1)+ (2):
[tex]\begin{gathered} 7x+3y+2z-4w=18\text{ }\operatorname{\lparen}\text{1}\operatorname{\rparen} \\ + \\ 5x-3y-2z+4w=6\text{ }\operatorname{\lparen}\text{2}\operatorname{\rparen} \\ 5x+7x+3y-3y+2z-2z-4w+4w=18+6 \\ 12x=24 \\ x=\frac{24}{12}=2 \end{gathered}[/tex]x=2
Now, we are going to sum (3)*2+(2).
[tex]\begin{gathered} 5x-3y-2z+4w=6\text{ }\operatorname{\lparen}\text{2}\operatorname{\rparen} \\ + \\ 2*(-3x+y+z-2w)=-5*2\text{ }\operatorname{\lparen}\text{3}\operatorname{\rparen} \\ 5x-6x-3y+2y-2z+2z+4w-4w=6-10 \\ -x-y=-4 \\ -2-y=-4 \\ y=-2+4=2 \end{gathered}[/tex]y=2.
Replacing y and x in (4) and (3):
[tex]\begin{gathered} -3(2)+2+z-2w=-5\text{ }\operatorname{\lparen}\text{3}\operatorname{\rparen} \\ -8(2)+4(2)+2z+3w=11\text{ }\operatorname{\lparen}\text{4}\operatorname{\rparen} \end{gathered}[/tex][tex]\begin{gathered} -6+2+z-2w=-5 \\ z-2w=-5+6-2 \\ z-2w=-1\text{ \lparen5\rparen} \end{gathered}[/tex][tex]\begin{gathered} -16+8+2z+3w=11 \\ 2z+3w=11+16-8 \\ 2z+3w=19\text{ \lparen6\rparen} \end{gathered}[/tex]Isolating w in (5) ans replacing in (6):
[tex]\begin{gathered} 2w=-1-z \\ w=\frac{-1-z}{2} \end{gathered}[/tex][tex]\begin{gathered} 2z+3(\frac{-1-z}{2})=19 \\ \frac{4z-3-3z}{2}=19 \\ z-3=19*2 \\ z=38-3=35 \end{gathered}[/tex]Answer: z=35.
Graph the polar equation.P = 16 cos20帶이
To make the graph we need to make a table with different pairs of angles and radius.
We can start with θ = 0, and calculate the radius for different values of θ. (π/6, π/3, π/4 and so on. Then, you can join the points.
The equation for radius will be:
[tex]\begin{gathered} r^2=16\cos 2\theta \\ r=\sqrt[]{16\cos2\theta} \\ r=4\cdot\sqrt[]{\cos2\theta} \end{gathered}[/tex][tex]\begin{gathered} \text{for }\theta=0 \\ r=4\cdot\sqrt[]{\cos2\cdot0} \\ r=4\cdot\sqrt[]{\cos0} \\ r=4\cdot\sqrt[]{1} \\ r=4 \end{gathered}[/tex]Then, in the line of θ = 0, you draw a point in the fourth circle.
Then, we get the following table of values:
θ r
04.00
π/63.72
π/43.36
π/32.83
π/20.00
Note that we can't evaluate angles whose cosine is negative (angles in quadrants 2 and 3) since we would be trying to calculate the square root of a negative number, which does not exist among real numbers. Then, we will evaluate angles in the first quadrant (already done) and the 4th quadrant.
θ r
-π/63.72
-π/43.36
-π/32.83
-π/20.00
In the last table we use negative angles, they can be "translated" to positive:
-π/6= π/6
-π/4= 7π/4
-π/3= 5π/3
-π/2= 3π/2
Now, we can draw the points:
Joining the points:
A triangle has side lengths of 5,6 and 8. Is it a right triangle?Explain why or why not?
ANSWER
Not a right triangle
EXPLANATION
In a right triangle, the hypotenuse is always the longest side. If these are the side lengths of a right triangle, the sides would be,
The Pythagorean theorem must be true for any right triangle,
[tex]8^2=5^2+6^2[/tex]Let's see if it is indeed true,
[tex]64=25+36[/tex][tex]64=61\to not.true[/tex]If the Pytagorean theorem is nort true, then this is not a right triangle
5. An expression is shown. 78 - 14 Between which two consecutive whole numbers does this value lie? Enter your numbers in the box. Between and
78 divide by 14
First, divide the numbers
78/14 = 5.57
5.57 lies between 5 and 6
Please help me with this quickly, I need to go to sleep, thank you
x = -43/4
Explanation:Given:
[tex]\frac{17-4x}{12}=5[/tex]To find:
the value of x
[tex]\begin{gathered} \frac{17-4x}{12}=5 \\ multiply\text{ both sides by 12:} \\ 17\text{ - 4x = 5\lparen12\rparen} \\ 17\text{ - 4x = 60} \end{gathered}[/tex][tex]\begin{gathered} add\text{ 4x to both sides:} \\ 17\text{ -4x + 14x = 60 + 4x} \\ 17\text{ = 60 + 4x} \\ \\ subtract\text{ 60 from both sides:} \\ 17\text{ - 60 = 4x} \\ -43\text{ = 4x} \\ \\ divide\text{ boh sides by 4:} \\ x\text{ = -43/4} \end{gathered}[/tex]Select the correct answer.6cis5pi/6Convert57to rectangular form.OA. 3V3 + 31O B. –313 + 3iO C. 373 – 3iOD. -3V3 – 31O E. 3 – 3731
Answer:
Choice B.
Explanation:
The equation can be rewritten as
[tex]6\text{cis}\frac{5\pi}{6}=6\cos \frac{5\pi}{6}+i\sin \frac{5\pi}{6}[/tex]Now since
[tex]6\cos \frac{5\pi}{6}=-3\sqrt[]{3}[/tex]and
[tex]6\sin \frac{5\pi}{6}=3[/tex]the expression becomes
[tex]-3\sqrt[]{3}+3i[/tex]Hence, choice B is the correct answer since it matches the answer we got above.
Suppose cluster sampling were being used to survey digital camera users, who amount to 77% of the population of the United States. Based on the table below, which city would be considered the best cluster?
The best cluster is Las Vegas, which has a percentage of 78% that is linearly close to 77%, the percentage of the whole population of the United States.
AnswerLas Vegas
Solve: 9/14 + 2/6 = ?
We have to solve the expression:
[tex]\frac{9}{14}+\frac{2}{6}[/tex]We have to find a common denominator for the fractions and then solve it.
We can start by simplifying the fractions that can be simplified, like 2/6.
[tex]\frac{9}{14}+\frac{2}{6}=\frac{9}{14}+\frac{1}{3}[/tex]Then, the common denominator between 14 and 3 is 14*3=42, so we end with:
[tex]\frac{9\cdot3}{14\cdot3}+\frac{1\cdot14}{3\cdot14}=\frac{27}{42}+\frac{14}{42}=\frac{27+14}{42}=\frac{41}{42}[/tex]Answer: 41/42
Solve the equation.– 2y - 15 = 4y + 15y=
Given the equation;
[tex]-2y-15\text{ = 4y+15}[/tex]You are to calculate the value of y. This is as shown below;
First collect the like terms;
[tex]\begin{gathered} -2y\text{ - 4y = 15+15} \\ \end{gathered}[/tex]Evaaluate the expression an find y;
[tex]\begin{gathered} -6y=30 \\ \end{gathered}[/tex]Divide both sides by -6;
[tex]\begin{gathered} \frac{-6y}{-6}=\frac{30}{-6} \\ y\text{ = -5} \end{gathered}[/tex]Hence the value of y is -5
the perimeter of a rectangle room is 60 feet. let x be the width of the room (in feet) and let y be the length of the room (in feet). select all of the questions below that could modle this situation
Given that,
The perimeter of a rectangle is 60.
The perimeter is generally defined as the length of the outline of the shape.
So, in rectangle having four sides, the perimeter would be sum of all the sides.
Length1 + length2 + length3 + length4 = perimeter
Here, length1 and length3 are equal, that are the lengths (y),
Similarly,
Length2 and length4 are equal, that is width (x).
Hence, the equation becomes,
x + y + x + y = perimeter
or
2x + 2y = 60
or
2 (x + y) = 60
Hence, the first two options are correct.
Solve M=2rt^3-3rx for x
You have the following equation:
M = 2rt³ - 3rx
In order to solve the previous equation for x, proceed as follow:
M = 2rt³ - 3rx subtract 2rt³ both sides
M - 2rt³ = -3rx divide by -3r both sides
(M - 2rt³)/(-3r) = x simplify left side
-M/3r + 2/3 t³ = x
???????????????????
Given,
g(x) = - x^2
now, in part (b), we have to find g(-2)
It can be done by replacing the value of x with -2, so
g(x) = - x^2
g(-2) = - (-2)^2
g(-2) = - 4
Part d:
g(m) = ?
So, here we will put the 'm' value in place of x.
g(x) = - x^2
g(m) = - (m)^2
g(m) = -m^2
Members of the football team hold a fundraising dinner to raise money for their annual trip. They must sell tickets to the event at a price that will earn them more money than the cost of food.Here's a formula for this scenario:t = n (p - c)wheret = total profit made from the eventn = number of tickets soldp = price charged for each dinnerC = cost for food per plate The team hopes to sell 100 tickets. The cost for food per plate is $1.75 and they hope to charge $11.75 for each dinner. How much profit should they receive from the event?Enter the correct answer.
t = n(p-c)
t=100(11.75 - 1.75)
t = 100(10)
t=$1000
total profit received = $1000
Solve the inequality. State the solution in inequality notation. 4(x - 5) + 10 > 2(5x – 2) – 4x
We will solve as follows:
[tex]4(x-5)+10>2(5x-2)-4\Rightarrow4x-20+10>10x-4-4x[/tex][tex]\Rightarrow4x-10>6x-4\Rightarrow-2x>6\Rightarrow x<-3[/tex]So, the solution is x < -3.
***Breakdown:
*After we obtain:
[tex]4x-10>6x-4[/tex]We operate like terms, that is we separate the variables and integers in the different side [Operating as if it were a normal equation]:
[tex]\Rightarrow4x-6x>-4+10\Rightarrow-2x>6[/tex]After this, we know that by dividing and/or multiplying by negative values in the inequality the orientation of the inequality will shift [That is if it was "<" then it will become ">" and viceversa], that is:
[tex]\Rightarrow x<\frac{6}{-2}\Rightarrow x<-3[/tex]Solve for 2. Enter the solutions from least to greatest.(x + 6)2 – 16 = 0lesser 1 =greater I =
The given expression is
[tex](x+6)^2-16=0[/tex]First, we add 16 on each side
[tex]\begin{gathered} (x+6)^2-16+16=16 \\ (x+6)^2=16 \end{gathered}[/tex]Then, we apply a square root on each side
[tex]\begin{gathered} \sqrt[]{(x+6)^2}=\sqrt[]{16} \\ x+6=\pm4 \end{gathered}[/tex]Now, we subtract 6 from each side
[tex]\begin{gathered} x+6-6=\pm4-6 \\ x_1=4-6=-2 \\ x_2=-4-6=-10 \end{gathered}[/tex]Therefore, the lesser solution is -10 and the greater solution is -2.QuestionWrite the following function in terms of its cofunction.csc (pi/4)
Two functions are called cofunctions if they are equal on complementary angles
[tex]\csc \theta=\sec (\frac{\pi}{2}-\theta)[/tex]Since
[tex]\theta=\frac{\pi}{4}[/tex]Substitute it in the rule above
[tex]\csc (\frac{\pi}{4})=sec(\frac{\pi}{2}-\frac{\pi}{4})[/tex][tex]\csc (\frac{\pi}{4})=\sec (\frac{\pi}{4})[/tex]The cofunction is sec(pi/4)
Use your number sense to find the values for x and y that satisfy the equations.4y = 8
y = 2
Explanation:The given equation is 4y
Divide both sides of the equation by 4
[tex]\begin{gathered} \frac{4y}{4}=\frac{8}{4} \\ \end{gathered}[/tex]y = 2
Also, since we are asked to use our number sense, we can find what we will multiply by 4 to give 8
Since 4 x 2 = 8, then y = 2
If sides AB and DC of a quadrilateral ABCD are parallel, which additional informationwould be sufficient to prove that quadrilateral ABCD is a parallelogram.ABACABDCACBDADABNone of the other answers are correct
We have a quadrilateral ABCD, where we know that AB || DC.
The other condition for the quadrilateral to be a parallelogram is that the other 2 sides of the parallelogram are congruent.
The other two sides are AC and BD, so the other condition needed is that AC and BD are congruent.
Answer: AC and BD are congruent.
[tex]AC\cong BD[/tex]The population of retired citizens in Memphis is 54000. If the population decreases at a rate of 5.9 % each year. What will the population of retirees be in 6 years?Write an exponential growth model for the future population P(x) where x is in years:
We will have the following:
First, we construct the exponential decay function, that is:
[tex]P(x)=54000(1-0.059)^x\Rightarrow P(x)=54000(0.941)^x[/tex]Now, we will determine the population after 6 years:
[tex]P(6)=54000(0.941)^6\Rightarrow P(6)=37491.38638[/tex]So, the population after 6 years will be of approximately 37491 people-
6/2(1+2)help me with math problem
THREE OF THE STATEMENTS BELOW ARE FALSE, USE THE TYPING TOOL TO FIND AND CORRECT THE FALSE STATEMENTS IN THE WHITE BOXES. A D The hypotonuse is the longest side of the right triangle The Pythagorean theorom applies to all triangles. The hypotenuse is always adjacent to the 90° angle E The Pythagorean theorem states that 2a + 2b - 20 INTRO TO PYTHAGOREAN THEOREM The logs, a and b, will always be adjacent to the 90° angle The square of the hypotonuts is always equal to the sum of the squares of the two legs in a right triangle Statement is false. || Statement is falso. Statement is fake Correct the statement: Correct the statement: Correct the statement er notes
We are asked to correct the following statements:
A. "The hypotenuse is the longest side of the right triangle" The statement is true.
B. "The Pythagorean theorem applies to all triangles". The statement is false. The Pythagorean theorem applies to RIGHT triangles.
C. "The hypotenuse is always adjacent to the 90° angle". The statement is false. The hypotenuse is opposite to the 90° angle.
D. "The Pythagorean theorem states that 2a + 2b - 2c". The statement is false. The Pythagorean theorem states that:
[tex]a^2+b^2=c^2[/tex]E. "The logs, a and b, will always be adjacent to the 90° angle". The statement is true, since a and b represent the adjacent sides of the 90 degrees angle.
F.
To which subsets of numbers does 1/3 belong?
1/3 is a rational number, which written as a decimal is an infinite period decimal.
12 posters for 36 students 21 poses for 36 students
In order to find Lorenzo's speed in miles per hour, we need to convert from yard to mile and from second to hour. The rates are:
1 yard = 1/1760 miles
1 second = 1/3600 hours
So we have that:
[tex]\text{speed}=5\frac{yards}{\sec ond}=5\frac{\frac{1}{1760}miles}{\frac{1}{3600}hour}=5\frac{3600}{1760}\frac{miles}{hour}=10.227\text{ miles/hr}[/tex]Lorenzo can ride 10.227 miler per hour.
the number line shown is divided into segments of equal length use the number line diagram to answer the following questions A. what is the length of each segment on the number line B.what number does point N represent C. what is the opposite of point N
A. We must divide the distance between the number of divisions
from 0 to 1 we have a distance of 1 and count 8 divisions
so
[tex]\frac{1}{8}=0.125[/tex]so the length of each segment is 1/8 or 0.125
B.
A product initially with a value of $21,800 has been depreciating at 8.1% p.a over 8 years. What is it's current value?
we get that:
[tex]v=21800\cdot(0.919)^8=11091.25[/tex]its current value is $11091.25
For f(x) = 2x and g(x) = x,find f (g(2))
I need help with math please
1. 92 .
2. 7
3. >=<
4. -
5. 8x3=24
Step-by-step explanation:
What be it’s value, to the nearest thousand dollars, in 13 years?
The Solution:
The value of the house in 13 years time can be calculated using the formula below:
[tex]F\mathrm{}V=P\mathrm{}V(1+\frac{r}{100})^n[/tex]In this case,
[tex]\begin{gathered} FV=\text{future value (value after 13 years)=?} \\ PV=\text{present value= \$249000} \\ r=\text{ rate \%=10.5\%} \\ n=\text{ number of years=13 years} \end{gathered}[/tex]Substituting these values in the formula above, we get
[tex]FV=249000(1+\frac{10.5}{100})^{13}=249000(1+0.105)^{13}[/tex][tex]FV=249000(1.105)^{13}=911819.68\approx\text{ \$911820}[/tex]Thus, the value of the house in 13 years is $911820 (to the nearest dollars)