Starting with the proportion:
[tex]\frac{12}{?}[/tex]Since it should be equal to 4/3, notice that if we divide both numerator and denominator by 3, then we should get 4 and 3 respectively:
[tex]\frac{12}{?}=\frac{12\div3}{?\div3}=\frac{4}{?\div3}=\frac{4}{3}[/tex]Therefore, ?÷3 is equal to 3.
Which number is equal to 3 when we divide it by 3?
That number is 9. 9÷3=3
Therefore, ?=9.
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
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.
Using the translation that maps (3,-4) to its image (1,0), what is the image of any point (x,y)?A. (x+2,y+4)B. (x−2,y−4)C. (x+2,y−4)D. (x−2,y+4)
Explanation
Given (3,-4), its image (1,0) can be produced below;
[tex]\left(3,-4\right)\Rightarrow\left(x−2,y+4\right)\Rightarrow\left(1,0\right)[/tex]Answer: Option D
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.
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
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
This is a maze where you find the answer starting from where it says start, and as you find the answer you highlight it along the way! Pls help I’m really bad at this
The start figure has two chords in the circle.
By theorem of internal division of chords it follows:
[tex]\begin{gathered} 21x=18\times14 \\ x=\frac{18\times14}{21} \\ x=12 \end{gathered}[/tex]Hence the value of x is 12.
The blank of a line is the x-coordinate of the point where the line crosses the x-axis. It occurs when y = 0.
Answer
The x-intercept of a line is the x-coordinate of the point where the line crosses the x-axis. It occurs when y = 0.
Hope this Helps!!!
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.
This expression 12(1.0515)t models the population of elephants in a wildlife refuge after years since 1975 is the population of elephants increasing or decreasing?
The function for an exponential growth/decay is given as follows;
[tex]f(x)=a(1+r)^x[/tex]Where,
[tex]\begin{gathered} x=\text{Number of years} \\ a=\text{initial value} \\ r=\text{rate of growth} \end{gathered}[/tex]Observe that from the equation provided, the rate is 1.015. This means there is a growth. If there was a decay(decrease), the rate would be less than 1 because, the formula then would be;
[tex]f(x)=a(1-r)^x[/tex]ANSWER:
Therefore, the population of elephants is INCREASING.
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
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.
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.
If a1 = 8 and an = 3an-1 then find the value of a4.
a_4= 216
1) Given that we have the first term and the Recursive Formula, let's find the fourth term of that Sequence
2) Let's find the second, the third to find the fourth since a Recursive formula depends on the prior term.
[tex]\begin{gathered} a_1=8 \\ a_n=3a_{n-1} \\ a_2=3(8)\text{ =24} \\ a_3=3(24)=72 \\ a_4=3(72)\text{ =216} \end{gathered}[/tex]3) Hence, the sequence is 8, 24, 72, 216 and the fourth term is 216
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
Rosa sells cosmetics. She is paid a commission of 3.16% of her first 1500 in sales during the week and 11% on all sales over 1500. What is her commission in a week during which she sells 2137.38 worth of cosmetics? Express your answer as a dollar amount and round to the nearest cent
ANSWER:
$ 117.51
STEP-BY-STEP EXPLANATION:
The commissions are divided into two payments, the first payment of the first $ 1500 with a commission of 3.16% and a second payment with a commission of 11% of all the remaining money of the first $ 1500.
Therefore, we calculate it as follows:
[tex]\begin{gathered} p_T=p_1+p_2 \\ p_1=1500\cdot\frac{3.16}{100}=47.4 \\ p_2=(2137.38-1500)\cdot\frac{11}{100}=637.38\cdot0.11=70.11 \\ p_T=47.4+70.11 \\ p_T=117.51 \end{gathered}[/tex]The total commission is $ 117.51
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]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
Solve x² + 6x + 7 = 0.x = -1 and x = -5 3+ √2-3+√2-3 ± √22
ANSWER
[tex]x=-3\pm\sqrt{2}[/tex]EXPLANATION
We want to solve for x in the equation:
[tex]x^2+6x+7=0[/tex]To do this, apply the quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]where a = 1, b = 6, c = 7
Therefore, substituting the values of a, b, and c into the formula and solve:
[tex]\begin{gathered} x=\frac{-6\pm\sqrt{6^2-4(1)(7)}}{2(1)}=\frac{-6\pm\sqrt{36-28}}{2} \\ \\ x=\frac{-6\pm\sqrt{8}}{2}=\frac{-6\pm2\sqrt{2}}{2} \\ \\ x=-3\pm\sqrt{2} \end{gathered}[/tex]That is the solution for x.
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]miguel saves the same amount of money into a bank account each week. the bank account started with some money in it. after 3 weeks, the bank account contained $250. after 10 weeks the bank account contained $600.write an equation that cqn be used to model tbe number of dollars, y,iguel saves in x weeks.exain what slope and y intercept of youre equation mean in the context of the aituation.enter your equation and your explanations in tbe space provided.
Answer:
An equation that can be used to model the number of dollars, y, Miguel saves in x weeks is;
[tex]y=50x+100[/tex]The slope of the equation in the context is the amount of money Miguel saves in the bank account each week. So, Miguel saves $50 each week.
The y-intercept of the equation in the context is the amount of money Miguel initially have in the bank account. So, the initial amount of money in the bank account is $100.
Explanation:
Given that Miguel saves the same amount of money into a bank account each week.
Let y represent the amount of money in the account after x weeks;
[tex]y=mx+b[/tex]After 3 weeks, the bank account contained $250;
[tex]\begin{gathered} 250=m(3)+b \\ 3m+b=250 \end{gathered}[/tex]After 10 weeks the bank account contained $600;
[tex]\begin{gathered} 600=m(10)+b \\ 10m+b=600 \end{gathered}[/tex]Solving for m and b;
subtract the first equation from the second.
[tex]\begin{gathered} 10m-3m+b-b=600-250 \\ 7m=350 \\ m=\frac{350}{7} \\ m=50 \end{gathered}[/tex]substituting the value of m into the first equation;
[tex]\begin{gathered} 3m+b=250 \\ 3(50)+b=250 \\ 150+b=250 \\ b=250-150 \\ b=100 \end{gathered}[/tex]Therefore, an equation that can be used to model the number of dollars, y, Miguel saves in x weeks is;
[tex]y=50x+100[/tex]From the equation above, the slope m of the equation is;
[tex]m=50[/tex]and the y-intercept b of the equation is;
[tex]b=100[/tex]The slope of the equation in the context is the amount of money Miguel saves in the bank account each week. So, Miguel saves $50 each week.
The y-intercept of the equation in the context is the amount of money Miguel initially have in the bank account. So, the initial amount of money in the bank account is $100.
There are 396 students who are enrolled in an introductory engineering course. If there are four boys to every seven girls, how many boys are in the course?
Solution
For this case we know that the total of students are 396 so we can do this:
x + y = 396
Where:
x= number of girls
y = number of boys
Then we have the following condition:
4x = 7y
Then solving for x we got:
x = 7/4 y
Replacing in the first equation we got:
7/4 y + y = 396
11/4 y= 396
y= 396*4/11 = 144
And x= 7/4 * 144 = 252
Then the answer would be:
252 girls and 144 boys
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
The weekly revenue for a product is given by R(x)=307.8x−0.045x2, and the weekly cost is C(x)=10,000+153.9x−0.09x2+0.00003x3, where x is the number of units produced and sold.(a) How many units will give the maximum profit?(b) What is the maximum possible profit?
Answer:
The number of units that will give the maximum profit is;
[tex]1900\text{ units}[/tex]The maximum possible profit is;
[tex]\text{ \$}239,090[/tex]Explanation:
Given that the weekly revenue for a product is given by ;
[tex]R(x)=307.8x-0.045x^2[/tex]and the weekly cost is ;
[tex]C(x)=10,000+153.9x-0.09x^2+0.00003x^3[/tex]Recall that
Profit = Revenue - Cost
[tex]P(x)=R(x)-C(x)[/tex][tex]\begin{gathered} P(x)=307.8x-0.045x^2-(10,000+153.9x-0.09x^2+0.00003x^3) \\ P(x)=307.8x-0.045x^2-10,000-153.9x+0.09x^2-0.00003x^3 \\ P(x)=153.9x+0.045x^2-0.00003x^3-10,000 \end{gathered}[/tex]Using graph to derive the maximum point on the function;
Therefore, the maximum point is at the point;
[tex](1900,239090)[/tex]So;
The number of units that will give the maximum profit is;
[tex]1900\text{ units}[/tex]The maximum possible profit is;
[tex]\text{ \$}239,090[/tex]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
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.
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.
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-
What is the measure of the "Central Angle" for the 20% section?
The sum of all central angle is 360.
Determine 20% of 360 to obtain central angle for 20% section.
[tex]\begin{gathered} \frac{20}{100}\times360^{\circ}=36^{\circ}\cdot2 \\ =72^{\circ} \end{gathered}[/tex]So answer is 72 degrees.
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: