Answer:
Step-by-step explanation:
let the plane intersects the join of points in the ratio k:1
let (x,y,z) be the point of intersection.
[tex]x=\frac{3k+2}{k+1} \\y=\frac{5k+4}{k+1} \\z=\frac{-4k+16}{k+1} \\\because ~(x,y,z)~lies~on~the~plane.\\2(\frac{3k+2}{k+1} )-3(\frac{5k+4}{k+1} )+\frac{-4k+16}{k+1} +6=0\\multiply~by~k+1\\2(3k+2)-3(5k+4)+(-4k+16)+6(k+1)=0\\6k+4-15k-12-4k+16+6k+6=0\\-7k+14=0\\k=2\\x=\frac{3*2+2}{2+1} =\frac{8}{3} \\y=\frac{5*2+4}{2+1}= \frac{14}{3} \\z=\frac{-4*2+16}{2+1} =\frac{8}{3}[/tex]
point of intersection is (8/3,14/3,8/3)
and ratio of division is 2:1
The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options. $8 $9 $11 $13 $14
Answer:
The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options.
$8 . YES
$9 . HELL NO
$11 . DEFINITLY NOT
$13 . GET OUTTA HERE
$14 . MMM YES
Step-by-step explanation:
Answer:
A and E or 8, 14
Step-by-step explanation:
Determine what type of model best fits the given situation: An Internet phone company presently provides service to 5,000 customers at a monthly rate of $20 per month. After a market survey, it was determined that for each $1 decrease in the monthly rate an increase of 500 new customers would result. A. linear B. quadratic C. none of these D. exponential
Answer:
The best fit is A. Linear model
Step-by-step explanation:
Given:
Monthly Rate = $20, Number of customers = 5000
If there is a decrease of $1 in the monthly rate, the number of customers increase by 500.
To find:
The type of model that best fits the given situation?
Solution:
Monthly Rate = $20, Number of customers = 5000
Let us decrease the monthly rate by $1.
Monthly Rate = $20 - $1 = $19, Number of customers = 5000 + 500 = 5500
Let us decrease the monthly rate by $1 more.
Monthly Rate = $19 - $1 = $18, Number of customers = 5500 + 500 = 6000
Here, we can see that there is a linear change in the number of customers whenever there is decrease in the monthly rate.
We have 2 pair of values here,
x = 20, y = 5000
x = 19, y = 5500
Let us write the equation in slope intercept form:
[tex]y =mx+c[/tex]
Slope of a function:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{5500-5000}{19-20}\\\Rightarrow -500[/tex]
So, the equation is:
[tex]y =-500x+c[/tex]
Putting x = 20, y = 5000:
[tex]5000 =-500\times 20+c\\\Rightarrow c = 5000 +10000 = 15000[/tex]
[tex]\Rightarrow \bold{y =-500x+15000}[/tex]
Let us check whether (18, 6000) satisfies it.
Putting x = 18:
[tex]-500 \times 18 +15000 = -9000+15000 = 6000[/tex] so, it is true.
So, the answer is:
The best fit is A. Linear model
On a separate piece of graph paper, graph y = |x - 3|; then click on the graph until the correct one appears.
ps : there's another picture it just didn't let me edit it its the opposite side of the shape facing up the graph.
Answer: Graph is shown in the attached image below
This is a V shaped graph with the vertex at (3,0). The V opens upward
Explanation:
The equation y = |x-3| is the result of shifting the parent function y = |x| three units to the right. The vertex moves from (0,0) to (3,0). The "x-3" portion moves the xy axis three units to the left. If we held the V shape in place while the xy axis moved like this, then it gives the illusion the V shape moved 3 spots to the right.
Side note: the equation y = |x-3| is composed of two linear functions y = x-3 and y = -x+3. The value of x will determine which gets graphed. When x < 3, then we'll graph y = -x+3; otherwise we graph y = x-3. This is known as a piecewise function.
A triangle has a base 12 inches and the height of 5 inches if 6 of these triangles are put together to form a hexagon what would be the area of the hexagon?
Use the distributive property to remove the parentheses -5(2x-3w-6)
Answer:
15w - 10x + 30.
Step-by-step explanation:
-5(2x - 3w - 6)
= (-5 * 2x) + (-5 * -3w) + (-5 * -6)
= -10x + 15w + 30
= 15w - 10x + 30.
Hope this helps!
Answer:
[tex] - 10x + 15w + 30[/tex]Step-by-step explanation:
[tex] - 5(2x - 3w - 6)[/tex]
Multiply each term in the parentheses by -5
[tex] - 5 \times 2x - 5 \times ( - 3w) - 5 \times ( - 6)[/tex]
Calculate the product
[tex] - 10x - 5 \times ( - 3x) - 5 \times ( - 6)[/tex]
Multiplying two negatives equals a positive [tex]( - ) \times ( - ) = ( + )[/tex]
[tex] - 10x + 5 \times 3w - 5 \times ( - 6)[/tex]
Calculate the product
[tex] - 10x + 15w - 5 \times ( - 6)[/tex]
Multiply the numbers
[tex] - 10x + 15w + 30[/tex]
Hope this helps..
Best regards!!
Tasha wants to find out if she is going to pass her test. She decides that she will
simulate her test by flipping a coin. This means
a) There is a 50-50 chance she will pass her test.
b) All of the questions are multiple choice.
c) She hasn't studied.
d) There is a 20% chance she will pass.
Answer:
A
Step-by-step explanation:
Since a coin only has two sides, the test must be referring to the fact that she has a 50, 50 shot at passing.
What can each term of the equation be multiplied by to eliminate the fractions before solving? x – + 2x = StartFraction one-half EndFraction x minus StartFraction 5 Over 4 EndFraction plus 2 x equals StartFraction 5 Over 6 EndFraction plus x. + x 2 6 10 12
Answer: while solving an equation involving fractions we eliminate the fraction by multiplying the LCD of all the denominators present in the equation . LCD means Least common Denominator so for this question when we try to eliminate the denominator we first try to find the LCM (2,4,6) because that will give us the LCD.
2=2
4=2·2
6=2·3
LCM = 2·2·3
LCM = 12
It means we need to multiply the 12 to each term of equation to eliminate the fractions before solving.
12
To eliminate the fractions, multiply the equation by the 12
Equation
A equation is an expression that shows the relationship between two or more variables and numbers.
Given the equation:
[tex]x-\frac{5}{4}+2x=\frac{5}{6}+x[/tex]
To eliminate the fractions, multiply by the L.C.M of the denominator of the fraction i.e. 12 to get:
12x - 15 + 24x = 10 + 12x
Find out more on Equation at: https://brainly.com/question/2972832
simplify. Remove all perfect squares from inside the square root. V180=
Answer:
6√5
Step-by-step explanation:
We have to solve the expression [tex]\sqrt{180}[/tex]
Break 180 into its factors which are in the perfect square form.
Since, 180 = 9 × 4 × 5
= 3² × 2² × 5
Therefore, [tex]\sqrt{180}=\sqrt{3^{2}\times 2^{2}\times 5}[/tex]
= [tex]\sqrt{3^2}\times \sqrt{2^{2}}\times \sqrt{5}[/tex] [Since [tex]\sqrt{ab}=\sqrt{a}\times \sqrt{b}[/tex]]
= 3 × 2 × √5
= 6√5
Therefore, solution of the given square root will be 6√5.
A 6 inch-y’all plant grew 3/4 of an inch one week and twice as much the following week. How tall is the plant now?
Answer:
8 inches
Step-by-step explanation:
3/4+(3/4*2)=3/4+6/4=9/4=2 1/4
2 1/4+6=8 1/4=8.25
Answer: 8.25 inches
Step-by-step explanation:
11.1/0.01= what is the answer
Answer:
1,110
Step-by-step explanation:
calculator
1
If the 2nd and 5th terms of a G.P are 6 and 48 respectively, find the sum of the first for term
If the first term is [tex]a[/tex], then the second term is [tex]ar[/tex], the third is [tex]ar^2[/tex], the fourth is [tex]ar^3[/tex], and the fifth is [tex]ar^4[/tex].
We're given
[tex]\begin{cases}ar=6\\ar^4=48\end{cases}\implies\dfrac{ar^4}{ar}=r^3=8\implies r=2\implies a=3[/tex]
So the first five terms in the GP are
3, 6, 12, 24, 48
Adding up the first four gives a sum of 45.
If you were asked to find the sum of many, many more terms, having a formula for the n-th partial sum would convenient. Let [tex]S_n[/tex] denote the sum of the first n terms in the GP:
[tex]S_n=3+3\cdot2+3\cdot2^2+\cdots+3\cdot2^{n-2}+3\cdot2^{n-1}[/tex]
Multiply both sides by 2:
[tex]2S_n=3\cdot2+3\cdot2^2+3\cdot2^3+\cdots+3\cdot2^{n-1}+3\cdot2^n[/tex]
Subtract this from [tex]S_n[/tex], which eliminates all the middle terms:
[tex]S_n-2S_n=3-3\cdot2^n\implies -S_n=3(1-2^n)\implies S_n=3(2^n-1)[/tex]
Then the sum of the first four terms is again [tex]S_4=3(2^4-1)=45[/tex].
For a chemical reaction to occur, at least one-third of the solution must be an acid. If there are five liters of acid, in interval form, how much solution is present?
A. [5,8)
B. (3/5,5]
C. (5/3,5]
D. [5,15]
Answer:
Amount of solution = 15 liter
Step-by-step explanation:
Given:
One third of solution is acid
Amount of acid = 5 Liter
Find:
Amount of solution
Computation:
Amount of solution = Amount of acid (1 / One third of solution is acid)
Amount of solution = Amount of acid (3)
Amount of solution = (5)(3)
Amount of solution = 15 liter
Suppose you place $10,000 in a retirement fund that earns a nominal interest rate of 8 percent. If you expect inflation rate to be 5 percent or lower, then calculate the real interest rate you are expecting to earn.
Answer:
Real interest rate= 3%
Step-by-step explanation:
Giving the following information:
Suppose you place $10,000 in a retirement fund that earns a nominal interest rate of 8 percent. The inflation rate is 5 percent.
The effect of the inflation rate on the interest rate is counterproductive. The inflation rate diminishes purchasing power.
Real interest rate= nominal interest rate - inflation rate
Real interest rate= 0.08 - 0.05= 0.03
Which situation can be represented by 80x > 150 + 50x?
Answer:
All numbers greater than 5, i.e., [tex]x>5[/tex] .
Step-by-step explanation:
The given inequality is
[tex]80x>150+50x[/tex]
Isolate variable terms on one side to find the solution.
Subtract 50x from both sides.
[tex]80x-50x>150+50x-50x[/tex]
[tex]30x>150[/tex]
Divide both sides by 30.
[tex]\dfrac{30x}{30}>\dfrac{150}{30}[/tex]
[tex]x>5[/tex]
It means, all the numbers which are greater than 5, are the solutions of the given inequality and 5 is not included in the solution set.
Given the coordinates for the function below, which of the following are
coordinates for its inverse?
Gallons Cost, in
of Gas Dollars
1
2
5
15
20
1.25
2.50
6.25
18.75
25.00
The coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
How to determine the inverse coordinates?The table of values is given as:
Gallons Cost
1 1.25
2 2.50
5 6.25
15 18.75
20 25.00
The inverse of the above table would have the following header
Cost Gallons
When the inverse table is populated, we have:
Cost Gallons
1.25 1
2.50 2
6.25 5
18.75 15
25.00 20
The coordinates are: (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
Hence, the coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
Read more about coordinates at:
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sin theta = x , sec theta =y . find cot theta pls answer fast i need to verify my answer . you can directly write the answer no issues
Answer:
[tex]\huge\boxed{\cot\theta=\dfrac{1}{xy}}[/tex]
Step-by-step explanation:
[tex]\bold{METHOD\ 1}[/tex]
[tex]\sin\theta=x\\\\\sec\theta=y\\\\\cot\theta=?\\\\\text{We know:}\\\\\sec x=\dfrac{1}{\cos x};\ \cot x=\dfrac{\cos x}{\sin x}\\\\\sec\theta=y\to\dfrac{1}{\cos \theta}=y\to\dfrac{\cos\theta}{1}=\dfrac{1}{y}\to\cos\theta=\dfrac{1}{y}\\\\\cot \theta=\dfrac{\frac{1}{y}}{x}=\dfrac{1}{xy}[/tex]
[tex]\bold{METHOD\ 2}[/tex]
[tex]\text{We know}\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\cot x=\dfrac{\cos x}{\sin x}=\dfrac{1}{\tan x}\\\\\sec x=\dfrac{1}{\cos x}\\\\\text{therefore}\\\\(sin x)(\sec x)=(\sin x)\left(\dfrac{1}{\cos x}\right)=\dfrac{\sin x}{\cos x}=\tan x\\\\\dfrac{1}{(\sin x)(\sec x)}=\dfrac{1}{\tan x}=\cot x[/tex]
[tex]\\\sin \theta=x;\ \sec\theta=y\\\\\text{substitute}\\\\\cot\theta=\dfrac{1}{xy}[/tex]
An exterior angle of a triangle is equal to the sum of________ opposite angle
Answer:
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
Answer:
Two remote interior angles.
What number :Increased by 130% is 69 i rlly need help!!!
Answer:
53.076923
Step-by-step explanation:
130% as a decimal is 1.3
Divide 69 by 1.3:
69 /1.3 = 53.076923
Answer:
30
Step-by-step explanation:
The unknown number is x.
Start with x.
To increase x by 130%, you need to add 130%of x to x.
x + 130% of x
The sum equals 69.
x + 130% of x = 69
x + 130% * x = 69
1x + 1.3x = 69
2.3x = 69
x = 30
Answer: The number is 30.
Last season, a softball team played 18 games. The team won 15 of these games. What is the ratio of the softball team's wins to its total number of games played ?
Answer:
5:6Step-by-step explanation:
Given the total number of games played by the softball team = 18 games
Total games won = 15 games
Ratio of the softball team's wins to its total number of games played can be gotten by simply dividing the total games won by the total games played
Ratio = [tex]\frac{total \ teams's win}{total\ number\ of \ games\ played}[/tex]
[tex]Ratio = \frac{15}{18}[/tex]
Expressing the ratio in its lowest term
[tex]Ratio = \frac{3*5}{3*6} \\\\Ratio = \frac{5}{6}[/tex]
Hence, the ratio of the softball team's wins to its total number of games played is 5:6
Select the statements that are true for the graph of y=−(x−0.5)^2 +9 . Choose all correct statements. The vertex is (−0.5,9) . The graph has a maximum. The graph has a minimum. The vertex is (0.5,9) .
Answer:
The second and fourth statements are correct.
Step-by-step explanation:
We are given the function for the graph of:
[tex]y=-(x-0.5)^2+9[/tex]
Note that this is a quadratic function in its vertex form, given by:
[tex]y=a(x-h)^2+k[/tex]
Where a is the leading coefficient and (h, k) is the vertex.
Rewriting our given equation yields:
[tex]\displaystyle y = (-1)(x-(0.5))^2 + (9)[/tex]
Therefore, a = -1, h = 0.5, and k = 9.
Therefore, the vertex of the graph is at (0.5 ,9).
Because the leading coefficient is negative, the parabola opens downwards.
Therefore, the parabola has a maximum value.
In conclusion, the second and fourth statements are correct.
1. the vertex is (0.5, 9)
2. it has a maximum.
John wants to nail a thumbtack on his circular board, pictured below. If the thumbtack is equally likely to be placed anywhere on the board, what is the probability that the thumbtack will be placed on the inner circle? Use 3.14 for , and round your answer to the nearest whole percent. A. 51% B. 55% C. 57% D. 60%
Answer:
[tex]Probability = 51\%[/tex]
Step-by-step explanation:
Given
Radius of inner circle = 5ft
Radius of outer circle = 7ft
Required
Determine the probability that the thumbtack will be placed on the inner circle
We start by calculating the area of both circles;
Inner Circle
[tex]Area = \pi r^2[/tex]
[tex]Area = 3.14 * 5^2[/tex]
[tex]Area = 3.14 * 25[/tex]
[tex]Area = 78.5[/tex]
Outer Circle
[tex]Area = \pi R^2[/tex]
[tex]Area = 3.14 * 7^2[/tex]
[tex]Area = 3.14 * 49[/tex]
[tex]Area = 153.86[/tex]
At this point, the probability can be calculated;
The probability = Area of Inner Circle / Area of Outer Circle
[tex]Probability = \frac{78.5}{153.86}[/tex]
[tex]Probability = 0.51020408163[/tex]
Convert to percentage
[tex]Probability = 0.51020408163 * 100\%[/tex]
[tex]Probability = 51.020408163\%[/tex]
Approximate
[tex]Probability = 51\%[/tex]
There are 39 chocolates in a box, all identically shaped. There 16 are filled with nuts, 13 with caramel, and 10 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting a nut chocolate followed by a caramel chocolate.
Answer:
16/117Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome of event/total outcome of event
Given the total amount of chocolate in a box = 39chocolates
Amount of nuts = 16
Mount of caramel = 13
Amount of solid chocolate = 10
If he randomly selects a nut chocolate and eat, the probability of selecting a nut chocolate = Amount of nuts/total chocolate in the box = 16/39
IF he selects a seconnd piece (caramel chocolate) and eat, the probability of selecting a caramel chocolate = Amount of caramel/total chocolate in the box = 13/39 = 1/3
The probability of selecting a nut chocolate followed by a caramel chocolate will be 16/39*1/3 = 16/117
There were some pieces of candy in a bowl. Shirley took half of them. Then Rose took half of the pieces left in the bowl. After that, Susan took half of the remaining pieces of candy. In the end there were 8 pieces of candy left in the bowl. How many candies were there in the bowl at the beginning?
Answer:
Number of pieces of candy in the bowl=64
Step-by-step explanation:
Let
x=number of pieces of candy in a bowl
Shirley took=1/2 of x
=1/2x
Remaining
x-1/2x
= 2x-x/2
=1/2x
Rose took half of the pieces left in the bowl=1/2 of 1/2x
=1/2*1/2x
=1/4x
Remaining
1/2x-1/4x
=2x-x/4
=1/4x
Susan took 1/2 of the remaining pieces of candy=1/2 of 1/4x
=1/2*1/4x
=1/8x
Remaining 8
1/8x=8
x=8÷1/8
=8*8/1
=64
x=64
41. In the diagram, a l b. Find the value of x. 55° (x+ 70)
Answer:
55°
Step-by-step explanation:
The corresponding image, which I will attach, is missing in order to solve the exercise.
We know that the flat angle is 180 °, which we know to be the one that is formed with the horizontal, therefore the following equation remains:
55 ° + (70 ° + x °) = 180 °
we solve x °
x ° = 180 ° - 55 ° - 70 °
x ° = 55 °
So the value of x is 55 °
A number is 30% of 20% of the number x.
Answer:
6/100x
Step-by-step explanation:
Answer:6/100x
Step-by-step explanation:
please help :) What is 7.7 x 10 to the 8 power written in standard form? A. 770,000,000 B. 77,000,000,000 C. 77,000,000 D. 7,700,000,000
Answer:
A. 770,000,000
Step-by-step explanation:
7.7x10^8 First step is to simplify
7.7x100,000,000 Then, multiply
770,000,000
Hope this helps, if it does, please consider giving me brainliest, it will help me a lot. If you still have any questions, feel free to ask.
Have a good day! :)
Aster corporation accepted a $20,000, 9 percent 120-day note dated august 25 from lee company in settlement of a past bill. On October 25, Aster Corporation decided to discount the note at a discount of 8 percent. The proceeds to Aster Corporation are (blank)
Answer:
$20, 533.33
Step-by-step explanation:
From the question, we are given the following values
Principal = $20000
Rate = 8% = 0.08
Time( in years) = 120days = 4 months = 4/12 years = 1/3 years
Interest = Principal × Rate × Time
Interest = 20,000 × 0.08× (1/4)
Interest = $533.33
Hence, the proceeds to Aster Corporation are
$20000 + $533.33
= $20,533.33
Which of the following is not a congruence theorem or postulate A. SSA B. SAS C. AAS D. SSS
Answer:ITS A
Step-by-step explanation:
SAS: side angle side
SSA: is not a congruence theorem
AAS:angle angle side
SSS:side side side
Answer:
The answer is A.
Step-by-step explanation:
Just took the test
Someone pls help if you want more points just go to my other questions and answer them pls
Answer:
I would say the answer is C.
The graph of y = h(x) is a line segment joining the points (1, -5) and (9,1).
Drag the endpoints of the segment below to graph y = h-'(x).
Answer:
Ok, i cant drag the endpoints of the segment, but i can tell you how to do it.
First, we know that h(x) joins the points (1, -5) and (9, 1), then h(x) is a line:
h(x) = s*x + b
First, for a line that goes through the points (x1, y1) and (x2, y2), the slope will be:
s = (y2 -y1)/(x2 - x1)
Then in this case, the slope is:
s = (1 - (-5))/(9 - 1) = 0.75
Then we have
h(x) = 0.75*x + b
now, the value of b can be found as:
h(1) = -5 = 0.75*1 - b
b = - 5 - 0.75 = -5.75.
Then our equation is:
h(x) = 0.75*x - 5.75
Now, i gues you want to find the graph of:
y = h(-x)
Then our new function is:
g(x) = h(-x) = -0.75*x - 5.75.
Now to find the points, we evaluate this function in the same values of x as before.
g(1) = -0.75*1 - 5,75 = -6,5
the point is (1, -6.5)
the second point is when x = 9.
g(9) = -0.75*9 - 5.75 = -12.5
The second point is (9, -12.5)
Answer:
(−6,7) (-1,-2)
Step-by-step explanation:
Khan