Answer:
No
Step-by-step explanation:
The constant of proportionality is k = y/x. In this case, k is 5. When you multiply k which is 5 with the x value you should get the y value. You will see that 2 X 5 = 10, 3 X 5 = 15, and 5 X 5 = 25 but 4X 5 is not equal to 24. This means the ordered pair (4, 24) does not lie on the straight line that is formed where all the other ordered pairs (2,10), (3,15), and (5,25) lie.
For a proportional relationship in a table, the k is constant for all the ordered pair x and y values. All the ordered pairs in the table should also lie on the same straight line.
So the answer is no.
1 more NEXT WILL BE ANOTHER 25 POINTS
Answer:
B.
Step-by-step explanation:
if x is 3 then you just substitue every instance of x as 3. 2(x-4) + 3x - x^2 =
2(3 - 4) + 3(3) - 3^2 =
6-8 + 9 - 9 =
-2
Find the slope of the line
Answer:
-3
Step-by-step explanation:
The points (3,-4) and (1,2) lie on the line.
m = (-4-2)/(3-1) = -3
Vanessa has 16 songs on a Classic Rock CD. Six of the songs are by the Beatles, 4 are by the Rolling Stones, 4 are by the Who, and 2 are by the Doors. Vanessa plays the CD. She selects a setting that randomly chooses songs to play.
Find the probability of each event:
a) The first 3 songs played are by the Beatles.
b) The first 2 songs played are by the Rolling Stones and the next 2 songs are by the Beatles.
c) The first 2 songs played are by the Doors, and the next song played is either by the Beatles or the Rolling Stones.
Using it's concept, it is found that the probabilities are given as follows:
a) 0.0527 = 5.27%.
b) 0.0088 = 0.88%.
c) 0.0098 = 0.98%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Item a:
6 out of 16 songs are of the Beatles, hence the probability of a single music being from the Beatles is:
[tex]pB = \frac{6}{16} = \frac{3}{8}[/tex]
Of three musics, the probability is:
[tex]p = \left(\frac{3}{8}\right)^3 = 0.0527[/tex]
Item b:
For the Rolling stones, the probability is:
[tex]pR = \frac{4}{16} = \frac{1}{4}[/tex]
For the four musics, the probability is:
[tex]p = \left(\frac{1}{4}\right)^2 \times \left(\frac{3}{8}\right)^2 = 0.0088[/tex]
Item c:
For the doors, the probability is:
[tex]pD = \frac{2}{16} = \frac{1}{8}[/tex].
For Beatles or Rolling stones, the probability is:
[tex]pBR = \frac{10}{16} = \frac{5}{8}[/tex]
For the three musics, the probability is:
[tex]p = \left(\frac{1}{8}\right)^2 \times \frac{5}{8} = 0.0098[/tex]
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If x is 300 percent of 25 and y is 25 percent more than
40, the x is what percent of y?
al 50%
c) 66.5%
b) 75%
d) 150%
Anyone here to help me!!!
Answer:
d) 150%
Step-by-step explanation:
[tex]x=25*300\%=25*3=75\\[/tex]
[tex]y=25\%*40+40=50[/tex]
[tex]x/y*100\%=75\div50*100\%=150\%[/tex]
Answer:d
150%
Step-by-step explanation:
Please help!!!!!!!! Asap, i need to finish
The solution to the given quadratic expression is x = -1 and x = 5
Factoring quadratic equationGiven the quadratic equation below
f(x) = x^2 - 4x - 5
Factorize
f(x) = x^2 - 5x + x - 5 = 0
f(x) = x(x - 5) + 1(x - 5) = 0
(x+1)(x-5) = 0
x = -1 and x = 5
Hence the solution to the given quadratic expression is x = -1 and x = 5
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Answer:
x = -1; x = 5
Step-by-step explanation:
Standard Form of a Quadratic Function: f(x) = ax² + bx + c, where a ≠ 0
Given function: f(x) = x² - 4x - 5
⇒ a = 1, b = -4, c = -5
We are asked to solve the following function by factoring. In order to do so, let's rewrite the middle term by finding the factors that give a product of the first and last terms (a • c = -5) and give us the sum of the middle term (b = -4).
Factors that give a product of a • c: 1 • -5 = -5
Factors that give a sum of b: 1 + (-5) = -4
Step 1: Substitute f(x) = 0.
⇒ 0 = x² - 4x - 5
Step 2: Rewrite the equation with the factors.
⇒ 0 = x² + x - 5x - 5
Step 3: Factor out x and -5.
⇒ 0 = (x² + x) + (-5x - 5)
⇒ 0 x(x + 1) - 5(x + 1) [ Factor out the common factor. ]
⇒ 0 = (x - 5)(x + 1)
Step 4: Apply the Zero-Product Property (if m•n = 0, then m = 0 or n = 0)
a) 0 = x - 5 ⇒ 0 + 5 = x - 5 + 5 ⇒ 5 = x
b) 0 = x + 1 ⇒ 0 - 1 = x + 1 - 1 ⇒ -1 = x
Therefore, the missing solution for this quadratic function is x = 5.
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the sum invested in CI becomes ₹ 2420 in 2 years and ₹ 2662 in 3 years. Find the sum and rate of interest.
Answer:
equate two simultaneous equations for r and solve
The difference between two positive integers is two if the smaller is added to the square of the larger the sum is 70
Step-by-step explanation:
ATTACHED IS THE SOLUTION.Tell me if you have any questions.URGENT!!! PLEASE HELP!!! Find x and y.
Answer:
x is 48 and y is 100
Step-by-step explanation:
Angle y = 100 degree
Angle x = 48 degree
How to rationalise 1000/3
Answer:
Step-by-step explanation:
there is no root in denominator so I think it is rationalised
Divide.
6√3 cis(7π/6) ÷ 3√5 cis(π/3)
[tex]\dfrac{6\sqrt 3~ \text{cis} \left( \dfrac{7 \pi} 6 \right)}{3 \sqrt 5 ~\text{cis} \left( \dfrac{\pi}{3}\right)}\\\\\\=\dfrac{2\sqrt 3 \cdot e^{i\tfrac{7\pi}{6}}}{\sqrt 5\cdot e^{i \tfrac{\pi}{3}}}\\\\\\=\dfrac{2 \sqrt 3}{\sqrt 5} \cdot \left(e^i \right)^{\tfrac{7\pi}{6} - \tfrac{\pi }{3}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[\text{cis}~ \theta = e^{i \theta}\right]\\\\\\=\dfrac{2 \sqrt{3}}{\sqrt 5} \cdot \left(e^i\right)^{\tfrac{5\pi}6}\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\cdot e^{i\tfrac{5 \pi}6}\\\\\\[/tex]
[tex]=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ \cos \left(\dfrac{5\pi}{6}\right) + i \sin \left(\dfrac{5\pi}{6}\right) \right]~~~~~~~~~~~~~~~~~~;\left[e^{i\theta} = \cos \theta + i \sin \theta} \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\left[ \cos \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) + i\sin \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ -\cos \left(\dfrac{\pi}{6}\right) + i \sin \left(\dfrac{\pi}{6}\right) \right]\\\\\\[/tex]
[tex]=\dfrac{2\sqrt{3}}{\sqrt 5}\left( -\dfrac {\sqrt{3}}{2} + i \cdot \dfrac 12 \right)\\\\\\=-\dfrac{3}{\sqrt 5} + i \dfrac{\sqrt 3}{\sqrt 5}[/tex]
Answer:
Step-by-step explanation:
Just took the test:
6sqrt3 cis (7pie/6)/ 3sqrt5 cis (pie/3)=
2sqrt15/5 cis (5pie/6)
I am greater than 62 but less than 67
What is the area of a regular octagon
having an apothem of 6 meters and a
side length of 7 meters?
The area of the octagon having an apothem of 6 meters and a side length of 7 meters is 168 meter square
How to the area of an octagonUsing the formula:
Area of an octagon = perimeter * apothem / 2
Note that perimeter of an octagon = 8 a
where a is the length of it's side
Perimeter = 8 * 7
Perimeter = 56 meters
Apothem = 6 meters
Substitute into the formula
Area = 56 * 6/ 2
Area = 336 / 2
Area = 168 meter square
Thus, the area of the octagon is 168 meter square
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Find the slope of every line that is parallel to the line on the graph.
Answer:
-1/5
Step-by-step explanation:
What are parallel lines?
Lines that are parallel never touch. They can extend infinitely and they will still never touch. In order for this to happen the slope of the two lines must be the same. So if we want to find the slope of every line that is parallel to the line on the graph, we simply find the slope of the line of the graph.
Finding the slope
We can find the slope using the following formula:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where the x and y values are derived from any given points on the line (x1,y1) and (x2,y2)
Here the given points are (-5,-1) and (0,-2)
So we have (x1,y1) = (-5,-1) meaning x1 = -5 and y1 = -1
We also have (x2,y2) = (0,-2) meaning x2 = 0 and y2 = -2
Now we plug these values into the formula
Recall formula : [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
==> Plug in x1 = -5 , y1 = -1 , x2 = 0 and y2 = -2
[tex]Slope=\frac{-2-(-1)}{0-5}[/tex]
==> simplify numerator and denominator
[tex]slope = \frac{1}{-5}[/tex]
So the slope of the line is -1/5
This means the slope of any parallel line to that line would also have a slope of -1/5
x^{2} +5x+6
[tex]x^{2} +5x+6[/tex]
Answer: No answer
Step-by-step explanation:
You can calculate for x, because the equation isn't equal to anything.
The total marks obtained in a mathematics test was 384 if the mean was 24 how many children took the test
The lowest point in the United States is the Death Valley in California. Its altitude is 282 feet below sea level. Identify the integer representing the lowest point (Death Valley).
Answer:
-282
Step-by-step explanation:
Any altitude below sea level would have a negative sign in front of it.
A negative number raised to an odd power is_____ negative.
always
never
sometimes
negative number taken to an odd power gives a negative result (because, after cancelling, there will be one minus sign left over).
the answer is always. negative numbers raised to odd powers remain negative. negative numbers raised to even powers become positive.
16-2t=3/2t+9 solve for t
answer: t=2
steps:
16-2t = 3/2t+9
7 = 3/2t + 2t
2 is 4/2
7 = 3/2t + 4/2t
7 = 7/2t
7/2t = 7
(2/7)7/2t=7(2/7)
t=7(2/7)
t=2
URGENT PLEASE HELP
If a+b= -5, find |a+b|+5 / |-a-b|
Answer:
2
Step-by-step explanation:
[tex]a+b=-5[/tex]
[tex]-(a+b)=-a-b=5[/tex]
[tex]\frac{|-5| + 5}{|5|}[/tex]
[tex]\frac{5+5}{5}[/tex]
[tex]2[/tex]
Answer:
2
Step-by-step explanation:
Given:
a + b = -5To find -a - b
Factor out the common term -1:
⇒ -a - b = -(a + b)
Substitute a + b = -5:
⇒ -a - b = -(-5)
Apply rule -(-x) = x:
⇒ -a - b = 5
Therefore:
[tex]\begin{aligned}\implies \sf \dfrac{|a+b|+5}{|-a-b|} & = \sf \dfrac{|-5|+5}{|5|}\\\\& = \sf \dfrac{5+5}{5}\\\\& = \sf \dfrac{10}{5}\\\\& = \sf 2\end{aligned}[/tex]
Note: |-x| = x
2. If D is the midpoint of segment AB, explain using transformations why AC = BC. Use complete sentences. (10 points)
AC is equal to BC by the corresponding side of a congruent triangle.
What is a line segment?
A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
The midpoint of a line segment means a point that lies in the mid of the given line segment.
If D is the midpoint of segment AB, then AD = BD.
So in a triangle ACD and BCD
AD = BD (by midpoint D)
angle ADC = angle BDC = 90
CD = CD (common)
Therefore, triangle ACD and BCD are congruent.
Hence, AC = BC by the corresponding side of a congruent triangle.
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For a 70-year-old investor, selling a weak stock at a loss may be (5 points)
O
a smart move to avoid potential additional future losses
® a poor decision, as the stock will most likely come back
an opportunity to buy as many as possible of the same stock
a red flag for the government to penalize that company
When you acquire stock in a firm, you are acquiring a little portion of that company known as a share. The correct option is A.
What are stocks?When you acquire stock in a firm, you are acquiring a little portion of that company known as a share. Investors buy stocks in firms they believe will increase in value. If this occurs, the value of the company's shares rises as well.
For a 70-year-old investor, selling a weak stock at a loss may be a smart move to avoid potential additional future losses.
Hence, the correct option is A.
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You have two exponential functions. One function has the formula g(x) = 5x. The other function has the formula h(x) = 5-x. Which option below gives formula for k(x) = (g - h)(x)? k( x) = 10 x k( x) = 5 x - 5 -x k( x) = 2(5 x) k( x) = 5 x + 5 -x
The correct option is k(x) = 5x - (5-x)
What is Function?The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, the given functions are;
g(x) = 5x h(x) = 5 - x
Now,
k(x) = (g - h)(x)
k(x) = g(x) - h(x)
k(x) = 5x - (5 - x)
Thus, the correct option is k(x) = 5x - (5-x).
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The coordinate grid shows points A through K. Which points are solutions to the
system of inequalities listed below? (2 points)
2x + y < 10
2x - 4y > 8
EFGHJ
EFG
ACDM
AEF
Answer:
E is the solution of the inequality Coordinates of points A = (-5,4)B = (4,7)C= (-2,7)D= (-7,1)E= (4, -2)F = (1 , -6)G= (-3, -10)H= (-4 , -4)I= (9, 3)J= (7 , -4)K= (2 ,3)putting the values of coordinates in equation to check for the solution.
For A
2x + y < 10
2(-5) + 4 < 10.
-10 - 4 < 10
-14 < 10 ( true)
2x - 4y > 8
2(-5) - 4(4) > 8
-10 - 16 > 8
-26 > 8
false..
it is not the solution of the equation.
similarly we can find for other coordinates.
E is the solution
Which graph represents the following system of inequalities? x < - 2x + 4; y < x + 3; x < 3
Graph C represents the following system of inequalities. For clarification refer to the attachment.
What is the definition of inequality?Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.
Given relations;
x < - 2x + 4
y < x + 3
x < 3
Hence graph C represents the following system of inequalities.
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Which of the following segments is tangent to the circle? 1 overline HI 2 ) overline DE 3) overline FG 4 ) overline AC
Answer:
DE
Step-by-step explanation:
a tangent is a straight line that only touches the circle at one point.
1. Solve.
2
The sides of a rectangle are represented by 4a-1 and 3a + 2. Find the expression for its perimeter.
Answer:
14a+2
Step-by-step explanation:
Perimeter of a rectangle: P=2(l+w) where l=length and w=width.
So P=2[(4a-1)+(3a+2)]=2(4a-1+3a+2)=2(4a+3a-1+2)=2(7a+1)=14a+2.
The expression to find the perimeter of the rectangle is 14a + 2.
What is Perimeter?Perimeter of a straight sided figures or objects is the total length of it's boundary.
Given that,
Sides of a rectangle is represented as 4a - 1 and 3a + 2.
Perimeter of a rectangle is represented as,
Perimeter = 2 (l + w)
Here l is the length and w is the width.
Substituting,
Perimeter = 2 (4a - 1 + 3a + 2)
= 2(7a + 1)
= 14a + 2
Hence the expression to find the perimeter is 14a + 2.
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20 poinnttsss !! help please
Janie writes a polynomial expression using only one variable, x, with degree 3. Max writes a polynomial expression using only one variable, x, with degree 7.
What can you determine about the degree of the sum of Janie’s and Max’s polynomials?
What can you determine about the degree of the difference of Janie’s and Max’s polynomials?
Answer:
The sum of the polynomials is a 7th degree polynomial.
The difference of the polynomials is a 7th degree polynomial.
Step-by-step explanation:
Janie's polynomial is a 3rd degree with only x terms. Maybe she wrote:
f(x) = x^3
or maybe she was fancy and wrote:
f(x) =
x^3 + 2x^2 - 7x + 4
could be anything really, but the biggest exponent is 3.
Then Max does like:
g(x) = x^7
or
g(x) = x^7-x^4-3x+2
Whatever he made up, but the biggest exponent is 7.
So if they add or subtract their two polynomials, there's no x^7 in Janie's to add with the x^7 in Max's. MAYBE Max put some x^3 or x^2 or x or constants that might combine with the terms in Janie's.
Either way, anything that Max put in his polynomial that is a bigger power than 3 (4th, 5th, 6th, or 7th power) is just going to end up in the sum or difference.
A grocery store had 38 employees but then they hired 4 more people. What is the percent change in their staff?
Answer:
+ 10.53 % change
Step-by-step explanation:
Percent change is 4 more people added to 38
4 / 38 * 100% = 10.53 %
Suppose a deposit of $ 2 , 000 in a savings account that paid an annual interest rate r (compounded yearly) is worth $ 2 , 209 after 2 years. using the formula a = p ( 1 + r ) t , we have 2 , 209 = 2 , 000 ( 1 + r ) 2 solve for r to find the annual interest rate (to the nearest tenth).
Answer:
5.1% (nearest tenth)
Step-by-step explanation:
Annual Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)t = time (in years)Given:
A = $2,209P = $2,000t = 2 yearsSubstitute the given values into the formula and solve for r:
[tex]\implies \sf 2209=2000\left(1+r\right)^{2}[/tex]
[tex]\implies \sf \dfrac{2209}{2000}=(1+r)^2[/tex]
[tex]\implies \sf 1.1045=(1+r)^2[/tex]
[tex]\implies \sf \sqrt{1.1045}=1+r[/tex]
[tex]\implies \sf r = \sqrt{1.1045}-1[/tex]
[tex]\implies \sf r = 0.05095194942...[/tex]
[tex]\implies \sf r = 5.095194942...\%[/tex]
Therefore, the annual interest rate is 5.1% (nearest tenth)
Ann reads 15 pages in 30 minutes. how many pages she can read in 2 hours
Answer:
60
Step-by-step explanation:
2hrs = 120
120/30= 4
4×15=60
Answer:
60 pages :)
Step-by-step explanation:
First we turn the hours into minutes to make it easier :)
1 hr = 60 minutes
2 hrs = 120 minutes
Now that we have done that, we divide :)
120/30 =4
And now we multiply 1 more time :)
4 x 15 = 60
Have an amazing day!!
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