Answer:
Step-by-step explanation:
convert y=-2x into standard form
a automobile race contains 15 racecars. in how many ways can the racecars finish in first, second, and third place?
There are 2730 ways in which 15 race cars can finish in first, second, and third place.
Let's examine this logically now. Any one of the 15 runners can cross the finish line in first place. You can still have any one of the 14 race cars who are still running finish in second place. Any one of the 13 race cars who haven't crossed the finish line yet can take third place.
As a result, multiplying all the possibilities will give us the number of ways ;
Number of ways =15*14*13
=2730
So, the total number of ways in which the race cars finish in first, second, and third place is 2730.
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The equation x^2-6x=72 ha a olution between 4 and 5
Ue a trial and improvement method to find thi olution
Give your anwer correct to 1 decimal place
The solution of the quadratic equation [tex]x^2 - 6x = 72[/tex] is
x = 12 or x = -6
What is a quadratic equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
The given quadratic equation is
[tex]x^2 - 6x = 72[/tex]
Now,
[tex]x^2 - 6x = 72\\x^2 - 6x - 72 = 0\\x^2 - 12x + 6x -72 = 0\\x(x -12)+6(x -12)=0\\(x-12)(x+6)=0\\x-12=0 \ or \ x+6 = 0\\x = 12 \ or \ x = -6[/tex]
The solution of the quadratic equation [tex]x^2 - 6x = 72[/tex] is
x = 12 or x = -6
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In the video about the construction of the insect phylogeny, the researchers faced the problem that there was not enough computational power in all of the world to construct every possible tree. What was the researchers’ solution?.
In the video about the construction of the insect phylogeny, the researchers faced the problem that there was not enough computational power in all of the world to construct every possible tree.
The use of computing algorithms, tools, and programmes to phylogenetic analysis is known as computational phylogenetics. The purpose is to create a phylogenetic tree that represents a hypothesis about a set of genes, species, or other taxa's evolutionary ancestry.
There was not enough computational power to construct every possible tree in all of the world. So the probable solution for this problem will be:
Use math to avoid constructing improbable trees
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factorise y^2 + 27y.
Answer:
y(y+27)
Step-by-step explanation:
as per it is y2 it is two times counted so
y(y+27)
5(6x+2),x=8 what is the answer
Answer:250
Step-by-step explanation:5((6(8))+2)=250 using pemdas start with parenthesis so 6*8=48 this puts the equation at 5(48+2) then do the parenthesis again so 48+2=50 this puts the equation at 5*50 then do your last step which will give you your answer of 250
The points (0, –10) and (15, 6) fall on a particular line. What is its equation in slope-intercept form?
Answer:
slope: (6+10)/(15-0)
M: 16/15
B = -10
y = 16/15x -10
A 9-inch candle burns down in 12 hours. At what rate does the candle burn, in inches per hour?
Answer:
0.75
Step-by-step explanation:
because 9/12 is 0.75
Let's establish what this rate indicates through an equation:
inches burned
hour
Now, plug in the information you have:
inches burned = 9
hour 12
9/12 = 0.75
0.75 inches of the candle is burned per hour
find 3x+4y when x is 6 and y is -3
Answer:
Step-by-step explanation:
3x + 4y when x = 6 and y = -3
Put in values of x and y:
3(6) + 4(-3) = 18 + (-12) = 6
For what value of x is line m parallel to line n?
Answer:
x = 42
Step-by-step explanation:
You want to know the value of x that makes alternate interior angles 105° and (3x-21)° congruent.
Congruent anglesWhen alternate interior angles are congruent, the lines forming them are parallel. Congruent angles have the same measure, so we want ...
3x -21 = 105
3x = 126 . . . . . . add 21
x = 42 . . . . . . . divide by 3
The value of x is 42 when the lines are parallel.
y - 3x = 7 What is the y-intercept of the equation above?
a.7
b.9
c.-7
d.-7/3
Answer:
A: 7
Since the slope is 3 and passes down (1, 10), the answer will be 7
re Stock Market Alexander is a stockbroker. He earns 14% commission each week. Last week. he sold $5.300 worth of Locks. How much did he make last week in commission? If he averages that me amount each week, how much did he make in commission in 2011?
Help meee
Alexander made $742 last week in commission. He made $40068 in commission in 2011.
Sold = $5300
Commission percent = 14%
Commission = 14% of 5300
= (14/100)*5300
= 14*53
= 742
No. of weeks in 2011 = 54
Commission = 54 * 742
= 40068
Hence, he makes $742 in weeks and $40068 in year 2011.
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Determine which postulate can be used to prove that the triangles are congruent.
The postulate which can be used to prove that the given triangles are congruent is SAS. Option A is correct.
First, let us understand the congruency of the triangle:
When two triangles have the same sides and angles, they are congruent. That is, one's three sides are equal to the other's three sides, and one's three angles are equal to the angles of the other.
In triangles ABD and CBD;
Side BD = side BD (common)
∠ABD = ∠CBD (90 degrees)
Side AB = side CB (common)
For this triangle pair, the postulate that fit are:
SAS since the two sides and the included angle are equal in both triangles.
Thus, the postulate which can be used to prove that the given triangles are congruent is SAS. Option A is correct.
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what percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line?
The percentage of the variation in y can be explained by the corresponding variation in x and the least - squares line
The value of the coefficient of determination r2 = 0.9617*0.9617 = 0.9249
percentage of the variation in y can be explained by the corresponding variation in x and the least - squares line is = 92.49%
So, percentage is unexplained = (100 - 92.49)%
= 7.51%
Therefore, the percentage of the variation in y that can be explained by the corresponding variation in x and the least-squares line is 92.49% . The percentage which is unexplained is 7.51% i.e. (100%−92.49%) .
Hence the variation in X and the least-squares line is 7.51%
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14.5 divided by 17.5
answer must be rounded 2 decimal places
Answer: 0.83
Step-by-step explanation:
14.5/17.5 = 0.828571429
We stop at the 2nd decimal placement after 0.82 but because the following number 8 > 0 we round up the hundredths place which gives us 0.83
principle is ___ ??????????????????????
- the original amount invested
- the total amount earned
- interest plus original amount invested
- interest on a loan
what is 18.92 divided by 11 equal explain your answer?
The decimal division of 18.92 by 11 gives us; 1.72
How to divide decimal numbers?
When dividing decimals we first of all have to convert the divisor to a whole number by moving the decimal point to the right. Thereafter, we now carry the dividend's decimal point up to the exact same number of places to the right and then divide the resultant numbers in the normal way like in regular long division.
We want to divide 18.92 by 11. Thus, let us apply that rule described above to get;
18.92/11 = 1892/1100
= 1 + (1892 - 1100)/1100
= 1 + (792/1100)
= 1 + 0.72
= 1.72
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Mrs. Becker wants to get family portraits taken and is comparing prices between two different photography studios. Murray Photography charges $25 per portrait sheet, plus $30 for the session fee. Lasting Memories Company charges $50 for the session fee and $15 per portrait sheet. If Mrs. Becker plans to purchase a certain number of portrait sheets, the cost will be the same at either studio. What would the total cost be?
Write a system of equations, graph them, and type the solution.
A system of equations to describe this situation is:
c(n) = 25n + 30
c(n) = 15n + 50
The total cost is equal to $80.
The solution to this system of equations is 2.
How to write a system of equations?In order to write a system of equations to describe this situation, we would assign variables to the number of portrait sheets and cost of a photography session respectively, and then translate the word problem into algebraic equation as follows:
Let the variable n represent the number of portrait sheets.Let the variable c represent the cost of a photography session.The cost for Murray Photography is given by:
c(n) = 25n + 30
The cost for Lasting Memories Company is given by:
c(n) = 15n + 50
Next, we would solve the system of equations as follows:
25n + 30 = 15n + 50
25n - 15n = 50 - 30
10n = 20
n = 20/10
n = 2.
Now, we can calculate the total cost:
c(n) = 25n + 30
c(2) = 25(2) + 30
c(2) = $80.
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y=2(x+1)^2 has how many real roots
The answer will be:
The equation has one real root. And the root is -1/2.
The equation y= 2[tex](x+1)^2[/tex] has one real root and that is x=-1.
What is real roots of the equation?
We are aware that when we resolve a linear or quadratic equation, we always arrive at the value variable of the equation, or, to put it another way, we always locate the equation's solution. This "solution" is what we refer to as the real roots. For instance, when the equation [tex]X^2[/tex]-7x+12=0 is solved, the actual roots are 3 and 4.
Here given,
=> y = 2[tex](x+1)^2[/tex]
Take y=0 then,
=> 2[tex](x+1)^2[/tex]=0
=> [tex](x+1)^2[/tex]=0
=>(x+1)=0
=> x=-1
Hence the given equation has one real root and that is x=-1.
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how many positive integers of 3 digits may be made from the digit 1,2,3,4,5, each digit may be used just once
60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.
According to the question,
We have the following information:
3 digits integers are to be made from 1,2,3,4 and 5
So, we will use permutation to find the possible number of digits that can be made if we apply all the given conditions.
Now, we have:
Total number of digits = 5
Number of digits to be made = 3
So, we have:
[tex]^{5} P_{3}[/tex]
Solving this expression:
5*4*3
60
Hence, 60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.
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Use the parabola to graph the quadratic function f(x)=-2(x+4)^2-3
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
*i’ve been trying to understand this question for so long and when i try to find the answer they don’t make sense!!*
Given that the directrix is -2 and the vertex is (-4,-3), the graph will be the parabola plotted in the negative quadrant.
What is parabola?Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. Three crucial components make up a parabola: a focus, a directrix, and a vertex. This upward-opening parabola illustrates how all points along its curve will be equally distant from the directrix and the focus.
Here,
The equation of the parabola is,
f(x)=-2(x+4)²-3
a=-2
(h,k)=(-4,-3)
The graph will be the parabola plotted in the negative quadrant as the directrix is -2. and the vertex is (-4,-3).
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A new company wants to offer a line queuing service where customers book someone to wait in line on their behalf through a smart phone app. What concept is represented by the possibility that no one wants to pay someone else to wait in line ?.
A new company wants to offer a line queuing service where customers book someone to wait in line on their behalf through a smart phone app.
The possibility that no one wants to pay someone else to wait in line can be represented by the concept of probability.
The probability of an event occurring is defined by probability.
The outcome of an event may be known to us or unknown to us. When this happens we say that there is a chance that the event will happen or not.
We can identify probability by simply dividing the favorable number of possibilities by the entire number of possible outcomes.
Hence, probability is a numerical representation of the chance that a specific event will take place.
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What is the greatest common factor of 42,21 and 49?
Answer:
GCF = 7
Step-by-step explanation:
The greatest common factor is equal to the product of the prime factors that all of the original numbers have in common.
The greatest common factor of 49, 21 and 49 is 7.
need help on this math question please
The sequence of transformations is described as follows:
B. Reflection over the y-axis, translation 6 units right and 4 units up, dilation with center (0,0) and scale factor 2.
What are the transformations?The two polygons have vertical symmetry, hence the reflection was over the y-axis.
Two equivalent vertices are given as follows:
R(4,-4) and V(2,-4).
After the reflection over the y-axis, the coordinates would be of:
R'(-2,-4).
The polygon increases after the transformation, hence the dilation has a scale factor greater than 1, which is of 2, as VZ = 8, RU = 4.
With a dilation with scale factor of 2, the coordinates of R'' would be given as follows:
R''(-4,-8).
The coordinates of V are:
(2,-4).
Hence the translation is:
6 units right.4 units up.Hence option B is correct.
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define your variables and set up a system of equations, then solve
Solving by the system of linear equations, the Cost per pound of peanuts is $3.79 and M&M's is $4.99.
What do you mean by system of linear equations?
A system of linear equations consists of two or more equations, each of which has two or more variables, and all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy each of the system's linear equations is necessary to identify the system's unique solution.
Let, the cost per pound of peanut be $x and for M&M's be y
so, according to the question, we are getting two linear equations,
$8x + $5y = $55.27..................(i)
$6x + $4y = $42.70....................(ii)
Solving this two systems of linear equations , x=$3.79 and y=$4.99
Hence, the Cost per pound of peanuts is $3.79 and M&M's is $4.99.
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2^30 ? 30^2 which is bigger
Answer:
2³⁰ > 30²
Step-by-step explanation:
Now the values of,
→ 2³⁰ = 1073741824
→ 30² = 900
Then the expression will be,
→ 2³⁰ ? 30²
→ 1073741824 > 900
→ 2³⁰ > 30²
Hence, answer is 2³⁰ > 30².
if you can help you get 30 points I need help
The measure of angles ∠1 = 60 degrees, ∠2=120 degrees, ∠3 = 60 degrees, ∠4=60 degrees, ∠5 = 120 degrees, ∠6= 120degreesa and ∠7 = 60 degrees
The measure of angle 3 = 180 - 120
= 60 degrees
Because the sum of angles on a straight line will be 180 degrees
The measure of angle 6 = 120 degrees
The measure of angle 3 = The measure of angle 7 = 60 degrees
Because the corresponding angle will be equal
The measure of angle 1 = 180-120
= 60 degrees
The measure of angle 2 = 180 - 60
= 120 degrees
Because the sum of angles on a straight line will be 180 degrees
The measure of angle 2 = The measure of angle 5 = 120 degrees
The measure of angle 1 = The measure of angle 4 = 60 degrees
Because the corresponding angles will be equal
Hence, the measure of angles ∠1 = 60 degrees, ∠2=120 degrees, ∠3 = 60 degrees, ∠4=60 degrees, ∠5 = 120 degrees, ∠6= 120degrees and ∠7 = 60 degrees
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Which expression is equivalent to 3 log2 x – 4 log2 y + 2 log2 z?
log base 2 of the quantity x cubed y to the fourth all divided by z squared end log
log base 2 of the quantity x times z to the fifth all divided by y end log
log base 2 of the quantity x cubed z squared all divided by y to the fourth end log
log base 2 of the quantity xy divided by z end quantity raised to the fourth end log
Answer:log base 2 of the quantity x cubed z squared all divided by y to the fourth end log
Step-by-step explanation:
one antifreeze solution is 26% alcohol and another is 20% alcohol. how much of each mixture should be added to make 45 l of a solution that is 24% alcohol?
30 L of 26% and 15L of 20% of each mixture should be added to make 45 l of a solution that is 24% alcohol.
What is concentration?The quantity of a substance, like salt, that is present in a specific volume of tissue or liquid, like blood, according to science. When there is less water present, the substance becomes more concentrated. You can determine how much solute has been dissolved in the solvent by looking at the concentration of the solution.
Here,
26x + 20(45-x) = 45(24)
26x -20x = 45(24) -(20(45)
6x = 4(45) = 180 x = 180/6 = 30 L of 26%
45-x = 45-30 = 15L of 20%
To make 45 l of a 24% alcohol solution, combine 30 l of 26% and 15 l of each mixture.
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Select the correct answer. What are the solutions to the equation x2 − 1 = 399? A. B. C. D.
Answer:
x=20
x= -20
Step-by-step explanation:
