The first step to find the equation of the line is to find its slope. To do it, we need to use the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where y2 and y1 are the y coordinates of 2 given points on the line, and x2 and x1 are the x coordinates of the same points. m is the slope.
Replace for the given values and find the slope:
[tex]m=\frac{15-0}{3-2}=\frac{15}{1}=15[/tex]Now, use one of the given points and the slope in the point slope formula:
[tex]y-y1=m(x-x1)[/tex]Replace for the known values:
[tex]\begin{gathered} y-0=15(x-2) \\ y=15x-30 \end{gathered}[/tex]The equation of the line is y=15x-30
Michael and Ashley each buy x pounds of turkey and y pounds of ham. Turkey costs $3 per pound at Store A and $4.50 per pound at Store B. Ham costs $4 per pound at Store A and $6 per pound at Store B. Michael spends $18 at Store A, and Ashley spends $27 at Store B. Could Michael and Ashley have bought the same amount of turkey and ham?
Step 1
Michael spends $18 at store A
He buys x pounds of turkey and y pounds of ham.
But turkey costs $3 in-store A and ham costs $4 in-store A
Therefore, we will have the following equation for Michael
[tex]3x+4y=18---(1)[/tex]Step 2
Ashley spends $27 in-store B
She buys x pounds of turkey and y pounds of ham.
But turkey costs $4.50 in-store B and ham costs $6 in-store B.
Therefore, we will have the following equation for Ashley
[tex]4.5x+6y=27----(2)[/tex]Step 3
Solve the equations graphically
If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. Since the graphs are the same, then there are infinitely many solutions true for both equations.
For instance, the points if we test for the points on the graph, we will conclude if both Michael and Ashley bought the same amount of turkey and ham.
[tex]\begin{gathered} 3x+4y=18_{} \\ 4.5x+6y=27 \\ At\text{ x =2 and y=3} \\ we\text{ have,} \\ 3(2)+4(3)=18_{} \\ 6+12=18 \\ 18=18 \\ 4.5(2)+6(3)=27 \\ 9+18=27 \\ 27=27 \\ \text{At x=6, y=0} \\ we\text{ have} \end{gathered}[/tex][tex]\begin{gathered} 3(6)+4(0)=18 \\ 18=18 \\ 4.5(6)+6(0)=\text{ 27} \\ 27=27 \end{gathered}[/tex]Therefore yes, Michael and Ashley could have bought the same amount of turkey and ham.
Multiply each term inside the parentheses by the factor outside the parentheses 2(x - 4) = 2 x + 2(-4) Multiply Simplify.2(×-4)=2x+2(-4)
We have the expression:
[tex]2(x-4)=2x+2(-4)[/tex]We solve as follows:
[tex]2x-8=2x-8[/tex]If we want to simplify further, we will get:
[tex]2x=2x\Rightarrow x=x\Rightarrow0=0[/tex]***
In order to simplify the expression:
[tex]2(x-4)=2x+2(-4)[/tex]We multiply 2 times x and add 2 times -4, that is:
[tex]2x+2(-4)=2x+2(-4)[/tex]Now, we multiply 2 times -4 in both sides, that is:
[tex]2x-8=2x-8[/tex]Test scores are normally distributed with a mean of 86 and a standard devotion of 2.2 what percent scored between 83.8 and 92.6? What percent scored below 83.8?
Z- Score formula is:
[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z\text{ is the z-score (Standard score)} \\ X\text{ is the value to be standardized} \\ \mu\text{ is the mean} \\ \sigma\text{ is the standard deviation} \end{gathered}[/tex]Here, the mean is 86, while the standard deviation is 2.2
Percent between 83.8 and 92.6 is;
[tex]P(\frac{83.8-86}{2.2}The percent between 83.8 and 92.6 = 0.83999[tex]P(Z<-1)=\text{ 0.15866}[/tex]Percent score below 83.8 is 0.15866
There is a total of $4,840 in an account after 2 years of earning compound interest at a rate of 10%. What was the original amount invested?
In order to find the original amount invested, we can use the following formula:
[tex]P=P_0(1+i)^t[/tex]Where P is the final amount, P0 is the original amount, i is the interest rate and t is the amount of time invested.
So, using P = 4840, i = 10% = 0.1 and t = 2, we have:
[tex]\begin{gathered} 4840=P_0(1+0.1)^2_{} \\ 4840=P_0\cdot1.1^2 \\ 4840=P_0\cdot1.21 \\ P_0=\frac{4840}{1.21} \\ P_0=4000 \end{gathered}[/tex]So the original amount invested is $4,000.
What is the value of the expression 2c( a + b) when a = 2, b = 5, and c = 4
The given expression is
2c(a + b)
From the information given,
a = 2
b = 5
c = 4
By substituting these values into the expression, it becomes
2 * 4(2 + 5)
= 8(7)
= 56
The value of the expression is 56
determine the lateral surface area of the cylinder
Question:
Solution:
Remember that the total area surface of the cylinders is given by the formula:
[tex]S\text{ = 2}\pi rh+2\pi r^2[/tex]where r is the radius of the cylinder and h is its height. Now, in this case, we have that r= 10 m and h = 5m, then replacing these values in the previous equation we obtain:
[tex]S\text{ = 2}\pi(10)(5)+2\pi(10^2)=942.48^{}[/tex]then, we can conclude that the correct answer is:
[tex]S\text{ =}942.48^{}[/tex]One cubic foot holds 7.48 gallons of water, and 1 gallon ofwater weighs 8.33 pounds. How much does 6 cubic feet ofwater weigh in pounds? In tons?
We know that
• 1 cubic foot holds 7.48 gallons of water.
,• 1 gallon of water weighs 8.33 pounds.
The given information is about ratios that we must use to find the answer. Remember that a ratio is a quotient between two magnitudes, that means each statement above represents a fraction which must multiply "6 cubic feet" in order to get the answer. As follows
[tex]6ft^3\cdot\frac{7.48gallons}{1ft^3}\cdot\frac{8.33lb}{1gallon}=\frac{6\cdot7.48\cdot8.33}{1}lb=373\text{.}85lb[/tex]Therefore, 6 cubic feet weighs 373.85 pounds.
On the other hand, 1 ton is equivalent to 2000 pounds. Knowing this, we calculate
[tex]373.85lb\cdot\frac{1ton}{2000lb}\approx0.19ton[/tex]Therefore, 6 cubic feet weighs about 0.19 tons.
Tan (a) cos (a)= sin (a)Trig: use trigonometric identities to transform the left side of the equation into the right side
hello
the question here relates to trionometric identies and we can easily solve this once we know some of the identities
for example
[tex]undefined[/tex]Which best represents the number of square centimeters in a square foot?A 366 square centimeters B 144 square centimeters C 930 square centimeters D 61 square centimeters
Answer:
C. 930 square centimeters
Explanation:
First, recall the standard conversion between cm and ft.
[tex]1\text{ ft}=30.48\operatorname{cm}[/tex]Therefore:
[tex]\begin{gathered} (1\times1)ft^2=(30.48\times30.48)cm^2 \\ =929.03\operatorname{cm}^2 \\ \approx930\text{ square cm} \end{gathered}[/tex]The correct choice is C.
Find the equation of the linear function represented by the table below in slope-intercept form.xy1-82-123-164-20
Given :
The table for y and x is given as
Explanation :
The slope-intercept form is determined as
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]First find the slope of the equation using the coordinates from the table.
[tex]m=\frac{-12-(-8)}{2-1}=\frac{-12+8}{1}=-4[/tex]Now substitute the values in the slope-intercept form.
[tex]\begin{gathered} y-(-8)=-4(x-1) \\ y+8=-4(x-1) \\ y=-4x+4-8 \\ y=-4x-4 \end{gathered}[/tex]Answer:
Hence the equation of line is determined as
[tex]y=-4x-4[/tex]Max packs cereal boxes into a larger box. The volume of each cereal box is 175 cubic inches. What is the approximate volume of the large box? Please help!!
Using mathematical operations, we can conclude that the volume of the larger box is approximately 2,800 in³.
What are mathematical operations?The rules governing the order of operations specify the order in which multiple operations should be performed to solve an expression. Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction are the order in which the operations are performed (from left to right).So, in the image, we can observe that the large box contains 6 boxes of cereals in front and possibly 8 boxes of cereals at the back.
In total, there are 16 small boxes in the big box.Then, the volume of the larger box can be:
175 × 16 = 2,800 in³Therefore, using mathematical operations, we can conclude that the volume of the larger box is approximately 2,800 in³.
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Solve the equation below by completing the square and then solving for x.2 + 14x + 24 = 0A. X=-12 or x= -2B. x=2 or x=-2C. X=-2 or x=-5D. X= 8 or x= 3
2x^2 + 14x + 24 = 0
x^2 + 7x + 12 = 0
Then
x^ + (14/2) x + 12 + [7x + 49 ] = 7x + 49
Now form square
[ x + 7x + 7x + 49 ] = 7x + 49 - 12
[ x + 7]^2 = 7x + 37
Then now find x
x^2 + 7x = -6
x^2 + 7x + 7^2/4 = 7^2/4 - 6
then
( x + 7/2)^2 = 49/4 - 24/4
(x + 7/2) = ±√ (25/4)
. x = 5/2 - 7/2
and. x = 5/2 + 7/2
Then solutions are
x = -2
x= -12
ANSWER IS
OPTION A
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write the vertex form equation of the parabola with, vertex: (10,9), passes through: (12,-7)
Th equation of a parabola in its vertex form is;
y = a(x-h)² + k
(h,k) are the coordinates of the vertex and a is a constant
(h, k) = (10, 9)
substitute the above into the equation
y = a(x- 10)² + 9 -------------------(1)
Next is to find the value of a
substitute x=12 and y= -7 into equation (1)
-7 = a (12 - 10)² + 9
-7 - 9 = 4a
-16 = 4a
a = -4
The equation of the parabola will be formed by substituting a = -4 in equation (1)
y = -4(x - 10)² + 9
Find x rounded to the nearest whole degree. Be sure to round correctly!
answer: 36°
i am stuck on this question. any help would be greatly appreciated
step 1
determine the slope of the given line
y=(3/5)x-17
The slope is m=3/5
Remember that
If two lines are parallel, then their slopes are equal
that means
The slope of the parallel line to the given line is m=3/5 too
step 2
Find out the equation of the line parallel to the given line
y=mx+b
we have
m=3/5
point (-5,15)
substitute and solve for b
15=(3/5)(-5)+b
15=-3+b
b=18
therefore
The equation of the line is
y=(3/5)x+18List the elements in the set
{x 1 x is a negative multiple of 5}
S={-5,-10,-15,-20,-25......}; these are few negative multiples of 5 as stated in the set builder form of set theory {x :x is a negative multiple of 5}.
What is set?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is the mathematical model for a collection of various things.
What is set builder form?Set builder notation is a type of mathematical notation used to describe sets by listing their components or highlighting the requirements that each member of the set must meet. We write sets in the form of in the set-builder notation.
{y | (properties of y)} OR {y : (properties of y)}
Here,
{x :x is a negative multiple of 5}
S={-5,-10,-15,-20,-25.....}
According to the set builder form of set theory, {x:x is a negative multiple of 5} S={-5,-10,-15,-20,-25...}; these are a few negative multiples of 5.
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Compare f(0) and g(0)f(0) is <, =, or > to g(0)
From the graph of f(x), it can be obseved that function f(x) value at x = 0 is -3, which means that f(0) = -3.
From the graph of g(x), it can be observed that g(0) = 0.
As value 0 is greater than -3. So f(0) is lesser than g(0).
Answer: f(0) < g(0)
What is the value of 3÷5?
Answer:
0.6
Step-by-step explanation:
Solve the system using any method. State your solution as an ordered pair. DO NOT include spaces in your answer.
Answer: (- 4, - 7)
Explanation:
The given equations are
y = 5x + 13
y = 2x + 1
We would equate both equations. We have
5x + 13 = 2x + 1
5x - 2x = 1 - 13
3x = - 12
x = - 12/3
x = - 4
Substituting x = - 4 into y = 2x + 1, we have
y = 2(- 4) + 1 = - 8 + 1
y = - 7
The solution is
(- 4, - 7)
Given the venn diagram below, what is the correct notation?A. ⊘B. (M∩F)′C. (M∪F)′D. none of these
Given
SolutionThe complement of a set using Venn diagram is a subset of U. Let U be the universal set and let A be a set such that A ⊂ U. Then, the complement of A with respect to U is denoted by A' or AC or U – A or ~ A and is defined the set of all those elements of U which are not in AThe shaded region is
[tex](M\cup\text{ F \rparen'}[/tex]The final answerOption C
Convert the following percent to a simplified fraction: 6%
Given:
6%
To convert the given percent into simplified fraction, we first divide it by 100 as shown below:
[tex]\begin{gathered} 6\%=\frac{6}{100} \\ Simplify \\ =\frac{3}{50} \end{gathered}[/tex]Therefore, the answer is:
[tex]\frac{3}{50}[/tex]The volume of cylinder is 504 pi cm^(3) & height is 14cm Find the curved surface area 8 total surface area.
The Solution:
The correct answers are:
Curved surface area = 527.79 squared centimeters
Total surface area = 753.98 squared centimeters.
Given that the volume of a cylinder with height 14cm is
[tex]504\pi cm^3[/tex]We are required to find the curved surface area and the total surface area of the cylinder.
Step 1:
We shall find the radius (r) of the cylinder by using the formula below:
[tex]V=\pi r^2h[/tex]In this case,
[tex]\begin{gathered} V=\text{volume =504}\pi cm^3 \\ r=\text{ radius=?} \\ h=\text{ height =14cm} \end{gathered}[/tex]Substituting these values in the above formula, we get
[tex]504\pi=\pi r^2\times14[/tex]Finding the value of r by first dividing both sides, we get
[tex]\begin{gathered} \frac{504\pi}{14\pi}=r^2 \\ \\ r^2=36 \end{gathered}[/tex]Taking the square root of both sides, we get
[tex]\begin{gathered} \sqrt[]{r^2}\text{ =}\sqrt[]{36} \\ \\ r=6\operatorname{cm} \end{gathered}[/tex]Step 2:
We shall find the curved surface area by using the formula below:
[tex]\text{CSA}=2\pi rh[/tex]Where
[tex]\begin{gathered} \text{ CSA=curved surface area=?} \\ h=14\operatorname{cm} \\ r=6\operatorname{cm} \end{gathered}[/tex]Substituting these values in the formula above, we have
[tex]\text{CSA}=2\times6\times14\times\pi=168\pi=527.788\approx527.79cm^2[/tex]Step 3:
We shall find the total surface area by using the formula below:
[tex]\text{TSA}=\pi r^2+\pi r^2+2\pi rh=2\pi r^2+2\pi rh[/tex]Where
TSA= total surface area and all other parameters are as defined earlier on.
Substituting in the formula, we get
[tex]\text{TSA}=(2\pi\times6^2)+(2\pi\times6\times14)=72\pi+168\pi[/tex][tex]\text{TSA}=240\pi=753.982\approx753.98cm^2[/tex]Therefore, the correct answers are:
Curved surface area = 527.79 squared centimeters
Total surface area = 753.98 squared centimeters.
Jamie paid the rent well past the due date for the months of April, May and June. As a result, he had been charged a total of $75 as a late fee. Howmuch did he pay as late fee per month?Use 'f to represent the late fee $$ per month.
Total fee = $75
Number of months = 3
Divide the total fee by the number of months
75/3 = $25 per month
Hello,
I have paid the $29.00 monthly subscription for my son (jalen); I have signed up only to pay the monthly payment. Sorry to say, he does not live with me. I earlier sent you an email explaining the same with no reply from you. So how does he proceed using his information to freely access your program?
Looking forward to hearing from you shortly.
THANKS,
climacus
Answer:
Step-by-step explanation:
In a student council election there are 2 people running for treasure 3 people running for secretary 4 running for vice president and 2 people running for class president How many possible outcomes are there?
Given:
There are given that the 2 people running for treasure, 3 people running for secretary, 4 running for vice president, and 2 people running for class president.
Explanation:
According to the concept of outcomes:
The outcomes are defined for the possible results of an experiment.
Then,
In the given question, the outcomes are:
[tex]\text{Outcomes}=2+3+4+2=11[/tex]Final answer:
Hence, the total number of outcomes is 11.
Linda's medicine bottlesays "If you will be driving, then youshould not take this medicine." What arethe inverse, converse, and thecontrapositive of this statement?
For two statements p and q, and the compounded statement "If p, then q", we have the following definitions for the inverse, converse, and contrapositive of this compounded statement:
inverse: If not p, then not q.
converse: If q, then p.
contrapositive: If not q, then not p.
So, for the presented statement, i. e., "If you will be driving, then you should not take this medicine" we have:
p: you will be driving
q: you should not take this medicine
Notice that:
not p: you will not be driving
not q: you may take this medicine
Then, using the above definitions, we write:
inverse: If you will not be driving, then you may take this medicine.
converse: If you should not take this medicine, then you will drive.
contrapositive: If you may take this medicine, then you will not be driving.
The boats rate is ____ mph(Type an integer or decimal)
Let
x ----> rate of the boat in still water (mph)
y ---> rate of the current (mph)
Remember that
The speed is equal to dividing distance by the time
speed=d/t
d=speed*time
so
Upstream
speed=x-y
time=5 hours
100=(x-y)*5
x-y=20 --------> equation 1
Downstream
speed=x+y
time=4.5 h
100=(x+y)*4.5
x+y= 100/4.5 --------> equation 2
Adds equation 1 and equation 2
x-y=20
x+y= 100/4.5
-----------------
2x=20+(100/4.5)
2x=190/4.5
x=190/9
x=21.11 mph
therefore
The answer is 21.11 mphCreate a polynomial of degree 6 that has no real roots. Explain why it has no real roots. Is it possible to have a polynomial with an odd degree that has no real roots? Explain.
Create a polynomial of degree 6 that has no real roots.
y = ( x^2 + 4) ( x^2 +7 ) ( x^2+5)
Multiplying all the terms together
y =x ^6 + 16 x^4 + 83 x^2 + 140
Using the zero product property
0= x^2 +4 x^2+7 =0 x^2 + 5 =0 will each give a complex solution
x^2 = -4 x^2 = -7 x^2 = -5
This means x = 2i or -2i x = i sqrt(7) or -i sqrt(7) x = i sqrt (5) or - i sqrt(5)
These solutions can be in the form a+bi
Therefor it will have no real roots
y = x^6 + 16 x^4 + 83 x^2 + 140 has no real solutions
Complex solutions come in pairs, so an odd degree must have a real solution
Which expression can be used to find the nth term in this sequence position: 1 2 3 4 5 nvalue of term: 2 5 10 17 26 ?
n²+1 where n is the position of the sequence
1) Considering the sequence (2,5,10,17,26,...) corresponding to 1,2,3,4,5,...
Let's figure out how that sequence grows:
5 -2 = 3
10 -5 = 5
17-10= 7
26-17= 9
And examining the differences from each difference we have:
5-3 =2
7-5 = 2
9-7 =2
2) So we can write the following table, where the first line is the sequence, then the positions, then the subtraction between them.
As it is a quadratic formula, we can write in the general form and then plug x=0
[tex]\begin{gathered} a_n=n^2 \\ 2\text{ 5 10 17 26} \\ 1\text{ 2 3 4 5 6 } \\ 1\text{ 4 9 25 36} \\ a_n=n^2+0n+1 \\ a_n=n^2+1 \end{gathered}[/tex]3) Hence, to find the 6th term, for instance, we plug n=6 so
6²+1 = 31. So the formula to find the nth term is n² +1
3) Finally, the sequence is given by n² +1 where n is the position of the term.