Answer:
0.5
Step-by-step explanation:
7 1/2 • 2 = 15
7 times 2 is equal to 14
1/2 times 2 is equal to 1
14 plus 1 is equal to 15
There is a gas station exactly halfway between Stan and Drew’s houses. The map coordinates for Stan’s house are 5 miles East and 2 miles north. The map coordinates for Drew’s house are 3 miles East and 4 miles north. Find the map coordinates for the gas station
Answer:
4 miles east and 3 miles north (4, 3)
Marco owed his father $210 and began paying him back $20 at the end of each week, beginning November 1. Joni owed her father $180 and began paying back $10 at the end of each week, beginning on the same day. What Marco owed his father in dollars at the end of n weeks can be represented by f(n) = 210 − 20n. What Joni owed her father in dollars at the end of n weeks can be represented by g(n) = 180 − 10n.
Find the value of n for which f(n) = g(n). What does that value mean in this situation?
After _____ weeks, Jonie and Marco each owed their fathers the same amount
In the given situation n gives us the number of weeks. after 3 weeks, Jonie and Marco each owed their fathers the same amount.
What are mean?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
We have been given that Marco owed his father in dollars at the end of n weeks can be represented by f(n) = 210 − 20n. and Joni owed her father in dollars at the end of n weeks can be represented by g(n) = 180 − 10n.
Also we get f(n) = g(n)
210 − 20n = 180 − 10n
Now n gives us the number of weeks thus solve for n
210 − 20n = 180 − 10n
210 - 180 = -10n + 20n
30 = 10n
n = 3
Now check your solution;
f(n) = 210 − 20n = 210 - 60 = 250
g(n) = 180 − 10n = 180 - 30 = 150
So our answer checks out after 3 weeks, Jonie and Marco each owed their fathers the same amount.
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Your goal in this section is to take a closer look at some aspects of the topic finding solutions of
quadratic equations. You are going to think deeper and test further your understanding about solving
quadratic equations using any of the four methods discussed.
1. Sheryl says that the solutions of the quadratic equations w² = 49 and
w² +49 = 0 are the same. Do you agree with Sheryl? Justify your answer.
2. Patricia says that it's more appropriate to use the method of factoring
than extracting square roots in solving the quadratic equation
4x² - 9 = 0. Do you agree with Patricia? Explain your answer.
3. If you are to choose between completing the square and factoring in
finding the solutions of each of the following equations, which would you
choose? Explain and solve the equation using your preferred method.
b. x² + 7x + 12 = 0
a. 4x² - 20x = 11
4. The values of a, b, and e of a quadratic equation written in standard form
are -2, 8, and 3, respectively. Another quadratic equation has 2, -8, and
-3 as the values of a, b, and c, respectively. Do you agree that the two
equations have the same solutions? Justify your answer.
"pa answer po please"..
1) Sheryl was wrong, the solution of w² = 49 and w² +49 = 0 are not same.
2) The solution of 4x² - 9 = 0 this quadratic equation is 3/2 and -3/2 through using factoring method.
3)
The solution of 4x² - 20x = 11 is 11/2 and -1/2, through using completing the square method.The solution of x² + 7x + 12 = 0 is -4 and -3, through using factoring method.4) The solution of both quadratic equations will give same results.
Explanation:
1) Sheryl says that the solutions of the quadratic equations w² = 49 and
w² +49 = 0 are the same. Do you agree with Sheryl? Justify your answer.
Solution:-
According to Sheryl says that the solutions w² = 49 and w² +49 = 0 are the same.
Let's find the solution of given quadratic equations
w² = 49w = √49 ( ∵√49 = 7 )
w = ±7
So the solution of this quadratic equation 7 and -7
w² + 49 = 0w² = -49
w = √(-49) ( ∵√49 = 7 )
w = ±7 √-1 ( ∵√-1 = i )
So the solution of this quadratic equation 7i and -7i
Both solutions are not same.2. Patricia says that it's more appropriate to use the method of factoring
than extracting square roots in solving the quadratic equation
4x² - 9 = 0. Do you agree with Patricia? Explain your answer.
Solution:-
Patricia says that it's more appropriate to use the method of factoring
than extracting square roots in solving the quadratic equation
4x² - 9 = 0.
We are agree with Patricia, the method of factoring is very easy to learn and best way to deliver the solution of this quadratic equation.Now, let's solve that quadratic equation through factoring method.
4x² - 9 = 0.(2x)² - (3)² = 0 {∵ a²-b²= (a-b)(a+b)
(2x-3)(2x+3) = 0
If (2x-3) = 0
2x-3 = 0
2x = 3
x = 3/2
And if (2x+3) = 0
2x+3 = 0
2x = -3
x = -3/2
The solution of 4x² - 9 = 0. is 3/2 and -3/2.3. If you are to choose between completing the square and factoring in
finding the solutions of each of the following equations, which would you
choose? Explain and solve the equation using your preferred method.
a. 4x² - 20x = 11
b. x² + 7x + 12 = 0.
Solution:-
a. 4x² - 20x = 11
For solve this quadratic equation, we can use completing the square method, because this equation is very hard to get it's factors.
So,
4x² - 20x = 11
[tex]x^2-5x+(\frac{5}{2})^2 = \frac{11}{4} +(\frac{5}{2})^2\\x^2-2\times \frac{5}{2} \times x+(\frac{5}{2})^2 = \frac{11}{4} +\frac{25}{4}\\(x-\frac{5}{2})^2 = \frac{11+25}{4}\\(x-\frac{5}{2})^2 = \frac{36}{4}\\(x-\frac{5}{2})^2 = 9\\(x-\frac{5}{2})^2 = (3)^2\\(x-\frac{5}{2}) = \pm (3)\\\\[/tex]
For taking + sign,
x - [tex]\frac{5}{2}[/tex] = 3
x = 3 + [tex]\frac{5}{2}[/tex]
x = [tex]\frac{6+5}{2}[/tex]
x = [tex]\frac{11}{2}[/tex]
For taking - sign,
x - [tex]\frac{5}{2}[/tex] = -3
x = [tex]\frac{5}{2}[/tex] - 3
x = [tex]\frac{5-6}{2}[/tex]
x = [tex]\frac{-1}{2}[/tex]
The solution of 4x² - 20x = 11 is 11/2 and -1/2, through using completing the square method.b. x² + 7x + 12 = 0.
For solve this quadratic equation, we can use factoring method, because that is very easy to get it's factors.
So,
x² + 7x + 12 = 0
x² + 4x +3x + 12 = 0
x(x+4) +3(x+4) = 0
(x+4)(x+3) = 0
If (x+4) = 0
x+4 = 0
x = -4
And if (x+3) = 0
x+3 = 0
x = -3
The solution of x² + 7x + 12 = 0 is -4 and -3, through using factoring method.4. The values of a, b, and e of a quadratic equation written in standard form are -2, 8, and 3, respectively. Another quadratic equation has 2, -8, and -3 as the values of a, b, and c, respectively. Do you agree that the two equations have the same solutions? Justify your answer.
Solution:-
We know that the standard form of quadratic equation is
ax²+bx+c = 0From question we have two values of a,b and c.
For 1st quadratic equation the value of a,b and c is -2, 8, and 3, respectively.
So, the quadratic equation is
-2x²+8x+3 = 0For 2nd quadratic equation the value of a,b and c is 2, -8, and -3, respectively.
So, the quadratic equation is
2x²-8x-3 = 0Now, we have to find the solution of both equations are same or not.
So, the solution of 1st quadratic equation
-2x²+8x+3 = 0
2x-8x-3 = 0 (multiplying - with both sides)
Now, this equation convert in the form of 2nd quadratic equation. So we can say that the solution of both quadratic equations will give same results.
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Write two complex numbers with a difference of 9.
pls help, its from alg 2 3.3 on big ideas math
Two complex of numbers with a difference of 9 is 19 + i3 and 10 + i3
What are complex numbers?
The term complex numbers is used in mathematics to refer to numbers that are of two parts the real part and the imaginary part. The real part of a complex number appears like a number real number while the imaginary part has the letter i before the number.
How to find two complex numbers with a difference of 9This is two numbers that there difference will be 9
so subtracting the two complex numbers we have:
( 19 + i3 ) - ( 10 + i3 )
= ( 19 - 10 ) - ( i3 - i3 )
= 9 - 0
= 9
Hence we can say that two complex of numbers with a difference of 9 is 19 + i3 and 10 + i3.
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The scale on the horizontal axis is 5 s per division and on the vertical axis 9 m per division. What is the time represented by the third tic mark on the horizontal axis? Answer in units of s.
From the given graph, we can conclude that at a time of 15, the position is 8m; At a time of the fourth tic on the x-axis, the position is 20.25 m
How to Interpret Distance Time Graphs?
From the given distance time graph, we can see that the y-axis is represented by position in meters while x-axis is represented by time taken.
A) Tracing x = 3 tic, we can get see that the time is at x = 3 * 5 = 15 s
B) Tracing the fourth tic mark on the graph, we can see that y = 2.25 = 2.25 * 9 = 20.25 m
C) Now, when t = 15 seconds, we can see that it will be the third tic on the x-axis and as such at the third tic,
(15 * 1.75)/3 = 8 m
Thus, we can conclude that at a time of 15, the position is 8m; At a time of the fourth tic on the x-axis, the position is 20.25 m
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points A(2, 3) B(-3,4).
area of triangle PAB = 8.5.
The equation of the locus of the point P so that the area of triangle PAB is 8.5 square units will be 5 k + h = 34.
Let coordinate of P be (h, t)
We are given the coordinates of A and B as:
A = (2,3) and B = (−3,4)
Now, we also know that Area of triangle PAB is:
A = 1 / 2 (h ( 3 − 4 ) + 2 ( 4 − k ) − 3 ( k − 3 ) )
± 8.5 = 1 / 2 ( h ( - 1 ) + 2 ( 4 - k ) - 3 ( k - 3 ) )
± 17 = ( - h + 8 - 2 k - 3 k + 9 )
± 17 = ( 17 - 5 k - h )
When + 17 is there:
5 k + h = 0
When - 17 is there:
5 k + h = 34
So, locus of the point P will be 5 k + h = 34.
Therefore, the equation of the locus of the point P so that the area of triangle PAB is 8.5 square units will be 5 k + h = 34.
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Your question was incomplete. Please refer the content below:
A(2,3) and B(−3,4) be two given points. Find the equation of the locus of P so that the area of triangle PAB is 8.5 square units.
I don’t understand the question 2 for this math equation.
Answer:
Step-by-step explanation:
Time/mph
what is the slope of a line that passes through the points open parentheses 6 comma 1 close parentheses and open parentheses short dash 3 comma 4 close parentheses?
Answer:
-1/3
Step-by-step explanation:
So we need to find the slope of a line that passes through (6, 1) and (-3, 4).
We know that the line passes through 2 points, and using this information, we can find the slope of this line using our slope formula which is [tex]\frac{y1-y2}{x1-x2}[/tex].
So we can do [tex]\frac{4-1}{-3-6}=-\frac{1}{3}[/tex].
That's your answer.
Let me know if you have any questions
please help −5×12=
(9)(−8)=
(14)(4)=
(−10)(−12)=
(0)(−7)=
please answer all
Calculate the kinetic energy of a 20 kg object that is moving with a speed of 10 m/s.
The kinetic energy is 1000J.
Kinetic energy is the energy of motion, observable as the movement of an object, particle, or set of particles. It is the measure of the work that an object does by virtue of its motion.
Kinetic energy is the product of half the product of mass and the square of the speed.
K.I = 1/2 m v²
Here m = 20kg, v = 10m/s
K.I = 1/2 × 20 × 10²
= 10 ×10²
= 1000
Therefore the kinetic energy is 1000J.
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Please answer these for linear review
Answer: See explanation
Step-by-step explanation:
g(x)=2x-2
g(x+9)=2(x+9)-2 ==> x+9
(1,2), (4,5)
x=1, x=4: ==> pick the x-coordinates for domain
[1, 4] ==> segment is from 1 to 4 and includes x=1 and x=4
You and a friend are playing a board game. your final score $x$ is $12$ points less than your friend's final score. write and solve an equation to find your final score. round 9 round 10 final score your friend 22 12 195 you 9 25 ? equation: $=195$ your final score is points.
The equation formed using the given data is 195 = x + 12 and your final score is 183 points.
How to form an equation?
Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say your final score is x
Given that,
Your final score x is 12 points less than your friend's final score.
So,
x = friend final score - 12
Now,
Friend final score = 195
So,
x = 195 - 12
x + 12 = 195
195 = x + 12
Now,
x = 195 - 12 = 183
Hence "The equation formed using the given data is 195 = x + 12 and your final score is 183 points".
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1. y=-4x+3
X
20
1
2
3
y
-5
-9
V
Answer:−4x+60X,1,2,3y−14
Step-by-step explanation:
1. simplify 3x x 20 to 60x
−4x+60X,1,2,3y−5−9
2. Simplify 3y- 5-9 to 3y - 14
−4x+60X,1,2,3y−14
\frac{3}{8} times \frac{1}{9} in simplest form help me
Answer: 3/72 is your answer.
Simplify the following
Need the answer asap pls
4/7 x 1/7 what is the answer
Answer:
[tex]\frac{4}{49}[/tex]
Step-by-step explanation:
4/7 × 1/7
= 4 × 1/7 × 7
= 4/49
25% of the normal price of a watch is $15. What is the normal price?
- Lyle needs 200 g of chocolate that is 86% cocoa
for a cake recipe. He has one kind of chocolate
that is 99% cocoa and another kind that is 70%
cocoa. How much of each kind of chocolate
does he need to make the cake? Round your
answer to the nearest gram.
Answer: 110 grams of the 99% cocoa, and 90 grams of the 70% cocoa.
===================================================
Work Shown:
x = amount of the 99% cocoa
200-x = amount of the 70% cocoa
0.99x = amount of pure coca from the first batch
0.70(200-x) = amount of pure cocoa from the second batch
0.99x+0.70(200-x) = total amount of pure cocoa
0.99x+0.70(200-x) = 200*0.86
0.99x+0.70*200-0.70x = 200*0.86
0.99x+140-0.70x = 172
0.29x+140 = 172
0.29x = 172-140
0.29x = 32
x = 32/0.29
x = 110.344827586207
x = 110
200-x = 200 - 110 = 90
Lyle needs 110 grams of the 99% cocoa, and 90 grams of the 70% cocoa.
Both of these values are approximate.
in a survey, 80 people were were questioned to find out how how many people read newspapers, S or D or both both. The survey revealed ya that 45 read D, 30 read read S and 10 read neither
Represents the information in a venn diagram.
Greetings from Brasil...
In this type of problem, we will use Set Theory
n(D ∪ S) = n(D) + n(S) - n(D ∩ S)
as n(U) - n(D ∪ S) = 10, then
n(D ∪ S) = 70, so
n(D ∩ S) = 5 (read both)
n(D) - n(D ∩ S) = 40 (read only D)
n(S) - n(D ∩ S) = 25 (read only S)
see attached figure
_________________________________
something similar
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Find the 11th term of the arithmetic seqence 2x+ 9, 7x+11 ,12x +13,...
Answer:
52x + 29.
Step-by-step explanation:
d = 7x + 11 - (2x + 9)
= 5x + 2.
11th term
= 2x + 9 + (11-1)(5x + 2)
= 2x + 9 + 50x + 20
= 52x + 29.
construct potential hypotheses or research questions to relate the variables in each of the following examples. also, write a brief statement explaining why you believe there is a relationship between the variables as specified in your hypotheses.
Construct potential hypotheses or research questions to relate the variables in each of the following examples -
Political party and support of the affordable care act -
Given this, there can be a relationship between the ideological group and the support of the moderate consideration act.that various ideological groups may support various types of government disability conspiracies and might have various goals.A few gatherings might focus on a list of topics or problems and might provide serious thought at some random time.which might facilitate the implementation of the Affordable Care Act, while others would be gradually forgiving toward such arrangements.The implementation and success of the Affordable Care Act may depend on the rise of certain ideological movements.and their ability to express what they think about the Act's purpose.
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6c+5d-4c-3d+3c-6d; c=4 and d=-2
Evaluate the expression for the given values of the variables.
show all work please
We are to evaluate the expression:
[tex]6c + 5d - 4c - 3d + 3c - 6d[/tex]
Where:
[tex]c = 4[/tex], [tex]d = 2[/tex]
Here, we just have to replace the variables with their given values, as shown below:
[tex]6(4) + 5(2) - 4(4) - 3(2) + 3(4) - 6(2)[/tex]
Now, we calculate.
[tex]→24 + 10 - 16 - 6 + 12 - 12[/tex]
Final answer
[tex] = 12[/tex]
5
8. A tent in the shape of a right pyramid has 4 poles that are each 2.1 m long.
The side length of the base of the tent is 1.5 m.
a) Sketch a diagram of the tent.
b) What is the slant height of the tent to the nearest tenth of a metre?
My brodas and sisters please help me out for the love of god
Answer:
1.96 m or 2m when rounded to nearest tenth
Step-by-step explanation:
The question is referring to a square right pyramid. The base is square and the perpendicular axis is vertical to the base.
These are the different parts of a square right pyramid .
See figure for detailed description(taken from Wolfram website)
The ones of interest here are
a = base side length = = 2.1m (given).Answer slant height s = 1.96 = 2 m when rounded to nearest tent
show your work, and explain and write the final answer in a complete sentence. i will give brainlest to whoever answers! due right now please help this will impact my grade!
Answer: Simplify the expression.
Scientific Notation:
4 ⋅ 10^7
Expanded Form:
40000000
Step-by-step explanation:
by doing 2.7*10^(5) divided by 6.75*10^(3)
you get the answer or now saying its
4 ⋅ 10^7 miles away basically. hope this helped
Select the correct slope, y-intercept, and graph for the equation below. 5x+y=4
Answer:(0,4)
Step-by-step explanation: Graph the line using the slope and y-intercept, or two points.
Slope: -5
y-intercept:
(0,4)
x y
0 4
1 -1
Explain how to use compensation to find the difference of 30,000 and 6,985.
The difference of 30000 and 6985 using compensation is 23015
The method of compensation refers to calculating mentally without any paper work.
Here, we are asked to find the difference of 30000 and 6985 which are comparatively large numbers. Everyone would prefer using pen and paper to calculate this. But we can do this by compensation within a few steps.
Add 15 to 6985 [Addition is simpler than subtraction]. We get 7000.Now subtract 7000 from 30000 [ more zeros in the numbers make the mental calculation easy]. We just have to subtract 7 from 30 and adjoin 3 zeros in 7000. So we get 23000.Lastly add the 15 from the first step again to 23000.So the final answer is 23015.
i.e., 30000-6985 = 23015
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Mr. Cruz bought 3 roses for $30 each. How much is his change if he paid with a $100?
a
O b
P
$100-(3 x $30)= N
$3 x $30-$100 = N
100-$30 x 3=N
(3 x $30) - 100 = N
Answer:
10 is the answerplease i
at a gathering of50 people, there are 30 people who all know each other and 20 people who know no one. people who know each other hug, and people who do not know each other shake hands. how many handshakes occur within the group?
Total 790 number of handshakes occur within the group.
According to the given question.
Total number of people = 50
Number of people who know each other = 30
Number of people who know no one = 20
Since, 20 people doesn't knw each any one, so they will shake hands.
So, the total number of hand shakes by these 20 people
= 20(20 -1)/2
= 10(19)
= 190
Also, we have to consider that other 30 people will also shake hands with these 20 people.
So, the total number of hanshakes by these 30 and 20 people = 30 × 20 = 600
Therefore, the total number of handshakes occur within the group
= 600 + 190
= 790
Hence, total 790 number of handshakes occur within the group.
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A, B & C form the vertices of a triangle.
∠
CAB = 90°,
∠
ABC = 61° and AB = 9.2.
Calculate the length of AC rounded to 3 SF.
Answer:
AC = 16.6
Step-by-step explanation:
Use sine rule
9.2 / sin(180-90-61) = AC/ sin(61)
The formula for the volume V of a cylinder is V = r²h, where r is the radius of the base and his the height of the
cylinder. Solve the formula for h. Then find the height of a cylinder with a volume of 36 cm³ and a base with a
radius of 3 cm.
Answer: h=V/r²
h=4 cm
Step-by-step explanation:
V = r²h solve for h
V/r² = r²h/r² ==> divide the formula by r² to isolate h
h=V/r²
h=36/(3)²
h=36/9
h=4 cm