Answer:
Step-by-step explanation:
Solution by substitution method
3x+5y=7
and 4x-y=5
Suppose,
3x+5y=7→(1)
and 4x-y=5→(2)
Taking equation (2), we have
4x-y=5
⇒y=4x-5→(3)
Putting y=4x-5 in equation (1), we get
3x+5y=7
⇒3x+5(4x-5)=7
⇒3x+20x-25=7
⇒23x-25=7
⇒23x=7+25
⇒23x=32
⇒x=32/23
→(4)
Now, Putting x=32/23
in equation (3), we get
y=4x-5
⇒y=4(32/23)-5
⇒y=(128-115)/23
⇒y=13/23
∴y=13/23 and x=32/23
12. A bag contains 12 red, 9 green and 5 black markers. If Cooper randomly selects 7 markers, how many
ways could this be done if EXACTLY 6 are to be the same color?
Answer:
Step-by-step explanation:
7 marks
6 same colors
from 12 red 6 same exactly the same
12 x 11 x 10 x 9 x7 x6
1 remainig
from 9 green 6 saem exactly the same
9 x 8 x 7 x 6 x5 x4
1 remaining
add the results above to get your final answer
26 markers in total
6 to be chosen of the same color from 7
What is the surface area of the figure? 9 ft 9 ft 15 ft 15 ft 4 ft
The surface area of the given composite figure is; 528 ft²
How to find the area of a composite figure?To get the surface area of the attached composite shape, we will have to break the object down into smaller shapes to get;
Surface area 1 = 2(15 * 4) = 120 ft²
Surface area 2 = 2(9 * 4) = 72 ft²
Surface area 3 = 2(6 * 4) = 48 ft²
Surface area 4 = 2((15 * 15) - (9 * 9)) = 288 ft²
Thus;
Total surface area = 120 + 72 + 48 + 288
Total surface area = 528 ft²
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20 percent of 180 hours
Answer:
36 hours
Step-by-step explanation:
To find the percentage of a number, change the percent to decimal form
20 percent = .20
Multiply this by the number
.20 * 180
36
20 percent of 180 = 36
4. In 2010, the amount in Raja's account was 40 Lakhs. He debited 8000 in 2011, and in 2012, he debited 2,07,000. In 2013, he credited 1,16,000, and in 2014 he credited 12,000. How much more he has to credit to be worth what it was at at the start of 2010
Answer:
don't know is is mathematics or any other subject
What factors do the numbers 16 and 36 have in common?
A. 1, 2, 4, 8
B. 1, 2, 4, 6
C. 1,2,4
D. 1, 2, 8, 16
Answer: C. 1, 2, 4
Step-by-step explanation:
A factor is an integer that is a divisor of a number. In other words, the number can be divided by this integer and result in another integer.
To answer this question, we can list the factors of both numbers. I have underlined and bolded integers that appear in both lists, giving us our answer.
Factors of 16: 1, 2, 4, 8 and 16
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
C. 1, 2, 4
Please answer all four of the questions I would really appreciate it <3
Answer:
1)A because 3 < 3.9 < 4
2)C because 8.2<8.23<8.3
3) D because 6.1>5.9
4)B because 3.6<3.625<3.7
Hope it helps!
Help me with this I’m stuck!!:)
The cardinality of the set indicated in the task content is; 11.
What is the cardinality of the set?It follows from the task content that the cardinality of the intersection set of set A compliment and set B compliment is to be determined.
Hence, it follows that the elements in the described set include the elements in set C only and the elements in the compliment of set A, B and C union.
On this note, it follows that the cardinality of the set is; 4 +7 = 11.
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what is the sum of the series
Answer: 925
Step-by-step explanation:
This is an arithmetic series with first term 1 and last term 3(25)-2=73, with a total of 25 terms.
Using the sum of an arithmetic series formula, we get the sum is:
[tex]\frac{25}{2}(1+73)=\boxed{925}[/tex]
For a population with μ = 60 , X=81, and σ = 12. Find the z-score for 81.
The z-score for 81 is 1.75
How to determine the z-score for 81?The given parameters are:
μ = 60 , X=81, and σ = 12
The z scores is calculated using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
Substitute the given values
[tex]z = \frac{81 - 60}{12}[/tex]
Evaluate the difference
[tex]z = \frac{21}{12}[/tex]
Simplify
z = 1.75
Hence, the z-score for 81 is 1.75
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Janelle and Jacob are considering a $130,000 mortgage for 30 years at 4.8%. With this information, their monthly payment
would be $682.06.
If they make only the minimum payment each month, what is the total payback of this loan?
How much of this total payback is interest?
4x + 2y=4 and 3x -y= -7
Answer:
y = 4
x = -1
Step-by-step explanation:
4x + 2y = 4 Eq. 1
3x - y = -7 Eq. 2
from the Eq. 2
3x = y - 7
3x + 7 = y Eq. 3
Replacing the value of the Eq. 3 in the Eq. 1
4x + 2(3x+7) = 4
4x + (2*3x + 2*7) = 4
4x + (6x + 14) = 4
10x + 14 = 4
10x = 4 - 14
10x = - 10
x = -10/10
x = -1
from the Eq. 3
3x + 7 = y
3*-1 + 7 = y
-3 + 7 = y
4 = y
Check:
from the Eq. 1
4x + 2y = 4
4*-1 + 2*4 = 4
-4 + 8 = 4
114
4. Line p contains point (6,-5) and is perpendicular to line q. The equation for line gis y = 3x + 5.
Write an equation for line p.
Part I: Find the slope of line q. (1 point)
Part II: Find the slope of line p. (Write the negative reciprocal of the slope you found in Part I.) (1 point)
that
Part III: Use the point given for line p and the slope you found in Part II to write an equation for line pin
point-slope form: y - y₁ = m(x-x₁). (1 point)
Line q has slope 3, as you've found.
Any line perpendicular to q will then have slope -1/3, as you've found.
Line p thus has slope -1/3 and we know it passes through (6, -5), so from the point-slope formula we get the equation
[tex]y - (-5) = -\dfrac13 (x - 6) \implies \boxed{y + 5 = -\dfrac13 (x - 6)}[/tex]
For the graph y = 12 find the slope of a line that is perpendicular to it and the slope of a line parallel to it. Explaln your
answer with two or more sentences.
The line y = 12 has a slope of 0 because it is a horizontal line, meaning that for any change in x, there is no change in y. Ths means the slope of a line parallel to it would be 0 (since parallel lines have the same slope), and the slope of a line perpendicular to it would be undefined (since perpendicular lines have slopes that are negative reciprocals of each other, and when you divide by 0, you get an undefined result).
Line AB and line BC form a right angle at point B with points A(2,5) and B(8,3) . What is the equation of line BC ?
Answer: y = 3x - 21
Step-by-step explanation:
If the lines form a right angle, this means that they are perpendicular. Therefore, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other (in other words, their slopes multiply to -1).
The slope of AB is [tex]\frac{3-5}{8-2}=\frac{-2}{6}=-\frac{1}{3}[/tex]. This means that the slope of BC is 3.
Substituting into point-slope form,
[tex]y-3=3(x-8)\\\\y-3=3x-24\\\\\boxed{y=3x-21}[/tex]
. In 1 hour, a car can cover 70 km. How much distance will it cover in 2 hours?
I need it fast
Answer:
140km
Step-by-step explanation:
Distance = Speed x Time
= 70km/h x 2 hours
= 140km
Solve the system of equations : y = x/2 , y = -x - 3 . You can use any method you wish for solving systems of equations. Check your answer.
Answer:
x=−2 and y=−1
Step-by-step explanation:
Problem:
Solve y=x2;y=−x−3
Steps:
I will solve your system by substitution.
y=1/2x;y=−x−3
Step: Solve y= 1/2x for y:
Step: Substitute 1/2 x for y in y=−x−3:
y=−x−3
1/2x= =−x−3
1/2x+x=−x−3+x(Add x to both sides)
3/2x = -3
3/2x/3/2 = -3/3/2 (Divide both sides by 3/2)
x=−2
Step: Substitute −2 for x in y=1/2x:
y=1/2x
y=1/2(-2)
y=−1(Simplify both sides of the equation)
Answer:
x=−2 and y=−1
Which expression is equivalent to (1−sinβ)(1+sinβ)/cos2β for all values of β for which (1−sinβ)(1+sinβ)/cos2β is defined?
Select the correct answer below:
tan2β
tanβ+secβ
tanβ
sec2β
1
Using a trigonometric identity, it is found that the equivalent expression is given by 1.
What are the trigonometric identities used to solve this question?Relating sine and cosine, we have that:
[tex]\sin^{2}{\beta} + \cos^{2}{\beta} = 1[/tex]
Then:
[tex]\cos^{2}{\beta} = 1 - \sin^{2}{\beta}[/tex]
For the tangent, we have that:
[tex]\tan{\beta} = \frac{\sin{\beta}}{\cos{\beta}}[/tex].
For the secant, we have that:
[tex]\sec{\beta} = \frac{1}{\cos{\beta}}[/tex].
In this problem, the expression is:
[tex]\frac{(1 - \sin{\beta})(1 + \sin{\beta})}{\cos^{2}{\beta}} = \frac{1 - \sin^2{\beta}}{\cos^2{\beta}} = \frac{\cos^2{\beta}}{\cos^2{\beta}} = 1[/tex]
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Write a linear equation in slope-intercept form using a slope and a given point. If a line has a slope of short dash 2 and goes through the point open parentheses 1 comma short dash 3 close parentheses, then the equation for the line in slope-intercept form is ______________. a.) y equals short dash 2 x minus 1 b.) y equals short dash 2 x plus 1 c.) y equals 2 x minus 5 d.) y equals 2 x plus 5
y equals short dash 2 x minus 1
In other words, y = -2x - 1 is the equation
=========================================================
Explanation:
Slope = m = -2
Point on the line is (x,y) = (1, -3)
Use these three items to find the y intercept b
y = mx+b
-3 = -2*1 + b
-3 = -2 + b
-3+2 = b
-1 = b
b = -1
The slope intercept form of y = mx+b turns into y = -2x-1 after plugging m = -2 and b = -1
what is the domain and range of this graph
Answer:
Domain: All real number
Range: y≤-4
The parabolas y = -x² and y= -x² - 4x + 6 are graphed below. What are the y-values of the solutions to this system of equations?
y= 1,9
y= 1,6
y= -0,6
y= -3,1
Answer:
y = 1, 9.
Step-by-step explanation:
They are the y values of the points of intersection of the 2 parabolas.
y = 1, 9.
I need help on questions d and e, not sure how to solve!
D.
[tex]m(x) = 0 \\ - 3x = 0 \\ x = 0[/tex]
E.
[tex]m(x) = \frac{ - 3}{25} [/tex]
[tex] \frac{ - 3x}{x {}^{2} + 2x - 24} = \frac{ - 3}{25} [/tex]
[tex] - 3(x {}^{2} + 2x - 24) = - 3(x)(25) \\ divide \: both \: sides \: by - 3[/tex]
[tex]x {}^{2} + 2x - 24 = 25x[/tex]
[tex]x {}^{2} - 23x - 24 = 0[/tex]
[tex](x - 24)(x + 1) = 0 [/tex]
[tex]x = 24 \\ x = - 1[/tex]
Answer:
D
x=0
Step-by-step explanation:
E)
[tex]\frac{-3x}{x^2+2x-24} =\frac{-3}{25} \\x^2+2x-24=25x\\x^2+2x-25x-24=0\\x^2-23 x-24=0\\x^2-24x+x-24=0\\x(x-24)+1(x-24)=0\\(x-24)(x+1)=0\\x=24,-1[/tex]
A giant tortoise can travel 0.11 miles in 1 hour. At this rate, how long would it take the tortoise to travel 3 miles?
Answer:
about 27.27 hours.
Step-by-step explanation:
If it can travel 0.11 miles in 1 hour, we need to divide 3 miles by 0.11 miles to get the number of hours it would take to travel 3 miles. 3/0.11 is 27.27 repeating.
Hope this helps!
Answer:
27.27 hours
Step-by-step explanation:
You need to set up a proportion. I did distance over time.
[tex]\frac{.11 mi }{1 hr} = \frac{3 mi}{x hr}[/tex]
Cross multiply
.11x = 3
Divide by .11
x = 27.27
Simplify (3^1\2x2^1\3)^1\2
Answer:
1.37
Step-by-step explanation:
3^1=3/2=1.5
2^(1/3)=1.26
1.5×1.26=1.89
1.89^(1/2)=1.37
You are given the steps for using a compass and a straightedge to construct a line perpendicular to a given line through a point not lying on the given line. Arrange the steps in the proper sequence.
Place the compass needle on the external
point R. Make the compass width greater
than the distance from R to the given line.
Draw an arc cutting the given line at
two points. Mark and label the points
of intersection P and Q.
Draw a line from the external point R to
the point where the arcs intersect, S.
Line RS is perpendicular to line PQ and
passes through the external point R.
Move the compass needle to P and make an
arc below the line. Keep the compass width,
and move the compass needle to Q. Draw an
arc below the line crossing the other arc.
Mark and label the point of intersection S.
The proper steps for the construction are given as 1, 2 4, and then 3.
Write the steps for construction?The proper steps for the construction are;
1. Place the compass needle on the external point R. Make the compass width greater than the distance from R to the given line.
2. Draw an arc cutting the given line at two points. Mark and label the points of intersection P and Q.
3. Move the compass needle to P and make an arc below the line. Keep the compass width, and move the compass needle to Q. Draw an arc below the line crossing the other arc. Mark and label the point of intersection S.
4. Draw a line from the external point R to the points where the arcs intersect, S. Line RS is perpendicular to line PQ and passes through the external point R.
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28.6% of city employees ride the bus to work. Last year, 29.7% of city employees rode the bus to work. What is the relative change from last year to this year?
(Express your answer rounded correctly to the nearest tenth of a percent!)
A percentage is a way to describe a part of a whole. The relative change from last year to this year is 3.7%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
28.6% of city employees ride the bus to work, therefore, the final value is 28.6. While Last year, 29.7% of city employees rode the bus to work, therefore, the initial value is 29.7.
Since relative change means change with respect to some value. Thus, the relative value with respect to last year is,
Relative value = (29.7-28.6)/29.7 = 0.037 = 3.7%
Hence, the relative change from last year to this year is 3.7%.
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Select the point that is a solution to the system of inequalities.
y≤2x-2
y≤ x²-3x
Both statements are true. Therefore (4,2) is a solution and option D is correct.
The given inequalities are [tex]y\leq 2x-2[/tex] and [tex]y\leq x^{2} -3x[/tex].
We need to select the point that is a solution to the system of inequalities (-2,-1), (1,3), (2,1) and (4,2).
What is an example of a system of inequalities in real life?Inequalities can be seen in the speed limits on roads, the minimum age for seeing certain movies, and the distance you have to walk to go to the park. Inequalities represent a limit of what is permitted or achievable rather than a precise quantity.
Any point is a solution to this system of inequality if it satisfies both inequalities.
Check the inequalities by each option.
For (-2, -1), [tex]-1\leq 2(-2)-2 \implies -1\leq -6[/tex].
This statement is false because -1 is greater than -6. Therefore (-2,-1) is not a solution and option A is incorrect.
For (1, 3), [tex]3\leq 2(1)-2 \implies 3\leq 0[/tex]
This statement is false because 3 is greater than 0. Therefore (1,3) is not a solution and option B is incorrect.
For (2,1), [tex]1\leq 2(2)-2 \implies 1\leq 2[/tex].
[tex]1\leq 2^{2} -3(2) \implies 1\leq -2[/tex]
This statement is false because 1 is greater than -2. Therefore (2,1) is not a solution and option C is incorrect.
For (4,2), [tex]2\leq 2(4)-2 \implies 2\leq 6[/tex]
[tex]2\leq 4^{2} -3(4) \implies 2\leq 4[/tex]
Both statements are true. Therefore (4,2) is a solution and option D is correct.
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This is a lengthy math problem. Help please! Thank you
Step-by-step explanation:
look at the attached and just plot the data. S on the x-axis and s(x) on the y-axis.
The domain of the piecewise function is (-infinity,infinity).
a. Graph the function.
b. Use your graph to determine the function's range.
f(x) =
3x if x≤0
3 if x>0
Answer:
The condantrnirte will be 3x if x is 0 (underfined)
Step-by-step explanation:
I need help with my geometry proof homework from 2-3
Answer: Tbh i don’t know anything besides that all the angles are equal to another and you have to prove it. I would just say: “90 degrees = 90 degrees
Sorry mate I can’t help
Step-by-step explanation:
HELP me find percentage qwq
Answer:
option B or 40%
Step-by-step explanation:
Well if 14/35 of the class is male. You divide 14 by 35. And after using calculator I see the answer is 40% of the class is male.
Thank