Answer:
Explained.
Step-by-step explanation:
The graph of a line on the coordinate system represents the points that are on the graph that will satisfy the equation of the line.
Now, if two lines on the coordinate plane are graphed and they pass through the same point (h,k) that means the point satisfies both the equations of the lines.
Let us have two curve equations [tex]y = 2^{(- x)}[/tex] and [tex]y = 4^{x} + 3[/tex] and they pass through the same point (h,k) on the coordinate plane.
Then we can write [tex]k = 2^{(- h)}[/tex] ......... (1) and
[tex]k = 4^{h} + 3[/tex] .......... (2)
Now, solving equations (1) and (2) we get
[tex]2^{(- h)} = 4^{h} + 3[/tex] ........... (3)
Therefore, we have to solve the above equation (3) to get the value of h i.e. the x-coordinate of the point/s where the graph of the equations (1) and (2) intersect.
Now, converting h to x we will get the same result. (Answer)
Bryce buys a treadmill online for $510. If shipping and handling are an additional 21 [tex]\frac{1}{2}[/tex] percent of the price, how much shipping and handling will Bryce pay?
Answer:
The shipping and handling charge that Bryce paid is $109.65
Step-by-step explanation:
Given as :
The online price of the treadmill = $510
The charge of shipping and handling = 21[tex]\dfrac{1}{2}[/tex] % of online price
Let The shipping and handling charge that Bryce paid = $x
Now, According to question
∵ The charge of shipping and handling = 21[tex]\dfrac{1}{2}[/tex] % of online price
So, x = [tex]\dfrac{43}{2}[/tex] % of $510
Or, x = [tex]\dfrac{43\times 510}{100\times 2}[/tex]
Or, x = $109.65
The shipping and handling charge that Bryce paid = x = $109.65
Hence,The shipping and handling charge that Bryce paid is $109.65 Answer
Only answer 28 ( I added this parentheses so that the thing would accept my question)
Answer:
(a). Number of protons in a chlorine atom = 17
(b). Atomic number of sodium = 11
Step-by-step explanation:
Let the number of protons in a sodium atom = x
Then, the number of protons in a chlorine atom = x + 6
Now, it is given that the atomic number of an element is equal to the number of protons per atom.
So, atomic number of sodium (Na) = x
Atomic number of chlorine (Cl) = x + 6
It is given that the atomic number of chlorine is 5 less than twice the atomic number of sodium.
∴ atomic number of chlorine (Cl) = 2 × atomic number of sodium (Na) - 5
⇒ x + 6 = 2x - 5
⇒ x - 2x = -5 - 6
⇒ -x = -11
Cancelling the minus sign from both sides, we get
x = 11
(a). Number of protons in a chlorine atom = x + 6
= 11 + 6 (∵ x = 11)
= 17
(b). Atomic number of sodium = x = 11
Complete the equation of the line through
(-8,8) and (1,-10).
use exact numbers
Y=
Answer:
Step-by-step explanation:
Find the equation of the line thru the points (2,1) and (3,5)
---------------------
This is a 2 step process. First find the slope of the line thru the points.
slope, m = diffy/diffx
m = (5-1)/(3-2)
m = 4
---------
Now use y = mx + b with either point to find b, the y-intercept.
y = mx + b
5 = 4*3 + b
b = -7
-------
Answer:
Step-by-step explanation:
Formula for calculating the equation of a line is expressed as shown below;
y = mx+c OR y-y1 = m(x-x1) where
m is the slope or gradient
c is the intercept (the point where the line cuts the y axis)
m = ∆y/∆x
m = y2-y1/x2-x1
Given the points (-8,8) and (1,-10).
x1 = -8, y1 = 8, x2 = 1, y2 = -10
m = -10-8/1-(-8)
m = -18/9
m = -2
The equation of a line can also be written as a point slope:
y-y1 = m(x-x1)
Substituting the value of x1, y1 and m into the equation we have;
y-8 = -2(x-(-8))
y-8 = -2(x+8)
y-8 = -2x-16
y= -2x-16+8
y = -2x-8
The equation of the line is y = -2x-8
In a certain country, the heights and depths of a road are measured in relation to sea level. Sea level has a value of 0. The lowest point of the country lies at −9 feet. The highest point of the country lies at +108 feet. Which of the following statements best describes the lowest and the highest points?
1. The lowest point is 9 feet below sea level, and the highest point is 108 feet above sea level.
2. The lowest point is 9 feet above sea level, and the highest point is 108 feet below sea level.
3. The lowest point is 9 feet below sea level, and the highest point is 108 feet above the lowest point.
4. The lowest point is 9 feet above sea level, and the highest point is 108 feet below the lowest point.
Answer:
1. The lowest point is 9 feet below sea level, and the highest point is 108 feet above sea level.
Step-by-step explanation:
The sea level is considered to be zero levels.
Now, the level +x feet means it is at x feet higher than sea level and the level -x feet means it is at x feet lower than the sea level.
Now, the lowest point of the country lies at −9 feet. The highest point of the country lies at +108 feet.
That means, the lowest point is 9 feet below sea level, and the highest point is 108 feet above sea level. (Answer)
(Easy Points, Will mark Brainliest) What number is point A on the number line?
Answer:
1/4
Step-by-step explanation:
There are 7 points from 0 to 7/4. This means each point represents 1/4. Therefore A is 1/4
Answer:
1/4
Step-by-step explanation:
If you count back from the 7/4, A will be at the 1/4 point.
Hope this helps :)
Round 5.19424860514 tho the 6 decimal
Answer:
It would be 5.1942486
Step-by-step explanation:
Becuase the 0 is after the 6 the 6 stays as it is and there is no need to round up or down
We're starting with 5.19424860514, and we need to round to the 6th decimal. 1st, we need to identify the 6th place. In this case, that is 8. Everything before that is the same no matter what. 5.19424 is our base. We need to look at the 860514. More specifically, the 86. 6 is over 4, so the 8 becomes a 9 using basic rounding rules. Therefore, our final answer is 5.194249
Hope this helps!
Type the correct answer in each box. Use numerals instead of words.
Consider this quadratic equation.
x^2 + 2x + 7 = 21
The number of positive solutions to this equation is____.
The approximate value of the greatest solution to the equation, rounded to the nearest hundredth, is____.
Answer:
1 positive solution
2.87.
Step-by-step explanation:
x^2 + 2x + 7 = 21
x^2 + 2x - 14 = 0
The product of its roots = c/a = -14 so it will have 1 positive solution.
x = -2 +/- sqrt (2^2 - 4*-14) / 2
x = -1 +/- sqrt60/2
= -1 +/- 3.873
GreATest solution is 2.87
40% of the children in a sports club play badminton. 25% of the children who play badminton also play squash. There are 11 children in the club who play both badminton and squash.
How many children are there in the sports club altogether?
Answer:
There are 110 children total in the sports club
Step-by-step explanation:
To get this answer, its actually easier than it seems. You might need a calculator however.
First you start with the 11 children who play both badminton and squash, then, you divide that by 0.25 (25%) to get 44.
Next you take 44 and divide it by 0.4 (40%) to get 110.
And there you go! If you want to make sure you got it right simply start with 110 and multiply it by 0.4 then multiply the number/decimal you get by 0.25. You should get 11 to confirm your answer :)
Y=10,000(0.97)x predict purchasing power of $10,000 ten years later
Answer:
It will be $7602.3
Step-by-step explanation:
The equation [tex] y = 10000(0.97)^{x}[/tex] gives the purchasing power of $10000 after x years.
Therefore, the sum of money $10000 will value [tex] 10000(0.97)^{x}[/tex] after x number of years.
Now, after 9 years i.e. x = 9 years, the sum value of $10000 will become [tex] y = 10000(0.97)^{9} = 10000 \times 0.76023 = 7602.3[/tex] dollars. ( Answer )
Mei works as a tutor during the school year. She charges her next door neighbor $9 an hour, which is a 40% discount from her regular hourly rate. What is the hourly rate, h, Mei Charges before the discount?
Mei charges $15 per hour as her regular hourly rate before applying a 40% discount to her next door neighbor, resulting in a discounted rate of $9 per hour.
To calculate the regular hourly rate Mei charges before the 40% discount, we set up an equation where the discounted rate is equal to 60% of the original rate, because 100% - 40% = 60%. Mei charges her neighbor $9 per hour after the discount. Let h represent Mei's regular hourly rate before the discount.
So, the equation would be 0.60h = $9. To find h, we divide both sides of the equation by 0.60:
h = $9 / 0.60
h = $15
Thus, Mei's regular hourly rate before the discount is $15 per hour.
Mei's regular hourly rate before the discount is $15.
To find Mei's regular hourly rate before the discount, let's denote it as h .
Given that Mei offers her neighbor a 40% discount, her neighbor pays only 60% of the regular rate. This can be represented as:
[tex]\[ 0.60h = 9[/tex]
To find ( h ), we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.60:
[tex]\[ \frac{0.60h}{0.60} = \frac{9}{0.60} \][/tex]
This simplifies to:
[tex]\[ h = \frac{9}{0.60} \][/tex]
Now, we can calculate:
[tex]\[ h = \frac{9}{0.60} = 15 \][/tex]
So, Mei's regular hourly rate before the discount is $15.
A quadrilaterals consecutive angles measure (3x+10), (9x+50), (4x), and (13x+10). Determine the value of x.
The value of x is 10
Step-by-step explanation:
We know that the sum of internal angles of a quadrilateral is 360 degrees
So,
Given
Angle 1 = A1 = 3x+10
Angle 2 = A2 = 9x+50
Angle 3 = A3 = 4x
Angle 4 = A4 = 13x+10
So,
[tex]A_1+A_2+A_3+A_4 = 360\\(3x+10)+(9x+50)+(4x)+(13x+10) = 360\\3x+10+9x+50+4x+13x+10 = 360\\3x+9x+4x+13x+10+50+10 = 360\\29x+70 = 360[/tex]
Subtracting 70 from both sides
[tex]29x+70-70 = 360-70\\29x = 290[/tex]
Dividing both sides by 29
[tex]\frac{29x}{29} = \frac{290}{29}\\x = 10[/tex]
Hence,
The value of x is 10
Keywords: Angles, Quadrilateral
Learn more about angles at:
brainly.com/question/725998brainly.com/question/7128279#LearnwithBrainly
What is 12001 ➗ 4180
Answer:
2.871052631578947
Step-by-step explanation:
this is exactly the answer.
3. Haley, Chuck, Dana, and Chris enter a contest to see who could bake the most chocolate chip cookies in an hour. Haley bakes 50, Chuck bakes 65, and Dana bakes 90. If they bake and average of 75 cookies, how many cookies does Chris bake?
Chris baked 95 cookies.
Step-by-step explanation:
Given,
Cookies baked by Haley = 50
Cookies baked by Chuck = 65
Cookies baked by Dana = 90
Average of them = 75
Let,
Cookies baked by Chris = x
Average = [tex]\frac{Sum\ of\ quantites}{No.\ of\ people}[/tex]
[tex]75=\frac{50+65+90+x}{4}[/tex]
Multiplying both sides by 4
[tex]4*75=\frac{50+65+90+x}{4}*4\\300=205+x\\300-205=x\\95=x\\x=95[/tex]
Chris baked 95 cookies.
Keywords: addition, average
Learn more about addition at:
brainly.com/question/11286417brainly.com/question/12884373#LearnwithBrainly
Given that (-3,5) is on the graph of f(x), find the corresponding point for the function f(x) - 4.
Answer:
(- 3, 1 )
Step-by-step explanation:
Given f(x) then f(x) + c represents a vertical translation of f(x)
• if c > 0 then shift up by c units
• if c < 0 then shift down by c units
Thus for f(x) - 4
(- 3, 5 ) → (- 3, 5 - 4 ) → (- 3, 1 )
For the given expression, which whole number (w) will make the expression true
5/6<w/8
3
4
5
7
Answer:
7Step-by-step explanation:
[tex]\dfrac{5}{6}<\dfrac{w}{8}\Rightarrow\dfrac{w}{8}>\dfrac{5}{6}\qquad\text{multiply both sides by 8}\\\\8\!\!\!\!\diagup\cdot\dfrac{w}{8\!\!\!\!\diagup}>8\!\!\!\!\diagup^4\cdot\dfrac{5}{6\!\!\!\!\diagup_3}\\\\w>\dfrac{20}{3}\\\\w>6\dfrac{2}{3}\\\\7>6\dfrac{2}{3}[/tex]
Answer: D ) 7
Step-by-step explanation:
7 is greater than 5
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what is ¾” x 6” x 10’ ?
Answer:
3/4 * 6 x 10 = 45/1 = 45
Step-by-step explanation:
Multiple: 3/4 * 6 = 3 · 6/4 · 1 = 18/4 = 9 · 2/2 · 2 = 9/2
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(18, 4) = 2. In the following intermediate step, cancel by a common factor of 2 gives 9/2.
In other words - three quarters multiplied by six is nine halfs.
Multiple: the result of step No. 1 * 10 = 9/2 * 10 = 9 · 10/2 · 1 = 90/2 = 45 · 2/1 · 2 = 45
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(90, 2) = 2. In the following intermediate step, cancel by a common factor of 2 gives 45/1.
In other words - nine halfs multiplied by ten is forty-five.
I need help with this problem
will mark as brainliest
Answer:
The shop can cut the cost of production per sandwich to $3.75. The revenue function would then be defined as R(x)=9x.
Step-by-step explanation:
We want to make as big profit as possible by making as little sandwiches as possible. This means that we want the profit, which is [tex]revenue- production\: cost[/tex] to be as big as possible.
For the first choice the profit per sandwich is [tex]8.25-4=4.25[/tex] dollars.
For the second choice the profit per sandwich is [tex]9-3.75=5.25[/tex] dollars.
For the third choice the profit per sandwich is [tex]8.5-3.5=5[/tex] dollars.
We see here that for the second choice the profit is greatest, therefore this choice is most suitably correct.
which system of inequalities is represented by the graph?
Answer:
[tex]y\leq 2x+4[/tex]
[tex]y\geq -x-6[/tex]
Step-by-step explanation:
step 1
Find the equation of the solid line with positive slope
we have the points
(0,4) and (-2,0)
Find the slope
[tex]m=(0-4)/(-2-0)=2[/tex]
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=2\\b=4[/tex]
substitute
[tex]y=2x+4[/tex]
step 2
Find the equation of the inequality with positive slope
we know that
The solution of the inequality, is the shaded area below the solid line
so
The equation of the inequality is
[tex]y\leq 2x+4[/tex] ----> inequality A
step 3
Find the equation of the line with negative slope
we have the points
(-6,0) and (-4,-2)
Find the slope
[tex]m=(-2-0)/(-4+6)=-1[/tex]
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=2\\point\ (-6,0)[/tex]
substitute
[tex]0=-(-6)+b[/tex]
solve for b
[tex]0=6+b[/tex]
[tex]b=-6[/tex]
so
The linear equation is
[tex]y=-x-6[/tex]
step 4
Find the equation of the inequality with negative slope
we know that
The solution of the inequality, is the shaded area above the solid line
so
The equation of the inequality is
[tex]y\geq -x-6[/tex] ----> inequality B
therefore
The system of inequalities is
[tex]y\leq 2x+4[/tex] ----> inequality A
[tex]y\geq -x-6[/tex] ----> inequality B
Each box contains 10 to the power of 2 pencils. The school store has 15 boxes of pencils. How many pencil does the school store have
Answer:
1500
Step-by-step explanation:
10×10=100
100×15=1500
A line passes though the points (7, 10) and (7, 20). Which statement is true about the line? It has a slope of zero because x2-x1 in the formula m=
Answer:
It has no slope because (x2-x1) in the formula [tex]m=\frac{y2-y1}{x2-x1}[/tex] is equal to zero, and the denominator of a fraction cannot be zero
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
the points (7, 10) and (7, 20)
substitute the values
[tex]m=\frac{20-10}{7-7}[/tex]
[tex]m=\frac{10}{0}[/tex] ----> is undefined
The line has a slope undefined ---> is a vertical line (parallel to the y-axis)
Reggie Means invested part of $31,000 in municipal bonds that earn 7.5% annual simple interest and the remainder of the money in 8.5% corporate bonds. How much is invested in each account if the total annual interest earned is $2,475?
Answer:
Principal Invested in Municipal Bonds is $16,000
Principal Invested in Corporate Bonds is $15,000
Step-by-step explanation:
If;
Principal Invested in municipal bonds = a
Principal Invested in corporate bonds = b
then we have;
a + b = $31,000 --------------------------------Equation 1
0.075a + 0.085b = $2,475 ---------------Equation 2
From equation 1 we have;
a = 31,000 - b
By putting the values of a in Equation 2 we get;
0.075 (31,000 - b) + 0.085b = 2,475
2,325 - 0.075b + 0.085b = 2,475
0.01b = 150
b = $15,000
By putting the values of b in equation 1 we get;
a = $16,000
Final answer:
Reggie Means invested $16,000 in municipal bonds at 7.5% interest and $15,000 in corporate bonds at 8.5% interest to earn a total annual interest of $2,475.
Explanation:
Let the amount invested in municipal bonds be $x. Thus, the amount invested in corporate bonds will be $(31,000 - x). The municipal bonds earn 7.5% annual interest and the corporate bonds earn 8.5% interest. The total annual interest from both investments is $2,475.
To calculate the interest from municipal bonds, use the formula Interest = Principal × Rate × Time. The interest from municipal bonds is 0.075x (since 7.5% is the same as 0.075).
Similarly, for corporate bonds, the interest will be 0.085(31,000 - x). The sum of these interests equals $2,475:
0.075x + 0.085(31,000 - x) = 2,475
Solving this equation:
Multiply through by 100 to clear decimals: 7.5x + 8.5(31,000 - x) = 247,500Distribute the 8.5 and combine like terms: 7.5x + 263,500 - 8.5x = 247,500Simplify and solve for x: x = (247,500 - 263,500) / (7.5 - 8.5)Calculate x to find the amount invested in municipal bonds: x = $16,000. Therefore, the amount in corporate bonds is $16,000.How do you graph
y=3x and y=-x-8
Answer:
The points for the given two linear equation as
[tex]x_1 , y_1[/tex] = - 2 , - 6
[tex]x_2 , y_2[/tex] = - 2 , 6
The graph so plotted as shown
Step-by-step explanation:
Given as :
The two linear equation are
y = 3 x ........A and
y = - x - 8 .........B
Solving equation A and B
Now, Put The value of y from eq A into eq B
So, 3 x = - x - 8
Or, 3 x + x = - 8
Or, 4 x = - 8
∴ x = [tex]\dfrac{-8}{4}[/tex]
I.e x = - 2
Now , Put the value of x into eq A
∵ y = 3 x
∴ y = 3 × (-2)
I.e y = - 6
Again, Put the value of x into eq B
∵ y = - x - 8
∴ y = - 2 - (-8)
I.e y = 6
So, for x = - 2 , y = - 6
And for x = - 2 , y = 6
Hence , The points for the given two linear equation as
[tex]x_1 , y_1[/tex] = - 2 , - 6
[tex]x_2 , y_2[/tex] = - 2 , 6
The graph so plotted as shown . Answer
37/50 of a number is what percent of that number
Answer:
The answer is 74%
Step-by-step explanation:
Method One:
1) Un-reduce the fraction to ger 74/100
2) Your answer is 74%
Method 2:
1) Divide 37 by 50
2) You get .74
3) Your answer is 74%
The cost of cleaning a rectangular ground is $120 per square m. Calculate the price to be paid if theatre length of ground is 145m and breadth is 85m
Answer:
it will cost $ 14,79,000
Step-by-step explanation:
Area of the rectangular theatre ground=L*B= 145*85= 12,325 m²
Cost of cleaning per square metre = $ 120
Total cost of cleaning = $120* 12,325= $ 14,79,000
Rafael is on his way home in his car. His drive is 22 miles long. He has finished one-half of the drive so far, how far has he driven
Answe
Step-by-step explanation:
he has drive 11 miles of his drive
if you divide 22 by 2 it equals 11
Please help I will mark previous
Answer:
[tex] \frac{5}{16}, \: 31.25\%[/tex]
5x+10 and 7x-12 are vertical angles, what is the value of x
Answer:
x = 11
Step-by-step explanation:
Vertical angles mean that their values are equivalent, which means that:
5x + 10 = 7x -12
Solve for x
22 = 2x
x = 11
Hope this helps :)
PLEASE HELP!!!
Acar depreciates at a rate kf 13% per year. the car was originally purchased for 28,000.
1. what is the decay factor of the car?
2. Wrtie a function for this situation with the value if the car as a function of the age of the car in years
3. How much will the car be worth in 6 years?
4. Rewrite the function for question 2 so it is an equivalent function with a negative exponent.
The country of Freedonia has decided to reduce its carbon-dioxide emission by %35 each year. This year the country emitted 40 million tons of carbon-dioxide. Write a function that gives Freedonia's carbon-dioxide emissions in million tons, E(t), t years from today.
[tex]E(t) = 40(0.65)^t[/tex]
Step-by-step explanation:
Given,
Current quantity of emission, P = 40 millions,
Reduction in emission per year, r = 35% = 0.35,
Thus, the quantity of emission after t years,
[tex]E(t)=P(1-r)^t[/tex]
[tex]E(t) = 40(1-0.35)^t[/tex]
[tex]\implies E(t) = 40(0.65)^t[/tex]
Which is the required function.
To represent Freedonia's carbon-dioxide emissions E(t), t years from now with a yearly reduction of 35%, use the function E(t) = 40 * (0.65)^t, where 40 million tons is the current emission and 0.65 is the remaining percentage of emissions after reduction.
Explanation:The student is asking to write a function that models the carbon-dioxide emissions of Freedonia in million tons, E(t), t years from today, given that the emissions are being reduced by 35% each year. The current emission level is 40 million tons of carbon-dioxide.
To create this function, we need to take into account the exponential decay of the emissions due to the percentage reduction. The general form for exponential decay is given by the equation E(t) = E_0 × (1 - r)^t, where E_0 is the initial amount, r is the rate of reduction (as a decimal), and t is the time in years. For Freedonia, E_0 is 40 million tons, and r is 0.35. Therefore, the equation becomes E(t) = 40 × (1 - 0.35)^t.
Explain how to find 3 × 5 × 2
Answer:
30
Step-by-step explanation:
3x5=15
15x2=30
Answer:
30
Step-by-step explanation:
Multiply 3 by 5 which is 15 and them multiply by 2 which is 30