the given expression is.,
[tex]\frac{9x}{x-2}=6[/tex][tex]\begin{gathered} 9x=6x-12 \\ 9x-6x=-12 \\ 3x=-12 \\ x=-\frac{12}{3} \\ x=-4 \end{gathered}[/tex]also, the given expression is,
[tex]\frac{7}{x+2}+\frac{5}{x-2}=\frac{10x-2}{x^2-4}[/tex][tex]\begin{gathered} \frac{7x-14+5x+10}{x^2-4}=\frac{10x-2}{x^2-4} \\ 12x-4=10x-2 \\ 12x-10x=4-2 \\ 2x=2 \\ x=\frac{2}{2}=1 \\ x=1 \end{gathered}[/tex]An inverted pyramid is being filled with water at a constant rate of 30 cubic centimeters per second . The pyramíd , at the top, has the shape of a square with sides of length 7cm and the height is 14 cm.
ANSWER :
The answer is 30 cm/sec
EXPLANATION :
We have an inverted square pyramid with a square side of 7 cm and a height is 14 cm.
We need to find the area of the square at 2 cm from below.
Using similar triangles, we will express the side view as 2D :
We need to find the side of the square at 2 cm level.
The ratio of the sides of the smaller triangle and bigger triangle must be the same :
[tex]\begin{gathered} \frac{\text{ smaller}}{\text{ bigger}}=\frac{x}{7}=\frac{2}{14} \\ \\ \text{ Solve for x :} \\ \text{ Cross multiply :} \\ 14x=7(2) \\ 14x=14 \\ x=\frac{14}{14}=1 \end{gathered}[/tex]So the value of x is 1, then the side of the square at 2 cm level is 1 cm
The area of that square is :
A = 1 x 1 = 1 cm^2
The inverted pyramid is filled with water at a constant rate of Q = 30 cm^3 per second.
And we are asked to find the rate when the water level is 2 cm or when the area of the square is 1 cm^2 from the result we calculated above.
Recall the formula of rate :
[tex]\begin{gathered} Q=AV \\ \text{ where :} \\ Q\text{ = constant rate in }\frac{cm^3}{sec} \\ \\ A\text{ = Area of the section in }cm^2 \\ \\ V\text{ = Velocity or rate in }\frac{cm}{sec} \end{gathered}[/tex]We have the following :
[tex]\begin{gathered} Q=30\text{ }\frac{cm^3}{sec} \\ \\ A=1\text{ }cm^2 \end{gathered}[/tex]Using the formula above, the rate is :
[tex]\begin{gathered} Q=AV \\ V=\frac{Q}{A} \\ \\ V=\frac{30\text{ }\frac{cm^{\cancel{3}}}{sec}}{1\text{ }\cancel{cm^2}} \\ \\ V=30\text{ }\frac{cm}{sec} \end{gathered}[/tex]On a circle of radius 9 feet, what angle would subtend an arc of length 7 feet?
________ degrees
The angle subtend an arc length of 7 feet is 44.56°
Given,
Radius of a circle = 9 feet
Arc length of a circle = 7 feet
Arc length :
The distance between two places along a segment of a curve is known as the arc length.
Formula for arc length:
AL = 2πr (C/360)
Where,
r is the radius of the circle
C is the central angle in degrees
Now,
AL = 2πr (C/360)
7 = 2 × π × 9 (C/360)
7 = 18 π (C/360)
7/18π = C/360
C = (7 × 360) / (18 × π)
C = (7 × 20) / π
C = 140 / π
C = 44.56°
That is,
The angle subtend an arc length of 7 feet is 44.56°
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The area of a rectangle is x2 – 8x + 16. The width of therectangle is x – 4. What is the length of the rectangle?-
To answer this question, we need to remember that the area of a rectangle is given by:
[tex]A_{\text{rectangle}}=l\cdot w[/tex]And we have - from the question - that:
[tex]A_{\text{rectangle}}=x^2-8x+16[/tex]And the width of the rectangle is:
[tex]w=x-4[/tex]If we factor the polynomial that represents the area, we need to find two numbers:
• a * b = 16
,• a + b = -8
And both numbers are:
• a = -4
,• b = -4
Since
• -4 * -4 = 16
,• -4 - 4 = -8
Therefore, we can say that:
[tex]x^2-8x+16=(x-4)(x-4)=(x-4)^2[/tex]Therefore:
[tex]l\cdot w=A_{\text{rectangle}}[/tex][tex]l=\frac{A_{rec\tan gle}}{w}[/tex]Then the length of the rectangle is:
[tex]l=\frac{x^2-8x+16}{x-4}=\frac{(x-4)(x-4)}{x-4}\Rightarrow\frac{x-4}{x-4}=1[/tex][tex]l=\frac{(x-4)}{(x-4)}\cdot(x-4)\Rightarrow l=x-4[/tex]In summary, therefore, the length of the rectangle is x - 4.
[tex]l=x-4[/tex][We can check this result if we multiply both values as follows:
[tex]A_{\text{rectangle}}=l\cdot w=(x-4)\cdot(x-4)=(x-4)^2_{}[/tex]And we already know that the area of the rectangle is:
[tex]x^2-8x+16=(x-4)^2[/tex].]
Find (and classify) the critical points of the following function and determine if they are local max, local min, or neither: f(x) =2x^3 + 3x^2 - 120x
As given by the question
There are given that the function:
[tex]f(x)=2x^3+3x^2-120x[/tex]Now,
To find the critical point, differentiate the given function with respect to x and put the result of function equal to zero
So,
[tex]\begin{gathered} f(x)=2x^3+3x^2-120x \\ f^{\prime}(x)=6x^2+6x-120 \end{gathered}[/tex]Then,
[tex]\begin{gathered} f^{\prime}(x)=0 \\ 6x^2+6x-120=0 \\ x^2+x-20=0 \\ x^2+5x-4x-20=0 \\ x(x+5)-4(x+5) \\ (x-4)(x+5) \\ x=4,\text{ -5} \end{gathered}[/tex]Now,
To find the y-coordinate, we need to substitute the above value, x = 4, -5, into the function f(x)
So,
First put x = 4 into the given function:
[tex]\begin{gathered} f(x)=2x^3+3x^2-120x \\ f(4)=2(4)^3+3(4)^2-120(4) \\ =128+48-480 \\ =-304 \end{gathered}[/tex]And,
Put x = -5 into the function f(x):
[tex]\begin{gathered} f(x)=2x^3+3x^2-120x \\ f(-5)=2(-5)^3+3(-5)^2-120(-5) \\ =-250+75+600 \\ =425 \end{gathered}[/tex]Hence, the critical point is, (4, -304) and (-5, 425).
Now,
To find the local maxima and local minima, we need to find the second derivative of the given function:;
So,
[tex]\begin{gathered} f^{\prime}(x)=6x^2+6x-120 \\ f^{\doubleprime}(x)=12x+6 \end{gathered}[/tex]Now,
The put the value from critical point into the above function to check whether it is maxima or minima.
So,
First put x = 4 into above function:
[tex]\begin{gathered} f^{\doubleprime}(x)=12x+6 \\ f^{\doubleprime}(4)=12(4)+6 \\ f^{\doubleprime}(4)=48+6 \\ f^{\doubleprime}(4)=54 \\ f^{\doubleprime}(4)>0 \end{gathered}[/tex]And,
Put x = -5 into the above function
[tex]\begin{gathered} f^{\doubleprime}(x)=12x+6 \\ f^{\doubleprime}(-5)=12(-5)+6 \\ f^{\doubleprime}(-5)=-60+6 \\ f^{\doubleprime}(-5)=-54 \\ f^{\doubleprime}(-5)<0 \end{gathered}[/tex]Then,
According to the concept, if f''(x)>0 then it is local minima function and if f''(x)<0, then it is local maxima function
Hence, the given function is local maxima at (-5, 425) and the value is -54 and the given function is local minima at point (4, -304) and the value is 54.
If quadrilateral WXYZ is transformed using the rule T(-1.2), in whatdirections should WXYZ be translated?O 1 unit down, 2 units rightO 1 unit left, 2 units upO 1 unit up, 2 units leftO 1 unit right, 2 units up
The entire company went in together to buy lottery tickets. Inside the safe are two different types of lottery tickets. The Mega Million Tickets cost $5 each and the Scratch Off Tickets cost $2 each. They bought 60 tickets totaling $246. what are my x and y variables?x=y=
we have the following system
[tex]\begin{gathered} \begin{cases}x+y=60 \\ 5x+2y=246\end{cases} \\ \end{gathered}[/tex]where x is the number of mega million ticktets and y the number of scratch off tickets, so we have that y=60-x and we get that
[tex]\begin{gathered} 5x+2(60-x)=246 \\ 5x-2x+120=246 \\ 3x=126 \\ x=\frac{126}{3}=42 \end{gathered}[/tex]so they bought 42 mega million tickets and 18 scratch off
Write a proportional that relates the corresponding sides. You must use all of the sides for both triangles in your statement.
Given
Answer
[tex]\Delta HGF\approx\Delta HKL[/tex]GF is proportional to KL
HG is proportional to HK
HF is proportional to HL
I'll send a pic of the problem
Weare given a graph that relates the number of strawberries to the number of containers in pairs (x, y)
being x the number of containers, and y the number of strawberries.
The points of the graph read:
(3. 57)
(5, 95)
(7, 133)
(9, 171)
and we are asked to find the proportionality between those values.
We then calculate the slope that joins the points, using for example the first two pairs:
slope = (y2 - y1) / (x2 - x1)
in our case:
slope = (95 - 57) / (5 - 3) = 38 / 2 = 19
we check this same type of calculation with another pair of points to see if it holds true as well:
slope = (171 - 133) / (9 - 7) = 38 / 2 = 19
So we can answer that the proportionality is 19 strawberries per container.
Question 3
If your rectangular yard is 8 feet wide and requires 160 pieces of sod that are cut into 1 foot squares. how
long is it?
The length of the rectangle yard is 2 feet.
What is a rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can also be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is an irregular shape with four equal sides.So, the length f the rectangular yard:
Width is 8 feet.Requires 160 pieces of sod.Then 160ft² is the area of the rectangular yard.
Now, calculate the length as follows:
A = l × w160 = l × 80l = 160/80l = 2 feetTherefore, the length of the rectangle yard is 2 feet.
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What is the solution for the system given below 4x + 8y = 20 and -4x + 2y = -30
You have the folloiwng system of equations:
4x + 8y = 20
-4x + 2y = -30
In order to solve the previous system, proceed as follow:
Sum the equations and solve for y:
4x + 8y = 20
-4x + 2y = -30
10y = -10
Divide by 10 both sides
y = -10/10
y = -1
Now, replace the previous value of y into the any of the equations of the system, for instance, into the first equation and solve for x:
4x + 8y = 20
4x + 8(-1) = 20
4x - 8 = 20
add 8 boht sides, simlplify and divide by 4 both sides:
4x = 20 + 8
4x = 28
x = 28/4
x = 7
Hence, the solution of the given system of equations is given by:
x = 7
y = -1
Please explain in depth. Thank you in advance for a response.
We have the function:
[tex]y=f(t)=(-18t-3)\cdot(t-2).[/tex]a. Zeros of the function
By definition, the zeros are the values of t such that f(t) = 0. In this case, we have:
[tex]f(t)=(-18t-3)\cdot(t-2)=0\text{.}[/tex]Rewriting the function, we have:
[tex]f(t)=(-18)\cdot(t+\frac{1}{6})\cdot(t-2)=0.[/tex]So the zeros of the function are:
[tex]\begin{gathered} t=-\frac{1}{6}, \\ t=2. \end{gathered}[/tex]b. Meaning of the zeros
The function y = f(t) represents the height of the ball at time t.
• So the zeros are the times at which the function reaches a height equal to zero.
,• We see that one zero is positive and the other negative. Only the positive zero (t = 2) is meaningful because the negative (t = -1/6) represents a negative value of time!
c. Initial height
The ball is thrown at time t = 0. The height of the ball at time t = 0 is:
[tex]y=f(0)=(-18\cdot0-3)\cdot(0-2)=(-3)\cdot(-2)=6.[/tex]So the ball is thrown from a height of 6 feet.
Answer
• a., The zeros are t = -1/6 and t = 2.
,• b., The zeros are the values of time at which the height of the ball is zero. Only a positive value of time makes sense, so only the zero t = 2 is meaningful.
,• c., The ball is thrown from a height of 6 feet.
a leaky faucet drips 5 teaspoons of water every 3 hours how long will it take the leaky faucet to drip 75 teaspoons of water
∵ 5 teaspoons of water dropped every 3 hours
∵ We need to find the time taken for 75 teaspoons
→ By using the ratio method
→ Time: teaspoons
→ 3 : 5
→ h : 75
→ By using cross multiplication
∵ 5 x h = 3 x 75
∴ 5h = 225
→ Divide both sides by 5 to find h
∴ h = 45
It will take 45 hours
Juliet has a choice between receiving a monthly salary of $1750 from a company or a base salary of $1600 and a 3% commission on the amount of furniture she sells during the month. For what amount of sales will the two choice be equal?The two salary choices will be equal when the amount of sales is [$ ]
For an amount of sales of $5,000, the two salary choice will be equal
Let the amount of sales be $x
The 3% she will receive will be;
[tex]\frac{3}{100}\times x\text{ = 0.03x}[/tex]We add this to the base salary and equate to the former monthy salary
We have this as;
[tex]\begin{gathered} 1750\text{ =1600 + 0.03x} \\ 1750-1600\text{ = 0.03x} \\ 150\text{ = 0.03x} \\ x\text{ = }\frac{150}{0.03} \\ x\text{ = \$5000} \end{gathered}[/tex]Passing through (- 4,-7) and (1,3) What is the equation of the line in point-slope form
To calculate the equation of the line passing through the points ( -4. -7) and (1, 3):
[tex]\begin{gathered} \text{ Equation of the line can be calculated by the formula } \\ y-y_1=m(x-x_1) \end{gathered}[/tex]where m = slope
(x1, y1) = any of the points given; say points (-4, -7). That is x1= -4, y1 = -7
To calculate the slope, m:
[tex]\begin{gathered} \text{ m = }\frac{y_2-y_{1_{}}}{x_2-x_1}_{} \\ \text{ where }(x_2,y_2)\text{ = (1, 3)} \\ m\text{ = }\frac{3\text{ - (-7)}}{1-(-4)} \\ m=\text{ }\frac{3+7}{1+4}\text{ = }\frac{10}{5} \\ m=2 \end{gathered}[/tex][tex]\begin{gathered} \text{ substituting m = 2, x}_1=-4,y_1=-7\text{ into the formula }y-y_1=m(x-x_1) \\ we\text{ have} \\ y-(-7)=2(x-(-4)\text{ )} \\ y+7=\text{ 2(x+ 4)} \end{gathered}[/tex]The equation of the line in point slope form is y + 7 = 2(x + 4)
Freya counted then number of cars that came to a complete stop at stop sign. of the 25 cars, 13 cars came to a complete stop. if Freya observes the next 75 cars that reach the stop sign, how many cars can she expect to come to a complete stop?
The expected value can be calculated with the formula
[tex]E(x)=x\cdot p(x)[/tex]Where p represents the probability, and x represents the new event.
Basically, we just have to find the probability of the 13 cars
[tex]p(x)=\frac{13}{25}=0.52[/tex]Then, we multiply by the numbers of cars x = 75.
[tex]E(75)=75\cdot0.52=39[/tex]Hence, the right answer is 39. The expected value is 39.4x^{3}=3y+2x^{3}y^{3}
Answer: This would be the answer to your question!!
Step-by-step explanation:
The graph of a toy car's speed y
over time x is a parabola that
shows a minimum speed of 2 m/s
after 3 seconds. After 5 seconds,
the car's speed is 3 m/s. What is
the equation in vertex form of the
parabola?
The equation in vertex form of the parabola is y=-1/30(x+23/2)²+529/120
Y axis represends the toy car's speed
X axis represents time
y=ax²+bx+c
c=0
y=ax²+bx
2=9a+3b multiplied with -5
-10 = -45a -15b........equation 1
3=25a+5b multiplied with 3
9 = 75a + 15b............equation 2
adding equation 1 and 2
9-10=75a-45a+15b-15b
30a=-1
a=-1/(30)
2=9×(-1/30)+3b
3b=2+3/10=23/10
b=23/30
y=-1/30 x²+23/30=-1/30(x²+23x+(23/2)²)+1/30 ×(529/4)
y=-1/30(x+23/2)²+529/120
Therefore, the equation in vertex form of the parabola is y=-1/30(x+23/2)²+529/120
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Sergio believes he is five years younger than double the age of Chloe and Chloe believes she is five yearsolder than half of Sergio's age. Are they both right?
Let S represent Sergio's age
Let C represent Chloe's age
Sergio believes he is five years younger than double the age of Chloe. This would be expressed as
S = 2C - 5
Chloe believes she is five years older than half of Sergio's age. This means that
C = 5 + S/2
If we multiply the second equation by 2, it becomes
2C = 10 + S
This means that both equations are not the same. Therefore, they are not right
Set A is the set of all whole numbers to 20. Set B is the set of all odd integers between 8 and 18. How many numbers do the two sets have in common?
ANSWER
5 numbers they have in common
EXPLANATION
Set A has all whole numbers to 20:
[tex]A\colon1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20[/tex]Set B has only odd integer between 8 and 18:
[tex]B\colon9,11,13,15,17[/tex]We can see that set B is inside set A, because it has whole numbers that are less than 20, so the amount of numbers they have in common is all of set B: 5 numbers.
Hiwhat is 18×18[tex]18 \times 18[/tex]
The answer for 18 x 18 is 324.
A car rental company’s standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function S = 15.75+0.50 M, where M is the number of miles driven. The company also offers an option to ensure the car against damage. The insurance charge I in dollars is given by the function I = 5.70+0.15 M. Let C be the total cost in dollars for a rental that includes insurance. Write an equation relating C to M.
Answer:
[tex]C\text{ = 0.65 M + 21.45}[/tex]Explanation:
Here, we want to write an equation that relates C to M
From the given question, we have to add the insurance to the standard charge to get the total cost
Mathematically:
[tex]C\text{ = S + I}[/tex]Now, we substitute the values for both S and I
That would be:
[tex]\begin{gathered} C\text{ = 15.75 + 0.50M + 5.70 + 0.15 M} \\ C\text{ = 0.65M + 21.45} \end{gathered}[/tex]if Em=11, Am=16,CF=27, What are the lengths of the following sides
We will have the following:
First, we calculate AE as follows:
[tex]AE=\sqrt[]{AM^2-EM^2}[/tex]Now, we replace values and solve it:
[tex]AE=\sqrt[]{16^2-11^2}\Rightarrow AE=3\sqrt[]{15}[/tex]From theorem AE = EC therefore EC = esqrt(15); so, the following is true:
[tex]AC=AE+EC\Rightarrow AC=2AE\Rightarrow AC=2(3\sqrt[]{15})\Rightarrow AC=6\sqrt[]{15}[/tex]Knowing this, we then determine FA as follows:
[tex]FA=\sqrt[]{AC^2-CF^2}[/tex]We then determine BE, DM & CM as follows:
Answer this fraction based Question I will make you btainliest & provide you 50 points
Answer:
i) 2/3, ii) 2/9,iii) 4/27,iv) Rs. 40000.Step-by-step explanation:
i)A person gives 1/3 of his wealth to his wife, then he is left with:
1 - 1/3 = 2/3 of the total amountii)Then he gives 1/3 of the remainder to his son, the son gets:
2/3*1/3 = 2/9 of the total amountiii)The remaining portion is:
2/3 - 2/9 = 6/9 - 2/9 = 4/9 of the total amountEach daughter gets 1/3 of it as there are three daughters:
4/9 * 1/3 = 4/27 of the total amountiv)If the total amount is x, the son gets 2/9x and a daughter gets 4/27x and the difference of the two is Rs 20000:
2/9x - 4/27x = 200006/27x - 4/27x = 200002/27x = 20000x = 20000*27/2x = 270000This is the total amount.
The amount obtained by a daughter is:
4/27*270000 = 40000The exponential function that represents an experiment to track the growth of agroup bacterial cells is f(x) = 2200(1.03)*, where f(x) is the number of cells and x isthe time in minutes.• Sketch this scenario, including variables, title, axes and appropriate scales.• How many bacterial cells were there to begin the experiment?• What is the percentage growth of the bacterial cells per minute?• How many bacterial cells are there after one-half hour? Round to the nearestthousand.• How long will it take for there to be 7500 bacterial cells? Round your answerto the nearest whole minute?
For this problem we are going to be working with the function:
[tex]f(x)=2200(1.03)^x[/tex]where x is the time in minutes and f(x) represents the number of bacteria at any given time x.
Part 1.
To sketch the graph we need to determine some points of it; to get them we give values to x and plug them in the expression for the funtion.
If x=0 we have that:
[tex]\begin{gathered} f(0)=2200(1.03)^0 \\ f(0)=2200 \end{gathered}[/tex]Then we have the point (0,2200).
If x=10 we have that:
[tex]\begin{gathered} f(10)=2200(1.03)^{10} \\ f(10)=2956.616 \end{gathered}[/tex]Then we have the point (10,2956.616).
If x=20 we have that:
[tex]\begin{gathered} f(20)=2200(1.03)^{20} \\ f(20)=3973.445 \end{gathered}[/tex]Then we have the point (20,3973.445).
If x=30 we have that:
[tex]\begin{gathered} f(30)=2200(1.03)^{30} \\ f(30)=5339.977 \end{gathered}[/tex]Then we have the point (30,5339.977).
If x=40 we have that:
[tex]\begin{gathered} f(40)=2200(1.03)^{40} \\ f(40)=7176.483 \end{gathered}[/tex]Then we have the point (40,7176.483).
If x=50 we have that:
[tex]\begin{gathered} f(50)=2200(1.03)^{50} \\ f(50)=9644.593 \end{gathered}[/tex]Then we have the point (50,9644.593).
Then we have the points (0,2200), (10,2956.616), (20,3973.445), (30,5339.977), (40,7176.483) and (50,9644.593). Plotting this points on the plane and joining them with a smooth line we have that the grah of the function is:
Part 2.
To determine how many bacteria were at the beginnning of the experiment we plug x=0 in the function describing the population, we did this in the previous question; therefore we conclude that there were 2200 bacteria at the beginning of the experiment.
Part 3.
We notice that the function fgiven has the form:
[tex]f(x)=a(1+r)^x[/tex]where a=2200 and r=0.03; for this type of function the growth rate in decimal form is given by r. Therefore we conclude that the percentage growth in this function is 3%.
Part 4.
To determine how many bacteria were in the experiment after one half hout we plug x=30 in the function give; we did this in part 1 of the proble.Therefore we conclude that after one half hour there were approximately 5340 bacteria cells. (for this part we roun to the neares whole number)
Part 5.
To determine how long it takes to have 7500 cells we plug f(x)=7500 in the expression given and solve the resulting equation for x:
[tex]\begin{gathered} 2200(1.03)^x=7500 \\ 1.03^x=\frac{7500}{2200} \\ 1.03^x=\frac{75}{22} \end{gathered}[/tex]To remove the base we need to remember that:
[tex]b^y=x\Leftrightarrow y=\log _bx[/tex]Then we have:
[tex]\begin{gathered} 1.03^x=\frac{75}{22} \\ x=\log _{1.03}(\frac{75}{22}) \end{gathered}[/tex]Now we use the change of base property for logarithms:
[tex]\log _bx=\frac{\ln x}{\ln b}[/tex]Then we have:
[tex]\begin{gathered} x=\log _{1.03}(\frac{75}{22}) \\ x=\frac{\ln (\frac{75}{22})}{\ln 1.03} \\ x=41.491 \end{gathered}[/tex]Therefore it takes 41 minutes to have 7500 cells.
Rebecca must complete 15 hours of volunteer work. She does 3 hours each day.
For the linear equation that represents y, the hours Rebecca still has to work after x days, what does the y-intercept represent?
The y-intercept represents the hours Rebecca must work.
How to represent linear equation?Linear equation can be represented in slope intercept from, point slope form and standard form.
Therefore, in slope intercept form it can be represented as follows:
Hence,
y = mx + b
where
m = slopeb = y-interceptShe must complete 15 hours of volunteer work. She does 3 hours each day. Let's represent Rebecca situation in linear form.
where,
y = hours Rebecca still has to work
x = the number of days
Therefore,
y = 15 - 3x
The y-intercept is 15 which implies the number of hours she must complete.
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The number of hours Rebecca must work is represented by the y-intercept in the linear equation.
What is the linear equation?An equation is said to be linear if the power output of the variable is consistently one.
The linear equation is y = mx + c, where m denotes the slope and c is its intercept.
Given that she is required to put in 15 hours of volunteer work. Each day, she works three hours.
As per the given situation,
If x represents the number of days and y represents the number of hours she must work
So the linear representation shows Rebecca's situation will be:
y = 15 - 3x
Therefore, the number of hours Rebecca must work is represented by the y-intercept in the linear equation.
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The product of two consecutive positive even integers is 48. Find the greatest positive integer.
From that statement we can create the following equation,
[tex]n\cdot \left(n+2\right)=48[/tex]solving for n,
[tex]\begin{gathered} n^2+2n=48 \\ n^2+2n-48=0 \\ n_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:1\cdot \left(-48\right)}}{2\cdot \:1} \\ n_{1,\:2}=\frac{-2\pm \:14}{2\cdot \:1} \\ n_1=\frac{-2+14}{2\cdot \:1},\:n_2=\frac{-2-14}{2\cdot \:1} \\ n=6,\:n=-8 \end{gathered}[/tex]We can only use the positive number for this problem, therefore n = 6
From the above, the set of numbers is 6 and 6+2=8, since 6*8=48.
Answer: the greatest integer is 8
A student sketched some art on an 8-inch x 10-inch piece of paper. She wants to resize it to fit a 4-inch x 6 inchframe (as shown below).What percent of the original sketch was still able to be included in the frame?
So,
The area of art can be found multiplying:
8in * 10in = 80in²
And, the area of the frame, can be also found multiplying the dimentions:
4in * 6in = 24in².
If we divide, we'll obtain a ratio between the area of the frame and the area of the art as follows:
[tex]\frac{24}{80}=0.3[/tex]And, 0.3*100% = 30%.
So,30 percent of the original sketch was still able to be included in the frame.
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Answer:
(see attached image)
Step-by-step explanation:
Imagine that there is a line drawn at y=x, when a problem wants you to "show the inverse of a function", imagine that y=x acts as a mirror and you have to make the "reflection" of your given function across that mirror.
There are 45 boys and 81 girls in a dance competition. What is the ratio of boys to girls, in the simplest form?
Answer
[tex]\frac{5}{9}[/tex]Explanation
Given
• 45 boys
,• 81 girls
Procedure
We have to find the ratio of boys to girls, which can be written as 45:81 or:
[tex]\frac{45}{81}[/tex]However, we have to simplify. Both numbers are multiple of 9, thus:
[tex]=\frac{\frac{45}{9}}{\frac{81}{9}}=\frac{5}{9}[/tex]Then every five boys there are 9 girls.
If you are not knowledgeable in college algebra please let me know so I can move on more quickly. Thanks in advance!
Given polynomial is
[tex]3x^5-4x^4-5x^3-8x+25[/tex]We have to check whether the polynomial x-2 is a factor.
If x-2 is a factor then x = 2 is a root of the given polynomial.
Substitute x = 2 in the given polynomial,
[tex]\begin{gathered} 3.2^5-4.2^4-5.2^3-8.2+25=96^{}-64-40-16+25 \\ =121-120=1 \end{gathered}[/tex]Hence 2 is not a root of given polynomial.
And so x - 2 is not a factor.