V= l*w*h
V=90
l=10
h=3
Replace the values in the expression and clear w
V= l*w*h
90=10*w*3
90=30w
w=3
If twice the age of a stamp is added to the age of a coin, the result is 45. The difference between three times the age of a stamp and the age of a coin is 5. What is the age of the stamp?
10 years
1) Considering that we can call the age of a stamp by "s" and the age of a coin by "c" we can write out the following system of Linear Equations:
[tex]\begin{gathered} 2s+c=45 \\ 3s-c=5 \end{gathered}[/tex]Note that we can solve it using the Elimination Method.
2) So let's add simultaneously both equations:
[tex]\begin{gathered} 2s+c=45 \\ 3s-c=5 \\ -------- \\ 5s=50 \\ \frac{5s}{5}=\frac{50}{5} \\ s=10 \end{gathered}[/tex]We can plug into that s=10 and find the age of a coin as well:
[tex]\begin{gathered} 2(10)+c=45 \\ c=45-20 \\ c=20 \end{gathered}[/tex]Note that we subtracted 20 from both sides.
3) Hence, the age of a stamp is 10 years
I need help with this. Also, i’m aware you can’t see all the graphs listed so just let me know what coordinates would be appropriate and i’ll choose whichever graph has those coordinates.
Answer: Provided the sunglasses inventory which has the number of sunglasses and days in two columns, we have to find the graph which represents this table.
The table can be modeled by a linear equation:
[tex]\begin{gathered} y(x)=mx+b\Rightarrow(1)\Rightarrow\text{ y glasses as function of days x} \\ \\ \end{gathered}[/tex]Finding the slope and y intercept of this equation (1) leads to the following:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{(42-58)}{(10-2)}=\frac{-16}{8}=--2 \\ \\ \\ \\ y(x)=-2x+b \\ \\ 58=-2(2)+b\Rightarrow b=58+4=62 \\ \\ \\ \therefore\Rightarrow \\ \\ y(x)=-2x+62\Rightarrow(2) \end{gathered}[/tex]The answer, therefore, is the plot of equation (2) which is as follows:
I am having a tough time solving this problem from my prep guide, can you explain it to me step by step?
The range in the average rate of change in temperature of the substance is from a low temperature of -[tex]22^{0}[/tex]F to a high of [tex]16^{0}[/tex]F
The domain of the function f(x) = sin x includes all real numbers, but its range is −1 ≤ sin x ≤ 1. The sine function has different values depending on whether the angle is measured in degrees or radians. The function has a periodicity of 360 degrees or 2π radians.
Given f(x) = -19sin(7/3x + 1/6) – 3
We have to the range in the average rate of change in temperature of the substance is from a low temperature of ___F to a high of ___F
We know that the range of sin x is [-1, 1]
f(x) = -19 sin(7/3x + 1/6) – 3
We know
-1 ≤ sin(7/3x + 1/6) ≤ 1
Now multiply with -19 on both sides
19 ≥ -19sin(7/3x + 1/6) ≤ -19
-19 ≤ -19sin(7/3x + 1/6) ≤ 19
Now subtract 3 from both sides
-19 - 3 ≤ -19sin(7/3x + 1/6) - 3 ≤ 19 - 3
-22 ≤ -19sin(7/3x + 1/6) ≤ 16
-22 ≤ f(x) ≤ 16
Therefore the range in the average rate of change in temperature of the substance is from a low temperature of -220F to a high of 160F
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A 76.00 pound flask of mercury costs $150.50. The density of mercury is 13.534 g/cm3.It takes 4.800 in^3 of mercury to make one manometer. Find the price of the mercury used to make 21 manometers by first calculating the cost of mercury for one manometer.What is the price of mercury used to make one manometer?
Price of one pound of mercury is derived as follows;
[tex]\begin{gathered} Price\text{ of 1lb of merc}=\frac{Cost\text{ of flask}}{Pounds\text{ of merc in the flask}} \\ \text{Price of 1 lb}=\frac{150.50}{76} \\ \text{Price of 1 lb}=1.98 \end{gathered}[/tex]This means 1 pound of mercury costs $1.98
1 pound = 453.6 grams
Therefore;
[tex]\begin{gathered} 1lb=453.6gms \\ 76lb=34,473.6gms \end{gathered}[/tex]The price of 1 gram of mercury would be;
[tex]\begin{gathered} Price\text{ of 1 gram}=\frac{Price\text{ per pound}}{\text{grams in 1 lb}} \\ \text{Price of 1 gram}=\frac{1.98}{453.6} \\ \text{Price of 1 gram}=0.004365 \end{gathered}[/tex]This means 1 gram of mercury costs $0.004365
Note that you have 13.534 grams per cubic centimeter of mercury. Therefore, the price of 1 cubic centimeter of mercury shall be calculated as follows;
[tex]\begin{gathered} \text{Price of 1 cubic cm}=grams\text{ per cubic cm x price of 1 gram} \\ \text{price of 1 cubic cm}=13.534\times0.004365 \\ \text{Price of 1 cubic cm}=0.059 \end{gathered}[/tex]This means 1 cubic centimeter of mercury would cost $0.059
Note also that, 1 cubic inch = 16.387 cubic centimeters. Hence,
[tex]\begin{gathered} Price\text{ of 1 cubic inch}=16.387\text{ cubic cm x }price\text{ of 1 cubic cm} \\ \text{Price of 1 cubic inch}=16.387\times0.059 \\ \text{Price of 1 cubic inch}=0.9668 \end{gathered}[/tex]This means 1 cubic inch costs $0.9668
It takes 4.800 cubic inches to make 1 manometer.
Therefore, the cost of 4.800 cubic inches would be;
[tex]\begin{gathered} Price\text{ of 4.800 cubic inches}=Price\text{ of 1 cubic inch x 4.800 cubic inches} \\ Price\text{ of 4.800 cubic inches}=0.9668\times4.800 \\ \text{Price of 4.800 cubic inches}=4.64 \end{gathered}[/tex]If it costs 4.800 cubic inches to make 1 manometer, then the cost of 1 manometer would be $4.64
Therefore, to make 21 manometers, we would have;
[tex]\begin{gathered} 1\text{ manometer}=4.64 \\ 21\text{ manometers}=21\times4.64 \\ 21\text{ manometers}=97.44 \end{gathered}[/tex]ANSWER:
The price of mercury required to make 21 manometers would be $97.44
A boat sails directly away from a skyscraper located on the edge of a large lake. The skyscraper is 120 meters tall. A photographer on the boat is taking pictures of the skyscraper with a camera that has a 28° viewing lens.
Let's begin by identifying key information given to us:
[tex]\begin{gathered} Height(h)=120m \\ \theta=28^{\circ} \\ d=\text{?} \end{gathered}[/tex]We will use the Trigonometric ratio (SOHCAHTOA) to solve for d. In this case, we will use ''TOA''
[tex]\begin{gathered} TOA\Rightarrow tan\theta=\frac{opposite}{adjacent} \\ tan\theta=\frac{opposite}{adjacent} \\ opposite\Rightarrow height=120m \\ adjacent\Rightarrow d \\ \theta=28^{\circ} \\ tan28^{\circ}=\frac{120}{d} \\ d\cdot tan28^{\circ}=120 \\ d=\frac{120}{tan28^{\circ}}=225.687\approx226 \\ d=226m \end{gathered}[/tex]what is 3(x+5) 12 please help I’ve been stuck on it
Given data:
The given inequality is 3(x+5) >12.
The given inequality can be written as,
[tex]\begin{gathered} 3\mleft(x+5\mright)>12 \\ 3x+15>12 \\ 3x>-3 \\ x>-1 \\ x\in(-1,\text{ }\infty) \end{gathered}[/tex]The graph of the above solution is,
Thus, the solution of the given inequality is (-1, ∞).
Need immediate help on 2 questions for my test tomorrow
The data that can be determined from the box plots are
a)
This is because the line in the middle of the box plot is the median of the box plot.
b)
The upper quartile of a box plot is the part of the box plot that is to the right of the line. In this case the median line is at the same location and the upper quartile ends at the same location.
and
The data that can not be determined is
c)
The reason this can not be determined is because the median is the average of the grades. This could mean some students scored in the higher levels and more scored below the median, which in turn drags it down.
d)
Would be following the same reason as C. It can be determined that there was a larger range lower grades in period 5 over period 3, but it can't be determined how many.
1.Orange paint uses 3 parts yellow to 2 parts red.The equation y=3/5t can be used to find the cups of yellow paint when given the total cups of paint.Use the equation to complete the table.t. 0 5 10 15 20 25 y _ _ _ _ _ _2.plot the point in the column in the table in problem 1.Then draw a line to represent the equation.3.The equation r=2/5t can be used to find the cups of red paint when given the total cups of paint.Draw a line represent the equation.
we have the equation
y=(3/5)t
so
Find the values of y for different valyes of t
For t=0
y=(3/5)(0)
y=0
For t=5
y=(3/5)(5)
y=3
For t=10
y=(3/5)(10)
y=6
For t=15
y=(3/5)(15)
y=9
For t=20
y=(3/5)(20)
y=12
For t=25
y=(3/5)(25)
y=15
Solve the following system of equations using the elimination method. Note that the method of elimination may be referred to as the addition method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, enter INFINITELY MANY.)20x − 5y = 208x − 2y = 8(x, y) =
Given
The system of equations,
20x − 5y = 20
8x − 2y = 8
To find: The solution.
Explanation:
It is given that,
20x − 5y = 20 _____(1)
8x − 2y = 8 _____(2)
That implies,
Divide (1) by 5 and (2) by 2.
Then, (1) and (2) becomes,
4x - y = 4.
Hence, there is infinitely many solution.
2x + 2/3y= -2 x, y intercept
We need to find the points at which the expression below intercept the axis of the coordinate plane:
[tex]2x+\frac{2}{3}y=-2[/tex]To find the "x" intercept we need to find the value of "x" that results in a value of "y" equal to 0. We have:
[tex]\begin{gathered} 2x+\frac{2}{3}\cdot0=-2 \\ 2x+0=-2 \\ 2x=-2 \\ x=\frac{-2}{2}=-1 \end{gathered}[/tex]To find the "y" intercept we need to find which value of "y" the function outputs when we make x equal to 0.
[tex]\begin{gathered} 2\cdot0+\frac{2}{3}y=-2 \\ \frac{2}{3}y=-2 \\ 2y=-6 \\ y=\frac{-6}{2}=-3 \end{gathered}[/tex]The x intercept is -1 and the y intercept is -3.
Which of the following functions have the ordered pair (2, 5) as a solution?4 + x = yy = 2 x7 - x = yx + 3 = y
Given
The ordered pair (2,5).
To find which of the functions have the ordered pair as a solution.
Explanation:
It is given that,
The ordered pair (2,5).
Then, put x=2, and y=5 in the function x+3=y.
That implies,
[tex]\begin{gathered} 2+3=5 \\ 5=5 \end{gathered}[/tex]Hence, the ordered pair (2,5) is a solution of the function x+3=y.
Also, substitute x=2, y=5 in the function 7-x=y.
That implies,
[tex]\begin{gathered} 7-2=5 \\ 5=5 \end{gathered}[/tex]Hence, the ordered pair (2,5) is a solution of the function 7-x=y.
Solve. 15 = 4n- 5solve for nn=
15 = 4n -5
Add 5 to both sides of the equation
15 +5 = 4n -5 + 5
20 = 4n
Divide both sides by 4:
20/4 = 4n /4
5 = n
n= 5
Find the area of a circle with a circumferenceof 261 feet.
It is given that Circumference of circle is 26П feet
The expression for the Circumference of circle is 2Пr.
So,
[tex]\begin{gathered} 2\Pi r=26\Pi \\ r=\frac{26\Pi}{2\Pi} \\ r=13 \end{gathered}[/tex]Radius of the circle is 13 feet
The expression for the area of circle is ПRadius²
[tex]\begin{gathered} \text{Area of circle =}\Pi\times r^2^{} \\ \text{Area of circle=3.14}\times13\times13 \\ \text{Area of circle = 530}.93\text{ f}eet^2 \end{gathered}[/tex]Answer: 530.9
A carnival ride is in the shape of a wheel with a radius of 25 feet. The wheel has 20 cars attached to the center of the wheel. Use 3.14 for pi and round answers to the nearest hundredth, if applicable.a.) What is the measure of each central angle between any two cars? (4 points)b.) What is the arc length of each sector between any two cars? (4 points)c.) What is the area of each sector between any two cars?
The carnival ride is in shape of wheel with 25ft radius.
The wheel has 20 cars attached to the center of the wheel. Since the cars are evenly distributed, we can thus find the
the measure of the angle between each car by dividing 360 degrees by 20.
#A:
The measure of each central angle between any two cars is:
[tex]\frac{360}{20}=18^0[/tex]#B:
Hence, we can find the length of the arch between any two cars is given by the length of arc formula given below:
[tex]\begin{gathered} \frac{\theta}{360}\times2\pi r \\ \text{where,} \\ r=\text{radius} \\ \theta=\text{measure of each central angle betw}een\text{ two cars} \end{gathered}[/tex]Let us calculate this length below:
[tex]\begin{gathered} \theta=18^0 \\ \frac{18}{360}\times2\pi\times25 \\ =2.5\pi=7.85\text{ (to the nearest hundredth)} \end{gathered}[/tex]#C:
We are asked to find the area of each sector between two cars.
The area of a sector of a circle is:
[tex]\frac{\theta}{360}\times\pi\times r^2[/tex]Since we have all the parameters, let us calculate this area:
[tex]\begin{gathered} Area=\frac{18}{360}\times\pi\times25^2 \\ \\ Area=98.13\text{ (to nearest hundredth)} \end{gathered}[/tex]Therefore, the final answers are:
#A: angle = 18 degrees
#B length = 7.85 feet
#C Area = 98.13 squared feet
hello, please help me solve to find the correct polynomials!
INFORMATION:
We have the next polynomials
And we must factor them to complete the next table
STEP BY STEP EXPLANATION:
1.
[tex]x^2-8x+15[/tex]To factor it, we must look for two number that multiplied be equal to 15 and added up be equal to -8.
These two numbers would be -5 and -3.
- -5 x -3 = 15
- -5 - 3 = -8
So, when we factor this polynomial, we obtain
[tex]\begin{gathered} x^2-8x+15=(x-5)(x-3) \\ \text{ So, }a=1,b=-5,c=1,d=-3 \end{gathered}[/tex]2.
[tex]2x^3-8x^2-24x[/tex]To factor it, we must first take the common factor 2x from the expression
[tex]2x(x^2-4x-12)[/tex]Now, we must factor the terms in the parenthesis. We must look for two number that multiplied be equal to -12 and added up be equal to -4. These two numbers would be -6 and 2.
- -6 x 2 = -12
- -6 + 2 = -4
So, when we factor this polynomial, we obtain
[tex]\begin{gathered} 2x(x+2)(x-6) \\ \text{ So, }a=1,b=2,c=1,d=-6 \end{gathered}[/tex]3.
[tex]6x^2+14x+4[/tex]To factor it, we must first take the common factor 2 from the expression
[tex]2(3x^2+7x+2)[/tex]Then, we divide the 7x term in the parenthesis in two terms
[tex]2(3x^2+6x+x+2)[/tex]Now, we can take the common factor x + 2 in the parenthesis
[tex]2(3x(x+2)+(x+2))[/tex]Finally, we can take the common factor x + 2 in the complete expression
[tex]\begin{gathered} 2(x+2)(3x+1) \\ \text{ Simplifying,} \\ =\left(3x+1\right)(2x+4) \\ \text{ So, }a=3,b=1,c=2,d=4 \end{gathered}[/tex]ANSWER:
Amy bought a car in 2009 valued at $32,500. The car is expected to depreciate at a rateof 11.1% annually. In how many years will Amy's vehicle be worth 50% of its originalvalue? Round your answer to the nearest tenth of a year,
ANSWER :
5.9 years
EXPLANATION :
Exponential function can be expressed as :
[tex]y=A(1\pm r)^t[/tex]where A = initial amount
r = (+) growth or (-) decay rate
t = time
y = amount after t years
From the problem, the initial value of the car is A = $32,500
It depreciates at a rate of 11.1% annually, so r = -11.1% or -0.111
The value of the car will be 50% of its original value, so y = 0.50(32,500) = $16,250
Using the formula above :
[tex]\begin{gathered} 16250=32500(1-0.111)^t \\ \frac{16250}{32500}=(0.889)^t \\ \\ 0.5=(0.889)^t \\ \text{ Take the ln of both sides :} \\ \ln(0.5)=\ln(0.889)^t \\ \ln(0.5)=t\ln(0.889) \\ \\ t=\frac{\ln0.5}{\ln0.889}=5.89\sim5.9yrs \end{gathered}[/tex]Graph the linear function using the slope and the y-intercept.y = 2x + 3CORTUse the graphing tool to graph the linear equatium. Use the slope and y-intercept when drawing the line.Click toenlargegraph
Answer:
Explanation:
If we have a linear equation of the form
[tex]y=mx+b[/tex]then m = slope and b = y-intercept.
Now in our case, we have
[tex]y=2x+3[/tex]which means that slope = 2 and y-intercept = 3
Therefore, we graph a line that has a slope of 2 and a y-intercept of 3.
A slope of 2 means that for every step you take to the right on a graph, you move 2 steps up to get to a point on the line.
The y-intercept of 3 means that the line passes through the point (0, 3).
Using these two facts about the line, we draw the following line.
From the above plot, we can clearly see that the line has a slope of 2 and a y-intercept of 3 - the same line described by y = 2x + 3.
Can someone please help me solve #6 on this packet?
The distance between the two camper stations are 60.44 km and 62.95 km. as calculated using the law of sines.
Let us consider the the first ranger station is A and the second ranger station is C and the camper is at the position B.
It is given that AC = 10 km
∠BAC = 100°
∠BCA = 71°
∴∠ABC = 180 - (100 + 71) = 9
Now we will use this to find the distance between each ranger station and the camper by using the law of sines.
From the law of sines we know that :
[tex]{\displaystyle {\frac {a}{\sin {\alpha }}}\,=\,{\frac {b}{\sin {\beta }}}\,=\,{\frac {c}{\sin {\gamma }}}\,}[/tex]
Now we will use this ratio to calculate the other sides of the triangle.
10 / sin 9 = BC / sin 100
or, BC = 10 × sin 100 / sin 9
or, BC = 62.95 km
Again:
10 / sin 9 = AB / sin 71
or. AB = 60.44 km
Therefore the distance between the two camper stations are 60.44 km and 62.95 km.
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A triangle on a coordinate plane is translated according to the rule T-3,5(X,Y) what is another way to write this ?
Given the translation rule as :
[tex]T_{-3,5}(x,y)[/tex]Solution
Another way of writing this is:
[tex](x,\text{ y) }\rightarrow\text{ (}x\text{ - 3, y + 5)}[/tex]This means that the original coordinates (x,y) would be translated 3 units to the left and 5 units upwards to give the new coordinates.
Answer: Option A
What is the horizontal and vertical shift for the absolute value function below?f(x) =|x-5|+1The graph shifts right 5 and up 1.The graph shifts left 5 and up 1.The graph shifts left 5 and down 1.The graph shifts right 5 and down 1.
The correct answer is option A;
The graph shifts right 5 and up 1
If y=kx, where k is a constant, and y=24 when x=6, what is the value of y when x=5?A. 6B. 15C. 20D. 23
First, we will find the value of k
We can do this by sybstituting y=24, x=6 in;
y=kx and then solve for k
24= k(6)
divide both-side of the equation by 6
24/6 = k
4 = k
k=4
Then when x = 5, we will substitute x=5 and k=4 in; y=kx and then solve for y
y= (4)(5)
y = 20
A surveyor wants to find the height of a tower used to transmit cellular phone calls. He stands 125 feet away from the tower and meandered the angle of elevation to be 40 degrees. How tall is the tower?
Given
Answer
[tex]\begin{gathered} \tan 40=\frac{h}{125} \\ 0,84\times125=h \\ h=105\text{ ft} \end{gathered}[/tex]height of tower is 105 ft
Geometry question - Given: AB and AC are the legs of isosceles triangle ABC, measure of angle 1 = 5x, measure of angle three = 2x + 12. Find measure of angle 2 (reference picture)
Since triangle, ABC is an isosceles triangle because AB = BC
Then the angles of its base are equal
Since the angles of its bases are <2 and <4, then
[tex]m\angle2=m\angle4[/tex]Since <3 and <4 are vertically opposite angles
Since the vertically opposite angles are equal in measures, then
[tex]m\angle3=m\angle4[/tex]Since measure of <3 = 2x + 12, them
[tex]m\angle4=m\angle2=2x+12[/tex]Since <1 and <2 are linear angles
Since the sum of the measures of the linear angles is 180 degrees, then
[tex]m\angle2+m\angle1=180[/tex]Since m<1 = 5x, then
[tex]\begin{gathered} m\angle1=5x \\ m\angle2=2x+12 \\ 2x+12+5x=180 \end{gathered}[/tex]Add the like terms on the left side
[tex]\begin{gathered} (2x+5x)+12=180 \\ 7x+12=180 \end{gathered}[/tex]Subtract 12 from both sides
[tex]\begin{gathered} 7x+12-12=180-12 \\ 7x=168 \end{gathered}[/tex]Divide both sides by 7
[tex]\begin{gathered} \frac{7x}{7}=\frac{168}{7} \\ x=24 \end{gathered}[/tex]Then substitute x by 24 in the measure of <2
[tex]\begin{gathered} m\angle2=2x+12 \\ m\angle2=2(24)+12 \\ m\angle2=48+12 \\ m\angle2=\mathring{60} \end{gathered}[/tex]The measure of angle 2 is 60 degrees
A training field is formed by joining a rectangle and two semicircle. The rectangle is 87m long and 64m wide. What is the length of a training track running around the field? ( Use the value 3.14 pie, and do not round your answer. Be sure to include the correct unit in your answer.)
The legth of running around this track will be the length of both semi-circles plus the two bigger sidesof the rectangle.
The length of a semi -circle is half the length of a circle, and can be expressed as:
[tex]S=\frac{2\pi r}{2}=\pi r[/tex]Where r is the radius of the semi-circle. The diameter of the semi-circles is the same as the smaller sides of the rectangle and its radius is half the diameter, so:
[tex]r=\frac{d}{2}=\frac{64}{2}=32[/tex]So, the total length, as said above, is the sum of the length of both semi-circles plus two times the bigger side:
[tex]\begin{gathered} L=2S+2w \\ L=2\cdot\pi r+2\cdot87 \\ L=2\cdot3.14\cdot32+2\cdot87 \\ L=200.96+174 \\ L=374.96 \end{gathered}[/tex]Al the measures used were in meters and length is given in meters to the first power, so the unit of the result is also meters, or just "m".
Thus the answer is 374.96 m.
Net force = ?Net force = ?16 NThe net force for example A isNAThe net force for example B is NA
Part A
The net force is 4 N up
Part B
The net force is 3 N to the left
What are the coordinates of point B on AC such that the ratio of AB to BC is 5 : 6
We have a segment AC, with the point B lying between A and C.
The ratio AB to BC is 5:6.
The coordinates for A and C are:
A=(2,-6)
C=(-4,2)
We can calculate the coordinates of B for each axis, using the ratio of 5:6.
[tex]\begin{gathered} \frac{x_a-x_b}{x_b-x_c}=\frac{2-x_b}{x_b+4}=\frac{5}{6}_{} \\ 6\cdot(2-x_b)=5\cdot(x_b+4) \\ 12-6x_b=5x_b+20 \\ -6x_b-5x_b=20-12_{} \\ -11x_b=8 \\ x_b=-\frac{8}{11}\approx-0.72\ldots \end{gathered}[/tex]We can do the same for the y-coordinates:
[tex]\begin{gathered} \frac{y_a-y_b}{y_b-y_c}=\frac{-6-y_b}{y_b-2}=\frac{5}{6} \\ 6(-6-y_b)=5(y_b-2) \\ -36-6y_b=5y_b-10 \\ -6y_b-5y_b=-10+36 \\ -11y_b=26 \\ y_b=-\frac{26}{11}\approx-2.36\ldots \end{gathered}[/tex]The coordinates of B are (-8/11, -26/11).
Nimol talks on the phone [tex]3 \frac{1}{2} [/tex] more than his brother. His parents scolded him and asked him to cut down on phone calls.He reduced[tex] \frac{2}{5} [/tex] of the time he used to. How long did his brother spend talking on the Phone.
His brother spent talking on the phone
Step - by - Step Explanation
What to find?
Time Nimol's brother spent talking on phone.
Let x be the time Nimol spent in talking on phone.
Let y be the time Nimol's brother spent talking on phone.
x = y + 3 1/2
x =2/5 ( y + 3 1/2)
Factor the given trinomial. If the trinomial cannot be factored, indicate “not factorable” 6v^5-18v^4-168v^3
The polynomial is given below as
[tex]6v^5-18v^4-168v^3[/tex]Step 1: Factor out the highest common factor which is
[tex]6v^3[/tex][tex]\begin{gathered} 6v^5-18v^4-168v^3=6v^3(\frac{6v^5}{6v^3}-\frac{18v^4}{6v^3}-\frac{168v^3}{6v^3}) \\ 6v^5-18v^4-168v^3=6v^3(v^2-3v-28) \end{gathered}[/tex]Step 2: Factorise the quadratic expression
[tex]v^2-3v-28[/tex]To factorize the quadratic expression, we will have to look for two factors that will multiply each other to give a -28, and then the same two factors will add up together to give -3
By try and error, we will have the two factors to be
[tex]\begin{gathered} -7\times+4=-28 \\ -7+4=-3 \end{gathered}[/tex]By replacing the two factors in the equation above, we will have
[tex]\begin{gathered} v^2-3v-28=v^2-7v+4v-28 \\ \text{group the factors to have} \\ (v^2-7v)+(4v-28)=v(v-7)+4(v-7) \\ v^2-3v-28=(v-7)(v+4) \end{gathered}[/tex]Hence,
[tex]6v^5-18v^4-168v^3=6v^3(v-7)(v+4)[/tex]Therefore,
The final answer is 6v³(v - 7)(v + 4)
Leslie has 3 pounds of peanuts, she uses 1 7/8 pounds to make trail mix. How many pounds does she have left?
What Leslie has is 3 pounds of Peanuts and she has used a fraction of it. That fraction is 1 7/8. To find out how many pounds more she has left, its a matter of subtracting 1 7/8 from 3 whole.
Let the leftover be called x, and you now have;
x = 3 - 1 7/8
Converting the other number to an improper fraction you now have
x = 3 - 15/8
x = 3/1 - 15/8
By using the LCM of both denominators which is 8, the expression now becomes,
x = 24/8 - 15/8
x = 9/8
x = 1 1/8
Les
Use the ordered pairs (3,56) and (7,85) to find the equation of a line that approximates the data. Express your answer in slope-intercept form. If necessary round the slope to the nearest hundredth and the y intercept to the nearest whole number
Equation of a line in slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ \\ m\colon\text{slope} \\ b\colon y-\text{intercept} \end{gathered}[/tex]1. Find the slope: Use two ordered pairs (x,y) in the next formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{Ordered pairs (3,56) and (7,85)} \\ m=\frac{85-56}{7-3}=\frac{29}{4}=7.25 \end{gathered}[/tex]Slope: m=7.25
2. Find the y-interept: Use one ordered pair and the slope to find b:
[tex]\begin{gathered} \text{ordered pair: (3,56)} \\ x=3 \\ y=56 \\ \\ \text{Slope: m=7.25}_{} \\ \\ y=mx+b \\ 56=7.25(3)+b \\ 56=21.75+b \\ 56-21.75=b \\ \\ b=34.25 \\ \\ b\approx34 \end{gathered}[/tex]y-intercept: b= 34
Then, the equation of the line is:[tex]y=7.25x+34[/tex]