Answers
Given:
Given the system of equations:
[tex]\begin{gathered} c+w+p=456 \\ c-p=80 \\ p=2w-2 \end{gathered}[/tex]Required: Solution of the system using Cramer's rule
Explanation:
The system of equations can be rewritten as
[tex]\begin{gathered} c+p+w=456 \\ c-p+0w=80 \\ 0c+p-2w=-2 \end{gathered}[/tex]Write down the augmented matrix.
[tex]\begin{bmatrix}{1} & {1} & {1} & {456} \\ {1} & {-1} & {0} & {80} \\ {0} & {1} & {-2} & {-2} \\ {} & {} & {} & {}\end{bmatrix}[/tex]Calculate the main determinant.
[tex]\begin{gathered} D=\det\begin{bmatrix}{1} & {1} & {1} \\ {1} & {-1} & {0} \\ {0} & {1} & {-2}\end{bmatrix} \\ =1\left(2-0\right)-1\left(-2-1\right) \\ =2+3 \\ =5 \end{gathered}[/tex]Substitute the c-column with RHS and find the determinant.
[tex]\begin{gathered} D_c=\det\begin{bmatrix}{456} & {1} & {1} \\ {80} & {-1} & {0} \\ {-2} & {1} & {-2}\end{bmatrix} \\ =456\left(2-0\right)-80\left(-2-1\right)-2\left(0+1\right) \\ =912+240-2=1150 \end{gathered}[/tex]Substitute the p-column with RHS and find the determinant.
[tex]\begin{gathered} D_p=\det\begin{bmatrix}{1} & {456} & {1} \\ {1} & {80} & {0} \\ {0} & {-2} & {-2}\end{bmatrix} \\ =1(-160-0)-1(-912+2) \\ =-160+910 \\ =750 \end{gathered}[/tex]Substitute the w-column with RHS and find the determinant.
[tex]undefined[/tex]Related Questions
Grace and Maria are practicing for a fitness test. Each day, they do as many curl-ups as they can in 1 min. Which measures could best be used to argue that Maria is better at doing curl-ups than Grace is? Mean MAD Min Q1 Median Q3 Max Grace 36 3.25 30 32.5 37 38.5 43 38 4.5 Maria 24 35.5 39 42.5 45
Answers
For option A:
MAD and IQR:
MAD means Mean Absolute Deviation:
This is the measure that records the deviation from the average number of curl-ups that both girls can do.
Therefore, if the value of MAD is higher, it just means that the person tends to vary by a larger value, on the number of curl-ups she does.
In this question, Maria has a higher MAD of 4.5 while Grace's MAD is 3.25. This means that Grace's curl-ups tend to be closer to the average number of curl-ups she does over a period of time. While Mar
Can 7/20 can be reduced to 3/5
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7/20 can't be reduced to 3/5
(3,5) and (-1,9) slope finding b and writing equation
Answers
Answer:
• Slope, m =-1
,• Equation: y=-x+8
Explanation:
Gien the points: (x1,y1)=(3,5) and (x2,y2)=(-1,9)
Slope
[tex]Slope,m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute the points:
[tex]\begin{gathered} m=\frac{9-5}{-1-3} \\ =\frac{4}{-4} \\ m=-1 \end{gathered}[/tex]The slope of the line is -1.
Equation of the Line
We use the point-slope form to find the equation of the line.
Using point (3,5) and slope, m=-1
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-5=-1(x-3) \\ y-5=-x+3 \\ y=-x+3+5 \\ y=-x+8 \end{gathered}[/tex]The equation of the line is y=-x+8.
A window is 3/4 m high and 2/3 of it is covered with frosted glass. What part of a meter is frosted glass?
Answers
Since 2/3 of the 3/4 m high window is covered with frosted glass, multiply 2/3 by 3/4 to find what part of a meter is frosted glass:
[tex]\frac{2}{3}\times\frac{3}{4}=\frac{2\times3}{3\times4}=\frac{6}{12}=\frac{1}{2}[/tex]Therefore, 1/2 of a meter is frosted glass.
given that triangle DEF is a right triangle with acute angles D and F and right angle E, which trigonometric function would be equal to Sin(F).
Answers
EXPLANATION
We can represent this situation as shown as follows:
The expression of Sin(F) is equal to Sin F = Opposite/Hypotenuse = DE/DF
[tex]\sin F=\frac{Opposite}{\text{Hypotenuse}}=\frac{DE}{DF}[/tex]The equivalent expression would be:
[tex]Cos\text{ D=}\frac{Adjacent}{\text{Hypotenuse}}=\frac{DE}{DF}[/tex]Point K is the center of the circle. Which segment is a radius?FGGEFHKEGDKHE
Answers
SOLUTION
The radius of a circle is a line segment that runs from the center of the circle to any point of the circumference
Hence from the option provided, only the line |KH| runs from the center to a point of the circumference, hence it is a radius
Therefore the right option is the last one
In ∆KLM, l= 56 inches , k =27 inches and < K=10°. Find all possible values of < L, to the nearest degree.
Answers
SOLUTION
In this question, we are meant to find the possible values of
This is just an application of SINE RULE, which says that:
[tex]\begin{gathered} \frac{L}{\sin\text{ L}}\text{ = }\frac{K}{\sin \text{ K}},\text{ we have that:} \\ \\ \frac{56}{\sin\text{ L }}\text{ = }\frac{27}{\sin \text{ 10}} \\ \text{cross}-\text{ multiplying, we have that;} \\ 27\text{ x sin L = 56 X sin 10} \\ \sin L\text{ =}\frac{56\text{ X sin 10}}{27} \\ \sin \text{ L = }\frac{56\text{ X 0.1736}}{27} \\ \\ \sin \text{ L = }\frac{9.\text{ 7216}}{27} \\ \sin L\text{ =0.3600} \\ \text{Taking sine inverse of both sides, we have:} \\ L=21.1^0 \\ L=21^{0\text{ }}(\text{correct to the nearest degr}ee) \end{gathered}[/tex]Steven and his family are traveling out of town for the weekend. They drove 60 miles during the first two hours of the trip. If there are 5280 feet in a mile, which of the following is equivalent to their rate of speed
Answers
The rate of speed is 33 feet/second
The difference between two identical objects that are moving at the same time is the distance they cover is called the rate of speed.
Given that Steven and his family are traveling out of town for the weekend. They drove 60 miles during the first two hours of the trip
We have to find if there are 5280 feet in a mile what is the rate of speed
Distance = 60 miles
Time = 2 hours
The formula for the Rate of speed is given by
Distance travelled / time elapsed = rate of speed
R = d/t
R = 60miles / 2hours
R = 30 miles/hour
Now to determine feet per hour
= 30miles/hour x 5280 feet/mile
= 158400 feet/ hour
To determine feet per second
= 158400feet/hour x 1 hour / 3600sec
= 33 feet/second
Therefore the rate of speed is 33 feet/second
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Write the equation, (2)x+(3)y=(24) in slope-intercept form
Answers
the equation in slope- intercept form:
y = -2x/3 + 8
Explanation:
GIven: (2)x+(3)y=(24)
To write in slope intercept form, we apply the formula for a linear equation:
y = mx + c
where m = slope, c = intercept
2x + 3y = 24
Make y the subject of formula by taking x to the other side of the equation:
3y = -2x + 24
Divide through by 3:
[tex]\begin{gathered} \frac{3y}{3}=\frac{-2x}{3}+\frac{24}{3} \\ y\text{ = }\frac{-2x}{3}+8 \end{gathered}[/tex]when we compare the above equation with the equation of line, they are in alignment.
Hence, the equation in slope- intercept form:
y = -2x/3 + 8
JetLine Airline provides Michael with the following measurements forcarry-on luggage: 14 in x 9 in x 22 in. Convert the dimensions tocentimeters.
Answers
Given that:
Dimensons of luggage = 14 in x 9 in x 22 in
Since 1 inch = 2.54 cm,
[tex]\begin{gathered} 14\text{ in = (14}\cdot2.54)cm \\ =35.56cm \end{gathered}[/tex][tex]\begin{gathered} 9\text{ in=(9}\cdot2.54)cm \\ =22.86cm \end{gathered}[/tex][tex]\begin{gathered} 22\text{ in=(22}\cdot2.54)cm \\ =55.88cm \end{gathered}[/tex]The dimension in centimeters is 35.56 cm x 22.86 cm x 55.88 cm.
Can you please help me solve this? It is for HW
Answers
Use a rule of three to find the number of won games in a season of 120 games.
If the rate is the same, then, you can write:
[tex]\frac{20}{110}=\frac{x}{120}[/tex]Now, solve for x and simplify:
[tex]\begin{gathered} x=\frac{20}{110}\cdot120 \\ x=21.81 \\ x\approx22 \end{gathered}[/tex]Hence, the Panthers would win 22 games
25% of what number w is 9?=25100
Answers
25 % of 36 is 9
Explanation
Step 1
the easy way to find the percentage of any number is:
[tex]\begin{gathered} y\text{ \% of x } \\ total\text{ =x*}\frac{y}{100} \end{gathered}[/tex]so
A) let
25% of what number w is 9?
let
[tex]\begin{gathered} nubmer(x)\text{ = W} \\ percentage\text{ \lparen y\rparen=25 \%} \\ total\text{ =}9 \end{gathered}[/tex]now, replace and solve for w:
[tex]\begin{gathered} y\text{ \% of x } \\ total\text{ =x*}\frac{y}{100} \\ 9=W*\frac{25}{100} \\ 9=W*0.25 \\ divide\text{ both sides by 0.25} \\ \frac{9}{0.25}=\frac{W\times0.25}{0.25} \\ 36=W \end{gathered}[/tex]therefore ,
25 % of 36 is 9
Susan's Jewelry Shop is having a sale on necklaces. The store is offering a sale pack of 4 necklaces for $48.80. What is the unit price of a necklace in the sale pack?
Carly's ClothinStore is also having a sale on necklaces. The unit price of any necklace at Carly's Clothing Store is the same as the unit price of a necklace at Susan's Jewelry Shop How much would it
cost a customer for 10 necklaces at Carly's Clothing Shop?
Answers
Unit Price
The store offers a sales pack of 4 necklaces for $48.80. This means each necklace in this pack has a unit price of:
$48.80 / 4 = $12.20
Now we know the unit price of any necklace at Carly's Clothing Store is the same as the unit price at the competing store. This means each necklace at Carly's Clothing Store has a price of $12.20.
If a customer bought 10 of these necklaces, he would have to pay
10 * $12.20 = $122,00
For 10 necklaces at Carly's Clothing Store, a customer would pay $122
Write each equation in standard form10. y + 1 = x + 213. y - 4 = -(x - 1)16. y - 10 = -2(x - 3)
Answers
Standard form of a line:
Ax + By = C
where A is a positive integer, B is an integer and C is a constant.
10. y + 1 = x + 2
y + 1 - y = x + 2 - y subtracting y at both sides
1 = x + 2 - y
1 - 2 = x + 2 - y - 2 subtracting 2 at both sides
-1 = x - y
13. y - 4 = -(x - 1)
(y - 4)*(-1) = -(x - 1)*(-1) Multiplying by -1 at both sides
-y + 4 = x - 1
-y + 4 + y = x - 1 + y Adding y at both sides
4 = x - 1 + y
4 + 1 = x - 1 + y + 1 Adding 1 at both sides
5 = x + y
16. y - 10 = -2(x - 3)
(y - 10)/(-2) = -2(x - 3)/(-2) Dividing by -2 at both sides
y/-2 +5 = x - 3
2*(y/-2 +5) = 2*(x - 3) Multiplying by 2 at both sides
-y + 10 = 2x + 6
-y + 10 + y = 2x + 6 + y Adding y at both sides
10 = 2x + 6 + y
10 - 6 = 2x + 6 + y - 6 subtracting 6 at both sides
4 = 2x + y
An airplane pilot flies due north from Ft. Myers to Sarasota, a distance of 150 miles. She then turns N50°E and flies to Orlando, a distance of 100 miles How far is it from Ft. Myers to Orlando? Round to the nearest tenths
Answers
115 miles
1) Sketching this to better grasp it we have:
2) Since we could draw the route as a triangle, we can use the Law of Cosines to find out the distance between Fort Myers and Orlando:
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cos (\alpha) \\ x^2=(100)^2+150^2-2(100)(150)\cos (50) \\ x^2=32500-2(100)(150)\cos (50) \\ x^2=13216.37 \\ \sqrt[]{x^2}=\sqrt[]{13216.37} \\ x\approx114.96\approx115 \end{gathered}[/tex]Note that we rounded off to the nearest tenth(114.9).
3) Hence, the answer is 115 miles
A certain town has two kinds of youth basketball teams. When is a school team (S) and the other is a rec team (R) . On any given Saturday in December the probability that school team will have the game is 0.8, and the probability that a rec team will have a game is 0.7 and probably that both where the game is 0.65.on any given Saturday in December, what is the probability that either a rec team or a school team has a game?Answer Choices:A. 0.65B. 0.7C. 0.8D. 0.85
Answers
Answer:
D. 0.85
Explanation:
We were given the following information:
Probability of S = 0.8
Probability of R = 0.7
Probability of S & R = 0.65
The probability that either a rec team or a school team has a game is given by:
[tex]\begin{gathered} P(S)=0.8 \\ P(R)=0.7 \\ P(S\cap R)=0.65 \\ \text{Since the events are overlaaping, the applicable formula is:} \\ P(S\text{ }or\text{ }R)=P(S)+P(R)-P(S\cap R) \\ P(S\text{ }or\text{ }R)=0.8+0.7-0.65 \\ P(S\text{ }or\text{ }R)=1.5-0.65 \\ P(S\text{ }or\text{ }R)=0.85 \\ \\ \therefore P(S\text{o}r\text{R})=0.85 \end{gathered}[/tex]Therefore, the answer is D
g(x)=1/2x. Graph the function and it's parent function and describe the transformation.
Answers
In order to graph the function, we need to know the degree from the function, since there are not exponents it means that this is a linear function that passes through the origin since there is not any y-intercept.
The parent function is
[tex]y(x)=x[/tex]The transformation of the function is to compress the function by a factor of 0.5
Can u help this problem
Answers
-0- -4 -325Determine the range of the function. If the range is a single value, enter the value. If the range is aninterval, write the interval using interval notation. Example: (2,3) or (-00,5). Enter -oo for negativeInfinity and oo for infinityNOTE: If you do not see an endpoint, assume that the graph continues forever in the samedirectionThe range is:Question Help: MessageinstructorOcType here to search
Answers
[-5,-3]
The Range is the set of corresponding outputs for the inputs in the Domain set
So for the function depicted
The Range is
[-5,-3] for these points are included
on the unit circle, in standard position, an angle of which measure is coterminal with an angle that measures pi/4 radians?
Answers
Coterminal angles are defined as the angles which possess the same terminal side.
The given angle measure is π/4 radians.
Consider that one full circle constitutes an angle measure of 2π radians.
So if we add 2π to the given angle, the resultant will represent the same terminal side.
[tex]undefined[/tex]some similarities and differences of xy plane and the complex plane
Answers
The difference between the xy plane and the complex plane is that in the first one we are representing an ordered pair (that is, two numbers) while in the complex plane we are representing only one number (but this number can be decomposed in an real part and an imaginary part).
Now, they are similar in that the construction is the same, that is, they are both made of two perpendicular lines that we call axis, the intersection is called the origin and is represented by the zero in each set.
all you need is on the photo pleaseeeee i really need help
Answers
We can find the y-intercept evaluating the function for x = 0, so:
[tex]\begin{gathered} y(x)=-5x^2+20x+60 \\ y(0)=-5(0)^2+20(0)+60=0+0+60 \\ y(0)=60 \end{gathered}[/tex]---------
We can find the zeros evaluating the function for y = 0. So using the factored form:
[tex]\begin{gathered} -5(x-6)(x+2)=0 \\ so\colon \\ x1=6 \\ and \\ x2=-2 \end{gathered}[/tex]-----------------------------------------------
The vertex V(h,k) is given by:
[tex]\begin{gathered} h=\frac{-b}{2a} \\ k=y(h) \end{gathered}[/tex]Or we can find it directly from the vertex form:
[tex]\begin{gathered} y=a(x-h)^2+k \\ so \\ for \\ y=-5(x-2)^2+80 \\ h=2 \\ k=80 \end{gathered}[/tex]So, the vertex is:
[tex](2,80)[/tex]---------
The symmetry axis is located at the same point of the x-coordinate of the vertex, so the axis of symmetry is:
[tex]x=2[/tex]-----------------------
The maximum value is located at the y-coordinate of the vertex (if it is positive) so, the maximum value is:
[tex]y=80[/tex]Yousef is cutting pieces of construction paper so he can make cards for his family . Each piece of paper is 11 1/2 inches wide. If he cuts that width so he would have two equal-sized smaller pieces, how wide will each smaller piece be? rocine she wants to try requires
Answers
The total width of each piece of paper:
[tex]\begin{gathered} W\text{ = 11}\frac{1}{2}\text{inches} \\ W\text{ = }\frac{23}{2}\text{inches} \end{gathered}[/tex]Yousef cuts the piece of paper into two pieces of paper of equal widths:
Let each of the smaller pieces have a width of w
W = 2w (since the smaller pieces have equal widths)
[tex]\begin{gathered} \frac{23}{2}=\text{ 2w} \\ 23\text{ = 4w} \\ \frac{23}{4}=\text{ w} \\ w\text{ = 5}\frac{3}{4}in \end{gathered}[/tex]tem = 462-5 h 1995. Central High School had a student population of 2250 students. By 2005, the student population was only 1.800 students. What is the percent of decrease in the student population? A 2002 B. 25% C. 75% D. 80% tem = 119766
Answers
Central High School had a student population of 2250 students.
By 2005, the student population was only 1.800 students.
What is the percent of decrease in the student population?
A 2002
B. 25%
C. 75%
D. 80%
Percentage of decrease = 100 - 100 * (1800/2250) = 100 - 100 * 0.8 = 100 - 80 = 20%
Circle O shown below has an arc of length 34 inches subtended by an angle of 2.1 radians. Find the length of the radius, x, to the nearest tenth of an inch.
Answers
16.2 inches
Explanation
the arc length is given by the formula:
[tex]\begin{gathered} arclength=\theta r \\ where\text{ } \\ r\text{ is the radius } \\ \theta\text{ is the angle in radians} \end{gathered}[/tex]so
Step 1
a)let
[tex]\begin{gathered} r=x\text{ \lparen unknown\rparen} \\ angle=\theta=2.1\text{ rad} \\ arclength\text{ = 34 inches} \end{gathered}[/tex]b) now, replace in the formula and solve for x
[tex]\begin{gathered} arclength=\theta r \\ 34\text{ inches=2.1 rad*x} \\ divide\text{ both sides by 2.1 rad} \\ 16.19\text{ inches =x} \\ rounded \\ x=16.2\text{ inches} \end{gathered}[/tex]
therefore, the answer is
16.2 inches
I hope this helps you
derermine if the whole numbers exhibit the closure property for the indicated ooerations or not. if not provide a counter example to justify your conclusion
Answers
EXPLANATION
Addition:
If we add two or more whole numbers, the result will be also a whole number.
Hence, they exhibit the closure property.
Subtraction:
If we subtracti two or more whole numbers, the result will not necessarily be a whole number. For example, subtraction 5-10 give us -5 --> Not a whole number. [NOT CLOSURE PROPERTY]
Division:
The division of two whole numbers could not necessarily be a whole number, as for instance, 6/12 = 1/2 [NOT CLOSURE PROPERTY]
if the inequality -8 < x > 10 was placed in interval notation it would be represented by
Answers
It would be represented by interval notation (-8,10].
Interval notation:
The collection of real numbers that are located between two numbers is known as an interval in mathematics. The starting and ending numbers will be shown using brackets in the interval notation method. There are two different styles of brackets on it: square and round. The end values are included if the interval is given in square brackets. The end values are not included when an interval is given in round brackets.
Instance: [7, 12] It refers to the range of values between 7 and 12, with 12 included but not 7.
Complete question:
If the inequality -8<x≤10 was placed in interval notation it would be represented by
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69). If a restaurant's gross receipts for one day total $39.500, of which $5,600 are expenses that percent of the gross receipts are expenses?
Answers
Total receipts = $39,500
Expenses = $5,600
Percentage expenses =
[tex]\frac{5600}{39500}\times100=\frac{5600\times100}{39500}=14.177\approx14.2\text{ \%}[/tex][tex]\text{ \% expenses =}\frac{Actual\text{ expenses}}{\text{Total Receipts}}\times\frac{100}{1}[/tex]Solution: The percentage of expenses is 14.2%
Find the terminal point on the unit circle determined by π2 radians.Use exact values, not decimal approximations.
Answers
Okay, here we have this:
Considering the provided information, we are going to determine the requested terminal point, so we obtain the following:
So for this we will first calculate how much the given angle is in degrees, from there then we proceed to observe in the unit circle, then we have:
(pi/2)*(180°/pi)=180°/2=90°
We can observe in the image of the unit circle that the terminal point of 90° is (0, 1).
Finally we obtain that the terminal point of pi/2 radians is (x,y)=(0, 1).
the US based motorcycle manufacturer says that it expects to build a 145000 motorcycles this year up from 135,000 last year find the percent of increase in production
Answers
The number of motor cycles produced last year is 135,000.
The number of motor cycles expected to produce is 145,000.
Therefore, the percentage of increase is,
[tex]\frac{(145000-135000)}{135,000}\times100[/tex]That is,
[tex]\begin{gathered} \frac{10000}{135000}\times100=\frac{10}{135}\times100 \\ =7.4 \end{gathered}[/tex]Therefore, the percentage of increase is 7.4%