First blank transitive propertySubtraction property of equalitySegment additionSubstitution property of equalitysecond blank AB does not equal YZ AC does not equal XZ AB equals YZ AC equals XZ
Answers
Given that:
[tex]BC=XY[/tex][tex]AB+BC\ne YZ+XY[/tex]According to the Segment Addition if B lies between A and C, then:
[tex]AB+BC=AC[/tex]In this case, knowing that:
[tex]AB+BC\ne YZ+XY[/tex]And knowing that B lies between A and C, and Y lies between X and Z:
[tex]\begin{gathered} AB+BC=AC \\ YX+XY=XZ \end{gathered}[/tex]Therefore, you can determine that:
[tex]AC\ne XZ[/tex]Hence, the answers are:
- First blank: Third option (Segment addition).
- Second blank: Second option (AC does not equal XZ).
Related Questions
Which equation shows the relationship between the variables in the table? number of packs of markers(m) 012345 cost in dollars (d) 048121620
Answers
The equation shows the relationship between the variables is y = 10.53x.
To show the relationship between the variables in the table:
Given m = 012345, d = 048121620
m d k
0 0 0
1 4 4
2 8 4
3 1 0.33
4 2 2
5 1 0.2
Total = 10.53
This constant represents the ratio between the two variables. This ratio will be the same for every set of ordered pairs that represent the relationship.
Equation: A proportional relationship can be represented by the equation y = kx y = k x , where k is the constant ratio.
Therefore, by substituting the value of k in the above equation, we get:
y = 10.53x
Hence the answer is the equation shows the relationship between the variables is y = 10.53x.
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1. On a number line, graph the solution to the inequality -5(x + 1) > 7x +31? Also, write thesolution in interval notation.
Answers
We have the following:
[tex]\begin{gathered} -5\cdot\left(x+1\right)>7x+31 \\ -5x-5>7x+31 \\ -5x-5+5>7x+31+5 \\ -5x-7x>7x+36-7x \\ -12x>36 \\ x>\frac{36}{-12} \\ x<-3 \end{gathered}[/tex]interval notation:
[tex](-\infty,-3)[/tex]graph:
Bob's Car Wash had to close 26 days last year because of bad weather. If last year had 365 days, what is the ratio of days closed to days open for Bob's Car Wash?OA. 26 to 339OB. 26 to 365OC. 365 to 26OD. 339 to 26
Answers
Days closed = 26
Days open = Total days - days closed = 365 -26 = 339
Days closed to days open:
26 to 339
A( graph the system (Let t be represented by the hot axis and p be represented by the vertical axis B) find the solution to the system (t p)
Answers
I) p = 3.5t + 5
II) p = 7t/2 - 5
A) For equation I, if we replace t with 0 we find p = 5 and if we replace t with 2 we find p = 3.5*2 + 5 = 12. Therefore, to graph the line represented by this equation, we just need to draw a line passing through the points (0,5) and (2,12)
For equation II, if we replace t with 0 we find p = -5 and if we replace t with 2 we find p = (7/2)*2 - 5 = 2. Therefore, to graph the line represented by this equation, we just need to draw a line passing through the points (0,-5) and (2,2).
Here is the system represented by a graph:
B) By the graph, we can see that the lines are parallel and never intercept each other. This happens because they have the same slope (3.5 = 7/2). Therefore, this system has no solution.
Calculate the percent error. Darwin’s coach recorded that he had bowled points out of in a bowling tournament.
Answers
Given:
The recorded value is 250 points.
The true value is 300 points.
To find the percent error:
Using the formula,
[tex]P\text{ercent error}=\frac{|recorded\text{ value}-\text{true value|}}{\text{True value}}\times100\text{ \%}[/tex]On substitution we get,
[tex]\begin{gathered} =\frac{|250-300|}{300}\times100 \\ =\frac{50}{300}\times100 \\ =16.67\text{ \%} \end{gathered}[/tex]Hence, the percent error is 16.67 %.
Angel is a senior in high school and works two jobs. He tutors for $20 per hour and walks dogs for $6 per hour. Angel's parents want him to work for no more than 18 hours per week. He wants to make at least $250 per week. Which system of linear inequalities represents this situation where t is the number of tutoring hours worked and w is the number of hours walking dogs E. t tw< 20 20t + 6w > 250 F. t tw 250 G. t +w< 250 20t + 6w< 18 H. 20t + 6w > 18 t + w > 18
Answers
Let:
t = time spent as tutor
w = time spent walking dogs
Angel's parents want him to work for no more than 18 hours per week, so:
t + w < 18
Besides, He tutors for $20 per hour and walks dogs for $6 per hour and He wants to make at least $250, so:
20t + 6w ≥ 250
Do You Know How? In 3-8, estimate each product using rounding or compatible numbers. 4. 104 x 0.33 3. 0.87 x 112 0.90x110=99 6. 0.54 x 24 5. 9.02 x 80 9x80=720 7. 33.05 x 200 a. 0,79 x 51
Answers
Estimating Products
Some operations can be estimated and its results approximated by using rounding and number that are easier to calculate.
For example the product 0.87*112 can be estimated by using 0.9 (a very close rounded number) and 110 instead of 112. One of the factors was rounded up and the other was rounded down. The product should be very close to the real exact product.
Now for 104*0.33. 104 can be rounded to 100 and it can be easily multiplied by 0.33. 100*0.33 = 33
0.54*24 can be estimated as 0.5*26=13 or as 0.6*30=18
33.05*200 is approximated as 33*200 = 6600
0.79*51 is estimated as 0.8*50 = 400
Some of the estimations above can be challenged and some people can propose better combinations for more accurate results. It's a subjective task.
On your first day of work at the Vanity Fur Grooming Shop, you groomed 3 dogs between 7:45 a.m. and 2:30 p.m., taking breaks that totaled 45 minutes. Your supervisor advises that you will be scheduling your own appointments when customers call to have their pets groomed. If you continue to work at the same rate, how much time should you allow for each grooming appointment?
Answers
Answer:
2 hours
Explanation:
First, calculate the length of time between 7:45 a.m. and 2:30 p.m.
[tex]\begin{gathered} \; \; 2\colon30P.M\text{.} \\ -7\colon45A.M\text{.} \\ _{----------} \\ 6\colon45 \end{gathered}[/tex]If the break totaled 45 minutes, the time spent grooming the 3 dogs = 6 hours.
Therefore, if you continue to work at the same rate, the time that should be allocated for each grooming appointment:
[tex]\begin{gathered} =\frac{6}{3} \\ =2\text{ hours} \end{gathered}[/tex]Inverse VariationThe variable y is inversely proportional to x if there is a nonzero constant, k, such that y=k/x.The number k is called the constant of variation or the constant of proportionality.Now, suppose that y is inversely proportional to x. If y is 2 when x is 7, we can find the constant of proportionality by first solving for k and then rewriting the equation to create an inverse variation equation.Start by substituting the values for y and x in to the standard equation and solve for k:2=k/714=ky=14/xPart AUse the equation we just found to determine the value of y when x = 21. Part BFind the value of x when y = 28. Part CLet’s look at a real-world example using inverse variation.In physics, Boyle’s law states that if the temperature is constant, then the pressure, P, of a gas is inversely proportional to the volume, V, of the gas. If the pressure of the gas in a cylinder is equal to 250 kilopascals when the volume of the container is 1.7 cubic meters, then determine the constant of proportionality for this situation. Show your work. Part DUse the constant of proportionality from part C to write an inverse variation equation to model this situation. Part EUsing the equation from part D, determine what the pressure would be in the container if the size of the container were to increase to 3.2 cubic meters. Part FWhat would the approximate volume need to be if you wanted the pressure to be 150 kilopascals? Part GReturning to the situation from part C, assume that the container was stored in a cooler room. Now, as the temperature of a gas increases, the pressure of the gas increases. Similarly, if the temperature of the gas decreases, the pressure of the gas decreases.So, assuming the container was placed in a cooler room, you know that the temperature of the gas has decreased by an unknown amount. Write an inequality to model this new situation. Part HUse the inequality from part G to write an inequality that represents the possible pressure of the gas if it is placed in a 3 cubic meter container. Give your answer in the form P < #. Part IYour answer from part H includes an infinite number of possibilities. However, in terms of this situation, some of the possible values are extraneous solutions. These are solutions that do not work given the situation. Rewrite your answer to remove any extraneous solutions and explain your answer.
Answers
Part A)
According to the text, the equation that relates x and y is:
[tex]y=\frac{14}{x}[/tex]Substitute x=21 to find the value of y when x=21:
[tex]y=\frac{14}{21}[/tex]Simplify the expression:
[tex]\frac{14}{21}=\frac{7\cdot2}{7\cdot3}=\frac{2}{3}[/tex]Therefore, the value of y when x=21 is:
[tex]\frac{2}{3}[/tex]Part B)
To find the value of x when y=28, substitute y=28 and solve for x:
[tex]\begin{gathered} y=\frac{14}{x} \\ \Rightarrow28=\frac{14}{x} \\ \Rightarrow28x=14 \\ \Rightarrow x=\frac{14}{28} \\ \therefore x=\frac{1}{2} \end{gathered}[/tex]Therefore, the value of x when y=28 is:
[tex]\frac{1}{2}[/tex]Part C)
Since the pressure P is inversely proportional to the volume V, then:
[tex]P=\frac{k}{V}[/tex]Solve for k and substitute P=250kPa and V=1.7m^2 to find the constant of proportionality:
[tex]\begin{gathered} \Rightarrow k=PV \\ =(250\text{kPa})(1.7m^3) \\ =425\text{kPa}\cdot m^3 \end{gathered}[/tex]Therefore, the constant of proportionality for this situation is:
[tex]425\text{ kPa}\cdot m^3[/tex]Part D)
Substitute the value of k into the equation that shows the inverse relation between P and V:
[tex]\begin{gathered} P=\frac{k}{V} \\ \Rightarrow P=\frac{425\text{ kPa}\cdot m^3}{V} \end{gathered}[/tex]Therefore, the inverse variation equation model for this situation, is:
[tex]P=\frac{425\text{ kPa}\cdot m^3}{V}[/tex]Part E)
Substitute V=3.2m^3 to find the pressure under those conditions:
[tex]\begin{gathered} P=\frac{425\text{ kPa}\cdot m^3}{3.2m^3} \\ =132.8\text{kPa} \end{gathered}[/tex]Therefore, the pressure would be:
[tex]132.8\text{kPa}[/tex]Part F)
Isolate V from the equation and substitute P=150kPa:
[tex]\begin{gathered} V=\frac{425\text{ kPa}\cdot m^3}{P} \\ =\frac{425\text{ kPa}\cdot m^3}{150\text{ kPa}} \\ =2.83m^3 \end{gathered}[/tex]Therefore, the approximate volume would have to be equal to:
[tex]2.83m^3[/tex]Part G)
Since the temperature has decreased, the pressure must be lower according to the description provided in the text. Then, an inequality to model this situation would be:
[tex]P<\frac{k}{V}[/tex]Part H)
Substitute the value of k and V=3m^3:
[tex]\begin{gathered} P<\frac{425\text{ kPa}\cdot m^3}{3m^3} \\ \Rightarrow P<141.7\text{ kPa}^{} \end{gathered}[/tex]Part I)
Mathematically, all numbers under 141.7 satisfy the inequality from part H. Nevertheless, negative pressures do not have a physical meaning under the context of the Ideal Gas Law. Therefore, we must include the condition that P is greater than 0:
[tex]0The volume of dis rectangular prism is zero. Seven to a cubic yards. What is the value of C in yards?
Answers
To get the volume of a prims, we do the products of the base times its height.
Being a rectangular prims, the area of its base is the product of its dimesions, so the volume of a rectangular prism is simply the product of its three dimensions:
[tex]V=l\cdot w\cdot h=1.3\cdot1.4\cdot c=1.82c[/tex]Since the volume is equal to 0.728 yd³, we have:
[tex]\begin{gathered} 0.728=1.82c \\ c=\frac{0.728}{1.82}=0.4 \end{gathered}[/tex]So, the measure of c is 0.4 yards.
The number of students showing up for a high school football team is 10% smaller than the previous year. A few minutes before tryouts begin, another 5 students show up. There are 75 students on the field to try out for football. Which equation represents this situation?
Answers
Given data:
The expression for the given statement is,
[tex]0.9x+5=75[/tex]Thus, the option (C) is correct.
1.Given the Graph Circle One: Arithmetic, Geometric, or Neither Circle One: Common Ratio or Common difference: recursive formula-explicit formula-find the 5th term-
Answers
We can see in the graph that for every increment in x, the y-value is halved (that is, multiplied by 1/2).
Since the y-values are being multiplied for every increment of x, we have a geometric sequence or function.
Also, the function has a common ratio, which is the value 1/2 that multiplies y for every increment of x.
Last, we have a recursive formula: each value of y is half of the previous value of y (a_n = (1/2) * a_(n-1))
In order to find the explicit formula, since we have an exponential function, we can use the model y = a*b^x.
Using the points (1, 32) and (2, 16), we have:
[tex]\begin{gathered} 32=a\cdot b^1\to a=\frac{32}{b} \\ 16=a\cdot b^2\to b^2=\frac{16}{a}=\frac{16b}{32}\to b=\frac{1}{2} \\ 32=a\cdot\frac{1}{2}\to a=64 \end{gathered}[/tex]So the explicit function is y = 64 * (1/2)^x.
Looking at the graph, the 5th term of the sequence (x = 5) is found by halving the value y = 8 two times, so the 5th term is 2.
slope of 1/3 and passing through the point (3,2)
Answers
To determine the equation of the line that has slope m=1/3 and passes through the point (3,2) you have to use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]Where
m is the slope of the line
(x₁,y₁) are the coordinates of one point of the line
Replace the formula above with the known information about the line:
[tex]y-2=\frac{1}{3}(x-3)[/tex]Next is to write the equation in slope-intercept form, which means that you have to leave the y term alone on the left side of the equation and all other terms have to be on the right side.
-First, distribute the multiplication on the parentheses term:
[tex]\begin{gathered} y-2=\frac{1}{3}\cdot3-\frac{1}{3}\cdot3 \\ y-2=\frac{1}{3}x-1 \end{gathered}[/tex]-Second, pass "-2" to the right side of the equation by applying the opposite operation, "+2", to both sides of the equal sign:
[tex]\begin{gathered} y-2+2=\frac{1}{3}x-1+2 \\ y=\frac{1}{3}x+1 \end{gathered}[/tex]So, the equation of the line with slope 1/3 that passes through the point (3,2), expressed in slope-intercept form is:
[tex]y=\frac{1}{3}x+1[/tex]What is the measure of the missing side of the right triangle? Sad see is the hypotenuse. Sides a and b are the legs
Answers
Using the Pythagorean theorem, the formula is:
[tex]a^2+b^2=c^2[/tex]Where:
a = 7.1 km
c = 8.4 km
And we will find the side b.
Substitute the values:
[tex]7.1^2+b^2=8.4^2[/tex]And solve for b:
[tex]\begin{gathered} 50.41+b^2=70.56 \\ \text{subtract 50.41 on both sides} \\ 50.41+b^2-50.41=70.56-50.41 \\ b^2=20.15 \\ b=\sqrt[]{20.15}=4.5 \end{gathered}[/tex]Answer: b = 4.5 km
when plqying a math game in class you drew 5 cards and had to find the sum of the numbers. your numbers were -9 3 2 - 5 4. what was the sum of your hand
Answers
We are required to sum up the numbers obtained. Our approach is to add the negative numbers separately and the positive numbers separately and then add up both.
[tex]\begin{gathered} (-9)+3+2+(-5)+4=3+2+4+(-9)+(-5) \\ 3+2+4=9 \\ -(9+5)=-14 \\ \text{Adding both} \\ 9+(-14)=9-14=-5 \end{gathered}[/tex]-5 is our answer.
In the diagram, line AB is parallel to DE. Also, line DE is drawn such that the length of line DE is half the length of line AB. If sin A=0.5, then what is sin E?
Answers
By alternate interior angle theorem. Angle A is congruent with Angle E.
This makes ΔAFB similar to ΔEFD.
IF sin A = 0.5, then sin E is also equal to 0.5.
t - 3 > 2Solve the inequalities and represent the possible values of the variable on a number line.
Answers
Answer:
The solution to the inequality is;
[tex]t>5[/tex]drawing the variable on the number line;
Explanation:
Given the inequality;
[tex]t-3>2[/tex]To solve, let's add 3 to both sides of the inequality;
[tex]\begin{gathered} t-3+3>2+3 \\ t-0>5 \\ t>5 \end{gathered}[/tex]Therefore, the solution to the inequality is;
[tex]t>5[/tex]drawing the variable on the number line;
It’s multi-step linear equations I have to solve for the x but in this question is asking “expand, and then solve for x” what did it mean by expand 5a - (2a + 15) = 24
Answers
Given:
[tex]5a-(2a+15)=24[/tex]To expand and solve for x:
On expanding the given expression, we have,
[tex]5a-2a-15=24[/tex]On solving we get,
[tex]\begin{gathered} 3a-15=24 \\ 3a=24+15 \\ 3a=39 \\ a=13 \end{gathered}[/tex]Therefore, the value of a is 13.
Suppose your final grade in this class is based on the following system:Class participation 10% homework 20%test average 30% final exam 25%quiz average 15%Given the grades listed below, what would your final grade in the class be?test grades(78, 87, 93, 75) quiz average (85)Class participation (95) homework(75)final exam(63)choices:A. 83B. 70C. 88D. 78
Answers
to find a percentage we multiply by the number and divide by 100
class participation
[tex]\begin{gathered} 95\times\frac{10}{100} \\ =9.5 \end{gathered}[/tex]homework
[tex]\begin{gathered} 75\times\frac{20}{100} \\ =15 \end{gathered}[/tex]test average
first find the average
[tex]\begin{gathered} \frac{78+87+93+75}{4} \\ =83.25 \end{gathered}[/tex]then the percentage
[tex]\begin{gathered} 83.25\times\frac{30}{100} \\ =24.975 \end{gathered}[/tex]Final Exam
[tex]\begin{gathered} 63\times\frac{25}{100} \\ =15.75 \end{gathered}[/tex]Quiz average
[tex]\begin{gathered} 85\times\frac{15}{100} \\ =12.75 \end{gathered}[/tex]finally we add to get the final grade
[tex]\begin{gathered} 9.5+15+24.975+15.75+12.75 \\ =77.97 \end{gathered}[/tex]the final grade is 78
Consider parallelogram ABCD below.Use the information given in the figure to find x, m ZADB, and m ZA.AB.3502x6m ZADB =m ZA = 11130С
Answers
ABCD is a parallelogram, which means that:
-The opposite sides are parallel, so AB || DC and AD || BC
-The opposite sides are congruent, so AB=DC and AD=BC
-Opposite angles are congruent
-Adjacent angles are supplementary
The congruent sides are equal which means that:
[tex]\begin{gathered} AD=BC \\ 2x=6 \end{gathered}[/tex]1) From this expression, you can determine the value of x, you have to divide both sides of the equal sign by 2:
[tex]\begin{gathered} \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}[/tex]2) The opposite angles are equal, which means that ∠C=∠A=113º
3) Lines AD and BC are parallel lines intersected by a transversal line DB, so that:
∠CBD and ∠ADB are alternate angles, which means that they are congruent, so ∠CBD=∠ADB=35º
Solve using the quadratic formula. x^2 +27=0 Enter your answers, as exact values, in the boxes x= or x=
Answers
By using the quadratic formula, the values of x are:
x = + 3√3ix = - 3√3iWhat is the quadratic formula?The quadratic formula is used to find the roots of a quadratic equation and these roots are called the solutions of the quadratic equation. A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients.However, there are several methods of solving quadratic equations such as factoring, completing the square, graphing, etc.So, the equation is: x² + 27 = 0
The quadratic formula: -b±√b²-4ac/2aNow, use the quadratic formula as follows:
x = 0 ± √0 - 4(27)/2ax = ± √-108/2x = 2(±√-27/2)x = ±√-27x = ±3√3iTherefore, by using the quadratic formula, the values of x are:
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A car's rear windshield wiper rotates 135°. The total length of the wiper mechanism is 21 inches and the length of the wiper blade is 12 inches. Find the area wiped by the wiper blade. (Round your answer to one decimal place.)
Answers
The area wiped by the wiper blade is 424.08 in².
How to find the area?Using this formula to find the area
A= 1/2r² Ф
Where:
A = Area
r = Radius
Let plug in the formula
A = [1/2 × (21)² × 135° ×π /180 ] - [1/2 × (21 -12)² × 135° ×π /180 ]
A = [1/2 × (21)² × 135° ×π /180 ] - [1/2 × (9)² × 135° ×π /180 ]
A = [1/2 × (441) × 135° ×π /180 ] - [1/2 × (81) × 135° ×π /180 ]
A = 519.54 - 95.43
A = 424.08 in²
Therefore the area is 424.08 in².
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what is the correct trigonometric ratio for the tangent of A?
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Using the trigonometric ratio;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]From the figure,
opposite =8 and adjacent= 15
[tex]\tan A=\frac{8}{15}[/tex]Sasha owes a total of $1,845.00 on revolving credit accounts that have total limits of $4,500.00. Calculate the amount she needs to pay on her debt to reduce her revolving credit accounts to reach a 25% debt-to-credit ratio. $705.00$720.00$988.00$1,125.00
Answers
Sashas total debt is 1845
Total limit on the credit card account is 4500
25 × 4500 / 100 = 1125
25% of 4500 is 1125
So in order to reach a 25% debt to credit ratio Sasha needs to payback 720 of her debt.
1845 - 1125 = 720
Option B is the answer
Determine the center and radius of the following circle equation:2² + y² – 2x – 6y – 54 = 0Center:13Radius:Submit Answer
Answers
Answer:
Centre = (1, 3)
radius = 8units
Explanation:
The standard equaton of a circle is expressed as;
[tex]x^2+y^2+2gx+2fy+C\text{ = 0}[/tex]The radius of the circle is expressed as;
[tex]r=\sqrt[]{g^2+f^2-C^{}}[/tex]The centre is at C(-g, -f)
Given the expression;
[tex]x^2+y^2-2x-6y-54=0[/tex]Get the centre of the circle.
Compare both equations
[tex]\begin{gathered} 2gx=-2x \\ g\text{ = -1} \end{gathered}[/tex]similarly;
[tex]\begin{gathered} 2fy=-6y \\ 2f=-6 \\ f=-\frac{6}{2} \\ f=-3 \end{gathered}[/tex]The centre will be located at C(-(-1), -(-3)) = C(1, 3)
Next is to get the radius
Recall;
[tex]\begin{gathered} r=\sqrt[]{g^2+f^2-C} \\ r=\sqrt[]{(-1)^2+(-3)^2-(-54)} \\ r=\sqrt[]{1+9+54} \\ r=\sqrt[]{64} \\ r=8\text{units} \end{gathered}[/tex]Hence the radius is 8units
Match each side length and angle to the correct answer. Simplify anyradicals.a= b=measure of angle C =measure of angle A=measure of angle B=c=
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Given data:
The given figure of the triangle.
The measure of the side a is,
a=4 units.
The measure of the side b is,
b= 4 units.
The measure of the angle C is 90 degrees.
As the side a is equal to side b, it means the given triangle is isosceles right angle triangle.
The measure of the angle B is equal to the measure of the angle A which is 45 degrees.
The side c can be calculated as,
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=4^2+4^2 \\ c^2=32 \\ c=4\sqrt[]{2} \end{gathered}[/tex]Thus, a= 4 units, b=4 units, c=4√2, ∠C=90 degrees, ∠A= 45 degrees, and ∠B=45 degrees.
what is 1+1how old are you
Answers
1 + 1 in base 10 is 2
Tim bought a pair of Zeus running shoes on sale that were marked down 20% to $100 what was the original price of the shoes
Answers
Given:
Tim bought a pair of shoes for $100 on 20% down.
Let 'x' be the original price of the shoes.
Percentage of amount paid for the shoes is 80%
[tex]100=x\times\frac{80}{100}[/tex][tex]100\times\frac{100}{80}=x[/tex][tex]x=\frac{10000}{80}[/tex][tex]x=125[/tex]Therefore, the original price of the shoes is $125
1,1,2,6,24,_,_,_,_A) explain and complete the sequenceB) write an explicit and recursive formula for the sequence
Answers
As you can notice, this sequence is detailed as follows:
[tex]\begin{gathered} 1\cdot1=1 \\ 1\cdot2=2 \\ 2\cdot3=6 \\ 6\cdot4=24 \end{gathered}[/tex]Now, let's find the next four terms:
[tex]\begin{gathered} 24\cdot5=120 \\ 120\cdot6=720 \\ 720\cdot7=5040 \\ 5040\cdot8=40320 \end{gathered}[/tex]A possible formula could be:
[tex]a_n=n\cdot a_{n-1}[/tex]Where "n" is the number of the term given and it starts from 1. (a0 is 1) This is:
[tex]\begin{gathered} a_1=1.a_{1-1}=1\cdot a_0=1_{} \\ a_2=2\cdot a_{2-1}=2\cdot a_1=2 \\ a_3=3\cdot a_{3-1}=3\cdot a_2=6 \\ \text{and so on } \end{gathered}[/tex]Select the correct answer from each drop-down menu.Phyllis bought 21 feet of wood to frame a window. If she makes a triangular window, what is the greatest area the window can have?For a given perimeter, the triangle with the largest perimeter isv triangle. Using this type of triangle, the sides wouldmeasureSo, the greatest area the window could be is aboutsquare feet
Answers
Equilateral Triangles
An equilateral triangle has all of its three sides of the same measure. Suppose the side length of an equilateral triangle is L.
The perimeter of such a triangle is:
P = 3L
Phyllis bought 21 feet of wood to frame a triangular window. This corresponds to the perimeter of the triangle, so we can calculate the side length:
L = P/3
L = 21 feet / 3
L = 7 feet.
Now we know the length of the side of the triangle, we calculate the area by using the formula:
[tex]A=\frac{\sqrt[]{3}}{4}L^2[/tex]Substituting L = 7 feet:
[tex]\begin{gathered} A=\frac{\sqrt[]{3}}{4}(7ft)^2 \\ A=\frac{\sqrt[]{3}}{4}49ft^2 \\ \text{Calculating:} \\ A\approx21.22ft^2 \end{gathered}[/tex]