Need help answering all these questions for the red bird.Quadratic equation of the red bird: h(x) = -x^2 + 10x - 9King Pig located at the point (11,9) Moustache Pig located at the point (10,4)
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The maximum heigh is located at the vertex. The vertex is:
[tex]\begin{gathered} V=(h,k) \\ where: \\ h=-\frac{b}{2a}=-\frac{10}{2(-1)}=5 \\ k=h(h)=-(5^2)+10(5)+9=-25+50-9=16 \end{gathered}[/tex]Therefore, the maximum height is the y-coordinate of the vertex which is 16.
The axis of symetry is located at the x-coordinate of the vertex,so:
The axis of symetry is x = 5.
The distance traveled can be found using the roots:
The roots of the equation are:
[tex]\begin{gathered} -x^2+10x-9=x^2-10x+9=(x-9)(x-1) \\ so \\ x=1 \\ or \\ x=9 \end{gathered}[/tex]So, the distance traveld is:
[tex]\Delta x=x2-x1=9-1=8[/tex]---
The bird will hit the ground on the second root, so:
The point where it hits the grund is (9,0).
The starting point is located at the first root, so the starting point is:
(1,0)
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Related Questions
Could you help me with this problem?There are 7 acts in a talent show.A comedian, a guitarist, a magician, a pianist, a singer, a violinist, and a whistler.A talent show host randomly schedules the 7 acts.Compute the probability of each of the following events.Event A: The magician is first, the comedian is second, and the whistler is third.Event B: The first three acts are the guitarist, the pianist, and the singer, in any order.Write your answers as fractions in simplest form.
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EXPLANATION
For the event B, the order of the first 3 acts doesn't matter.
So, the number of acts taken from the seven acts when the order doesn't matter is calculated using combinations.
[tex]C(m,n)=\frac{m!}{n!(m-n)!}[/tex][tex]C(7,3)=\frac{7!}{3!(7-3)!}=\frac{7!}{3!4!}[/tex]Computing the factorials:
[tex]C(7,3)=\frac{5040}{6\cdot24}=\frac{5040}{144}=35[/tex]Hence, the number of ways the three acts could be given are 1:C(7,3)
Therefore, the probability of the event B is:
[tex]P(B)=\frac{1}{35}[/tex]For the event A, the order matters, so the difference between combinations and permutations is ordering. When the order matters we need to use permutations.
The number of ways in which four acts can be scheculed when the order matters is:
[tex]P(m,n)=\frac{m!}{(m-n)!}[/tex][tex]P(m,n)=\frac{7!}{(7-3)!}=\frac{5040}{24}=210[/tex]The number of ways the magician is first, the comedian is second and the whistler is third are 1:P(7,4)
Therefore, the probability of the event A is.
[tex]P(A)=\frac{1}{210}[/tex]I need help for problem number 9. On the right side of the paper.
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Constant of variation ( k ):
• y = 2/3
,• x = 1/4
[tex]k=\frac{y}{x}=\frac{\frac{2}{3}}{\frac{1}{4}}=\frac{8}{3}[/tex]k = 8/3
Based on k we can find the value of y when x =3/4 as follows:
[tex]\begin{gathered} k=\frac{y}{x} \\ y=k\cdot x \\ y=\frac{8}{3}\cdot\frac{3}{4}=2 \end{gathered}[/tex]Answer:
• k = 8/3
,• When ,x, = ,3/4,,, y = 2
is 826,456 divisible by 8
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Answer:
Yes, because if you divide the two numbers, you get a whole number which means it is. Also, since the last numbers are 56, 8 can go into 56 so yes.
Step-by-step explanation:
Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set.
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Answer:
(D) {xIx ≥ 5} or [5, ∞)
Explanation:
Given inequality: 5x - 11 ≥ 9 + x
By collecting the like terms, we have
5x - x ≥ 9 + 11
4x ≥ 20
Divide bothsides by 4
4x/4 ≥ 20/4
x ≥ 5
In set notation, we have {5, ∞}
The graph of the solution set is
How to find postulate
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Note that if plane N and plane M intersects each other in two points (say A and B) it follows that they intersects each other in the line that contains A and B. So they cannot intersect exactly in only two points. Postulate number 10
8.
What is the measure of angle x in the figure?
40°
A 69°
B 71°
C 109°
D 111°
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Answer:
C 109
Step-by-step explanation:
First add all the known angles inside the triangle first to get 109°
Then since all angles in a triangle add to 180°
you take away 109 from 180 so
180-109 which equals 71
Then since all angles on a straight line add up to 180°
you take 71 from 180 so
180-71 = 109
so x = 109°
May I please get help with this. I need help with finding the original and final points on the figure and also finding out where I should put my reflection?
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Answer:
Step-by-step explanation:
The rule for a reflection over the y-axis is represented by the following equation:
[tex](x,y)\rightarrow(-x,y)_{}[/tex]Therefore, for the given figure and given point:
Which expression would be easier to simplify if you used the associativeproperty to change the grouping?
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In option A, if expression is simplify with out using associative property then addition of 4/9 and -2/9 is easy, as compare to addition 6 and 4/9. So no need to apply associateive property to option A.
In option B, 60 and 40 can be easily add as compare to 40 and -27 so this expression do not need to apply associative property.
In option C, the expression is easier to simplify if 5/2 and -1/2 is added, which is possible if associative is apply to the expression.
[tex]\begin{gathered} (2+\frac{5}{2})+(-\frac{1}{2})=2+(\frac{5}{2}-\frac{1}{2}) \\ =2+(\frac{5-1}{2}) \\ =2+2 \\ =4 \end{gathered}[/tex]Thus option C use associative property to make the simplification easier.
Answer: Option C.
Find the median and mean of the data set below: 3, 8, 44, 50, 12, 44, 14 Median Mean =
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the median is 25, because:
[tex]=\frac{3+8+44+50+12+44+14}{7}=\frac{175}{7}=25[/tex]the mean value is :
[tex]14[/tex]Coronado co. sells product p-14 at a price of $52 a unit. the per unit cost data are direct materials $16, direct labour $12, and overhead $12 (75% variable) Coronado has no excess capacity to accept a special order for 38,700 units at a discount of 25% from the regular price. Selling costs associated with this order would be $3 per unit. Indicate the net income/loss
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The net loss from accepting the special order at a discount of 25% from the regular price, without the existence of excess capacity is $38,700.
How is the net loss determined?Since Coronado Co. lacks the excess capacity for special orders, it implies that it will incur fixed costs per unit of the special order in addition to the variable costs.
Therefore, the company will incur a per unit cost of $40 ($16 + $12 + $9 + $3) while generating a revenue of $39 per unit.
This results in a loss of $1 per unit.
Selling price per unit = $52
Unit Costs:
Direct Materials = $16
Direct Labor = $12
Variable Overhead = $9 (75% of $12)
Total variable cost per unit = $37
Fixed Overhead = $3 (25% of $12)
Special order price per unit = $39 ($52 x 1 - 75%)
Contribution margin per unit = $2 ($39 - $37)
Total contribution margin = $77,400 ($2 x 38,700)
Fixed Overhead without excess capacity = $116,100 ($3 x 38,700)
Net loss = $38,700 ($77,400 - $116,100)
Thus, without excess capacity, it is inadvisable for Coronado to accept the special order at a total loss of $38,700.
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Find the length of the third side. If necessary, write in simplest radical form. 9 5 Submit Answer Answer:
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The Pythagorean theorem states:
[tex]c^2=a^2+b^2[/tex]where a and b are the legs and c is the hypotenuse of a right triangle.
Substituting with c = 9 and a = 5, we get:
[tex]\begin{gathered} 9^2=5^2+b^2 \\ 81=25+b^2 \\ 81-25=b^2 \\ 56=b^2 \\ \sqrt[]{56}=b \\ \sqrt[]{4\cdot14}=b \\ \sqrt[]{4}\cdot\sqrt[]{14}=b \\ 2\sqrt[]{14}=b \end{gathered}[/tex]The side of a square lot is (5×-3) meters. How many meters of fencing materials are needed to enclose the square lot?
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The length of the fencing will be the perimeter of the given square with side (5x - 3) thus (20x - 12) meters will be the fencing length.
What is a square?A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.
As per the given,
Side of square = 5x - 3
The fencing around the square will cover the complete perimeter of the square.
Since the perimeter of the square = 4 × side
Therefore,
Length of fencing = 4 × (5x - 3)
Length of fencing = 20x - 12
Hence "The length of the fencing will be the perimeter of the given square with side (5x - 3) thus (20x - 12) meters will be the fencing length".
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Write the trig equation needed to solve for X. Then solve for X. Round answers to the nearest tenth.
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In order to solve for x, we need to use the tangent relation of the angle 48°.
The tangent relation is equal to the length of the opposite leg to the angle over the length of the adjacent leg to the angle.
So we have:
[tex]\begin{gathered} \tan (48\degree)=\frac{x}{17} \\ 1.1106=\frac{x}{17} \\ x=1.1106\cdot17 \\ x=18.88 \end{gathered}[/tex]Rounding to the nearest tenth, we have x = 18.9.
Approximate 14 plus cube root of 81 to the nearest tenth.
15.8
17.9
18.0
18.3
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The Approximation of 14 plus cube root of 81 to the nearest tenth is 18.0
How can the terms be simplified?The concept that will be used to solve this is finding cube root of 81 which same thing as [tex]81^{\frac{1}{3} }[/tex].
Firstly we will need to find the cube root of 81, which can be expressed as this: [tex]\sqrt[3]{81}[/tex] and this can be calculated as 4.33.
This implies that the cube root of 81 will now be 4.33.
Then we can proceed to the simplification that was asked from the question which is 14 plus cube root of 81 and this can be expressed as ( 14) + (4.33) = 18.33
Then we were told to express in the the nearest tenth which is 18.0
Therefore, the third option is correct.
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Fanuela walked for 3.9 miles per hour for 0.72 hours. How far did she walk?
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Answer: Fanuela walked 2.808 miles.
Step-by-step explanation:
If 3.9 = 100 and we need to work out what 72 is we can do this/
3.9 ÷ 10 = 0.39 which = 10
0.39 ÷ 10 = 0.039 which = 1
so with these calculations we can solve the problem.
To get the 70 in 72 we can do 0.39 x 7 (10 x 7) which = 2.73.
To get the remaining 2 in 72 we can do 0.039 x 2 (1 x 2) which = 0.078.
2.73 + 0.078 = 2.808.
Fanuela walked 2.808 miles.
Hope this helps! Feel free to ask any questions if you're still unsure.
3.9=d/0.72
d= 3.9 x 0.72
d= 2.808 miles
5. Helen, Riley, and Derrick are on a running team. Helen ran 15 1/4 kilometers last week. Riley ran 4 1/12 less kilometers than Helen, and Derrick ran 7 3/8 more kilometers than Riley. If their goal is to run 60 kilometers in total, how much further do they need to run to meet their goal? I
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Given in the scenario:
a.) Helen ran 15 1/4 kilometers last week.
b.) Riley ran 4 1/12 less kilometers than Helen.
c.) Derrick ran 7 3/8 more kilometers than Riley.
d.) Their goal is to run 60 kilometers in total.
To be able to determine how much further do they need to run to get 60 kilometers in total, we must first determine how many kilometers did Riley and Derrick run.
We get,
A.)
[tex]\text{Riley: }4\frac{1}{12}\text{ less kilometers than Helen}[/tex][tex]\text{ = 15 }\frac{1}{4}\text{ - 4 }\frac{1}{12}[/tex]Recall: To be able to subtract mixed numbers, you must first convert them into an improper fraction with a common denominator. The LCM of the two denominators must be their denominator when converted.
The LCM of 4 and 12 is 12. We get,
[tex]\text{ 15 }\frac{1}{4}\text{ = }\frac{1\text{ + (4 x 15)}}{4}\text{ = }\frac{1\text{ + 60}}{4}\text{ = }\frac{61}{4}\text{ = }\frac{(61)(3)}{12}\text{ = }\frac{183}{12}[/tex][tex]4\text{ }\frac{1}{12}\text{ = }\frac{1\text{ + (4 x 12)}}{12}\text{ = }\frac{1\text{ + 48}}{12}\text{ = }\frac{49}{12}[/tex]Let's now proceed with the subtraction,
[tex]15\frac{1}{4}-4\frac{1}{12}=\frac{183}{12}\text{ - }\frac{49}{12}\text{ = }\frac{183\text{ - 49}}{12}\text{ = }\frac{134}{12}\text{ = }\frac{\frac{134}{2}}{\frac{12}{2}}\text{ = }\frac{67}{6}\text{ or 11}\frac{1}{6}[/tex]Conclusion: Riley ran 11 1/6 kilometers.
B.)
[tex]\text{Derrick: }7\frac{3}{8}\text{ more kilometers than Riley}[/tex][tex]\text{ = 11}\frac{1}{6}\text{ + 7}\frac{3}{8}[/tex]Recall: To be able to add mixed numbers, you must first convert them into an improper fraction with a common denominator. The LCM of the two denominators must be their denominator when converted.
The LCM of 6 and 8 is 24. We get,
[tex]11\frac{1}{6}\text{ = }\frac{1\text{ + (11 x 6)}}{6}\text{ = }\frac{1\text{ + 66}}{6}\text{ = }\frac{67}{6}\text{ = }\frac{(67)(4)}{24}\text{ = }\frac{268}{24}[/tex][tex]7\frac{3}{8}\text{ = }\frac{3\text{ + (7 x 8)}}{8}=\frac{3\text{ + 56}}{8}=\frac{59}{8}=\frac{(59)(3)}{24}=\frac{177}{24}[/tex]Let's now proceed with the addition,
[tex]11\frac{1}{6}\text{ + 7}\frac{3}{8}\text{ = }\frac{268}{24}\text{ + }\frac{177}{24}\text{ = }\frac{268\text{ + 177}}{24}\text{ = }\frac{445}{24}\text{ or 18}\frac{13}{24}[/tex]Conclusion: Derrick ran 18 13/24 kilometers.
C.) To be able to determine how much further do they need to run to get 60 kilometers in total, we subtract 60 by the sum of distance the three people ran.
We get,
[tex]\text{ 60 - (15 }\frac{1}{4}\text{ + 11}\frac{1}{6}\text{ + 18}\frac{13}{24})[/tex]The same process that we did, convert all numbers into similar fractions.
The LCM of 4, 6 and 24 is 24. We get,
[tex]15\frac{1}{4}\text{ = }\frac{1\text{ + }(15\text{ x 4)}}{4}\text{ = }\frac{1\text{ + 60}}{4}\text{ = }\frac{61}{4}\text{ = }\frac{(61)(6)}{24}\text{ = }\frac{366}{24}[/tex][tex]11\frac{1}{6}\text{ = }\frac{1\text{ + (11 x 6)}}{6}\text{ = }\frac{1\text{ + 66}}{6}\text{ = }\frac{67}{6}\text{ = }\frac{(67)(4)}{24}\text{ = }\frac{268}{24}[/tex][tex]\text{ 18}\frac{13}{24}=\text{ }\frac{13+(18\text{ x 24)}}{24}\text{ = }\frac{13\text{ + 432}}{24}\text{ = }\frac{445}{24}[/tex][tex]60\text{ = }\frac{60\text{ x 24 }}{24}\text{ = }\frac{1440}{24}[/tex]Let's proceed with the operation,
[tex]\text{ 60 - (15 }\frac{1}{4}\text{ + 11}\frac{1}{6}\text{ + 18}\frac{13}{24})\text{ = }\frac{1440}{24}-(\frac{366}{24}\text{ + }\frac{268}{24}\text{ + }\frac{445}{24})[/tex][tex]\text{ }\frac{1440\text{ - (366 + 268 + 445)}}{24}\text{ = }\frac{1440\text{ - 1079}}{24}[/tex][tex]\text{ = }\frac{361}{24}[/tex]Therefore, they need to run a total of 361/24 kilometers to be able to meet their goal.
which of the following is an integer ) 58/81) π) -11) 27.4444....
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-11 is an integer number
Use your knowledge of area and perimeter to complete the following problems. Use 3.14 for  and round to the nearest hundredths place, whenever necessary. Show all work.Part 1:A farmer bought 30 feet of fencing to build a circular pen for his pigs. What is the diameter of the pen he can build with 30 feet of fencing?The farmer also needs to buy a certain type of seed for the grass in the pen. Each bag of seed can cover 50 square feet of land. How many bags of seed will the farmer need to buy?
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Which is an equation of the line with a slope of2323 passing through the point (4,-1).Group of answer choices=14+23 =−4+23 =23−53 =23−113
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Given that the slope of a line is 2/3, that passes through the point (4, -1), i.e
[tex]\begin{gathered} m=\frac{2}{3} \\ (x_1,y_1)\Rightarrow(4,-1) \end{gathered}[/tex]The formula to find the equation of straight line is
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where m is the slope of the line} \end{gathered}[/tex]Substitute the values into the formula of the equation of a straight line
[tex]y-(-1)=\frac{2}{3}(x-4)[/tex]Solve for y i.e make y the subject
[tex]\begin{gathered} y-(-1)=\frac{2}{3}(x-4) \\ y+1=\frac{2}{3}(x-4) \\ \text{Open the bracket} \\ y+1=\frac{2}{3}x-\frac{2}{3}(4) \\ y+1=\frac{2}{3}x-\frac{8}{3} \\ y=\frac{2}{3}x-\frac{8}{3}-1 \\ y=\frac{2}{3}x-(\frac{8}{3}+1) \\ y=\frac{2}{3}x-(\frac{8+3}{3}) \\ y=\frac{2}{3}x-\frac{11}{3} \end{gathered}[/tex]Thus, the answer is
[tex]y=\frac{2}{3}x-\frac{11}{3}[/tex]Thus, the answer is the last option.
Question is stated in picture. The figure is a triangular piece of cloth
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Answer:
Alternative D - 8 sin(35°)
Step-by-step explanation:
Sin(x) is defined as:
[tex]\begin{gathered} \sin (x)=\frac{\text{Opposite side}}{Hypotenuse\text{ }} \\ \end{gathered}[/tex]In this exercise,
BC is the opposite side to 35°
AC is the hypotenuse and measures 8 in
Then:
[tex]\begin{gathered} \sin (35\degree)=\frac{BC}{8} \\ \sin (35\degree)\cdot8=BC \\ BC=8\sin (35\degree) \end{gathered}[/tex]You can use a calculator to approximate the logarithm. Round to four decimal place
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This is a simple question to solve when we use the calculator (as the question allows us to use it).
For this problem when we have :
[tex]\log \pi[/tex]It can be read as "log base 10 of pi", and using a calculator we find:
And that is the final answer.
NOTE: this result means that:
.
f(a)=92.39 and the average rate of change of f over the interval from x=a to x=a+266 is 0.16. What is the value of f(a+266)?f(a+266)=
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Average rate is f(a+266)-f(a))/266
so f(a+266) equals (0.16 x 266) + f(a)
f (a+266)= (0.16 x 266) + 92.39
Correctz is jointly proportional to x and y. If z = 115 when x = 8 and y = 3, find z when x = 5 and y = 2. (Round off your answer to the nearest hundredth.)
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When we have a number that is jointly proportional to two other numebrs, the formula is:
[tex]a=kcb[/tex]This means "a is jointly proportional to c and b with a factor of k"
Then, we need to find the factor k.
In this case z is jointly proportional to x² and y³
This is:
[tex]z=kx^2y^3[/tex]Then, we know that z = 115 when x = 8 and y = 3. We can write:
[tex]115=k\cdot8^2\cdot3^3[/tex]And solve:
[tex]\begin{gathered} 115=k\cdot64\cdot27 \\ 115=k\cdot1728 \\ k=\frac{115}{1728} \end{gathered}[/tex]NOw we can use k to find the value of z when x = 5 and y = 2
[tex]z=\frac{115}{1728}\cdot5^2\cdot2^3=\frac{115}{1728}\cdot25\cdot8=\frac{2875}{216}\approx13.31[/tex]To the nearest hundreth, the value of z when x = 5 and y = 2 is 13.31
Miss Taylor drove 30 miles in March she drove 9 times as many miles in May as she did in March she drove 2 times as many miles in April as she did in May how many miles did Miss Taylor Drive in April.
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then we use the statement to solve
Miss Taylor drove 30 miles in March
[tex]March=30[/tex]she drove 9 times as many miles in May as she did in March
[tex]\begin{gathered} May=9\text{March} \\ May=9\times30=270 \end{gathered}[/tex]she drove 2 times as many miles in April as she did in May
[tex]\begin{gathered} April=2May \\ April=2\times270=540 \end{gathered}[/tex]Taylor Drove 540 Miles in April
Which statement is true about the relation shown on the graph below?
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We know that a function has a unique value of y for each value in x so the correct statement is:
c. it is not a function because there are multiple y values for a given x value
In the lab, Deandre has two solutions that contain alcohol and is mixing them with each other. Solution A is 10% alcohol and Solution B is 60% alcohol. He uses200 milliliters of Solution A. How many milliliters of Solution B does he use, if the resulting mixture is a 40% alcohol solution?
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The percentage of alcohol of a solution i is given by the quotient:
[tex]p_i=\frac{v_i}{V_i},_{}[/tex]where v_i is the volume of alcohol in the solution i and V_i is the volume of the solution i.
From the statement of the problem we know that:
1) Solution A has 10% of alcohol, i.e.
[tex]p_A=\frac{v_A_{}}{V_A}=0.1.\Rightarrow v_A=0.1\cdot V_A.[/tex]2) Solution B has 60% of alcohol, i.e.
[tex]p_B=\frac{v_B}{V_B}=0.6\Rightarrow v_B=0.6\cdot V_B.[/tex]3) The volume of solution A is V_A = 200ml.
4) The resulting mixture must have a percentage of 40% of alcohol, so we have that:
[tex]p_M=\frac{v_M}{V_M}=0.4.[/tex]5) The volume of the mixture v_M is equal to the sum of the volumes of alcohol in each solution:
[tex]v_M=v_A+v_{B\text{.}}_{}[/tex]6) The volume of the mixtureVv_M is equal to the sum of the volumes of each solution:
[tex]V_M=V_A+V_B\text{.}[/tex]7) Replacing 5) and 6) in 4) we have:
[tex]\frac{v_A+v_B}{V_A+V_B_{}}=0.4_{}\text{.}[/tex]8) Replacing 1) and 2) in 7) we have:
[tex]\frac{0.1\cdot V_B+0.6\cdot V_B}{V_A+V_B}=0.4_{}\text{.}[/tex]9) Replacing 3) in 8) we have:
[tex]\frac{0.1\cdot200ml_{}+0.6\cdot V_B}{200ml_{}+V_B}=0.4_{}\text{.}[/tex]Now we solve the last equation for V_B:
[tex]\begin{gathered} \frac{0.1\cdot200ml+0.6\cdot V_B}{200ml_{}+V_B}=0.4_{}, \\ \frac{20ml+0.6\cdot V_B}{200ml_{}+V_B}=0.4_{}, \\ 20ml+0.6\cdot V_B=0.4_{}\cdot(200ml+V_B), \\ 20ml+0.6\cdot V_B=80ml+0.4\cdot V_B, \\ 0.6\cdot V_B-0.4\cdot V_B=80ml-20ml, \\ 0.2\cdot V_B=60ml, \\ V_B=\frac{60}{0.2}\cdot ml=300ml. \end{gathered}[/tex]We must use 300ml of Solution B to have a 40% alcohol solution as the resulting mixture.
Answer: 300ml of Solution B.
A store had 896 swimsuits that were marked to sale at $44.95/swimsuit. Each suit was marked down $16.90. Find the reduced price using the formula M = S - N, where M is the markdown, S is the original selling price, and N is the reduced price. The reduced price is ?
Answers
Given:
The original selling price of 1 swimsuit = $44.95
The selling price of 1 marked down swimsuit = $16.90
Using the provided formula:
[tex]M\text{ = S - N}[/tex]Where,
M is the markdown
S is the original selling price
N is the reduced price
Substituting we have:
[tex]16.90\text{ = 44.95 - N }[/tex]Solving for N:
[tex]\begin{gathered} \text{Collect like terms} \\ -N\text{ = 16.90 - 44.95} \\ -N\text{ = -28.05} \\ \text{Divide both sides by -1} \\ \frac{-N}{-1}=\text{ }\frac{-28.05}{-1} \\ N\text{ = 28.05} \end{gathered}[/tex]Hence, the reduced price is $28.05
Answer:
$28.05
Solve the following system of equations using the elimination method. Give the final answer in (x,y) form.
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Anisha used the substitution method to solve the system of equations.
She is missing the value of y.
To find it we plut the value of x in the first equation, then:
[tex]y=4-5=-1[/tex]Therefore the solution is (4,-1)
Problem 14.f(2)(a) Determine the equations of the perpendicular bisectors througheach side of the triangle.C(4,6)B(7,3)A(2,2)I
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The product of the slopes of the perpendicular lines is -1, which means if the slope of one of them is m, then the slope of the perpendicular line is -1/m
In triangle ABC
The perpendicular bisector of the side BC is drawn from the opposite vertex A
Then to find it find the slope of BC and reciprocal it and change its sign to get its slope and find the midpoint of BC to use it in the equation of the perpendicular bisector
Since B = (7, 3) and C = (4, 6)
Let us find the slope of BC, using the rule of the slope
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Let (x1, y1) = (7, 3) and (x2, y2) = (4, 6)
[tex]\begin{gathered} m_{BC}=\frac{6-3}{4-7} \\ m_{BC}=\frac{3}{-3} \\ m_{BC}=-1 \end{gathered}[/tex]Now to find the slope of the perpendicular line to BC reciprocal it and change its sign
Since the reciprocal of 1 is 1 and the opposite of negative is positive, then
Then the slope of the perpendicular line is 1
Now, let us find the mid-point of BC
The rule of the midpoint is
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]Then the mid-point of BC is
[tex]\begin{gathered} M_{BC}=(\frac{7+4}{2},\frac{3+6}{2}) \\ M_{BC}=(\frac{11}{2},\frac{9}{2}) \\ M_{BC}=(5.5,4.5) \end{gathered}[/tex]Now we can form the equation of the perpendicular bisector of BC using its slope 1 and the point (5.5, 4.5)
The form of the equation using a point and a slope is
[tex]y-y1=m(x-x1)[/tex]m is the slope and (x1, y1) is a point on the line
Since m = 1 and (x1, y1) = (5.5, 4.5), then
[tex]\begin{gathered} m=1,x1=5.5,y1=4.5 \\ y-4.5=1(x-5.5) \\ y-4.5=x-5.5 \end{gathered}[/tex]Add 4.5 to both sides
[tex]\begin{gathered} y-4.5+4.5=x-5.5+4.5 \\ y=x-1 \end{gathered}[/tex]The equation of the perpendicular bisector of BC is
[tex]y=x-1[/tex]We will do the same to AB and AC
15. (09.03) Jim picked a card from a standard deck. What is the probability that Ilm picked a heart or an ace? (1 point) OI 52 O 2 52 O 16 52 O 17 52
Answers
The probability of picking a heart or an ace is 17/52
Here, we want to get the probability
The number of cards in a standard deck is 52 cards
Now, we need to know the number of hearts and the number of ace
There are 13 hearts, and 4 aces
The probability of picking a heart is;
[tex]\frac{13}{52}[/tex]The probability of picking an ace is;
[tex]\frac{4}{52}[/tex]The probability of picking an ace or a heart is the sum of both which is;
[tex]\frac{4}{52}+\frac{13}{52}\text{ = }\frac{17}{52}[/tex]