Kyle throws a baseball straight up from a height of 5 feet with an initial speed of 41feet per second.What is the maximum height of the baseball?
Answers
We will determine the maximum height of the baseball as follows:
We will need the following formulas:
[tex]v=u+at[/tex][tex]s=ut+\frac{1}{2}at^2[/tex]Here "u" represents the original speed, "t" represents the time, "a" the acceleration of the body and "s" is the total discance moved. [We will find s to solve the problem].
So:
First we have that the acceleation that the body will experience is -9.8m/s^2 [Since the object is going upwards and gravity is pulling on it towards the ground]. [acceleration of gravity using feet over second squared is 32.17 ft/s^2].
[tex]v=(12.4968)+(-9.8)t[/tex]But the maximum height will be reached when the velocity after certain time has passed is 0 ft/s, so:
[tex]0=(12.4968)+(-9.8)t\Rightarrow9.8t=12.4968[/tex][tex]\Rightarrow t=1.275183673\ldots\Rightarrow t\approx1.3[/tex]So, at approximately 1.3 seconds the maximum heigth willl be reached.
Now, we solve for s:
[tex]s=(12.4968)(1.275183673)+\frac{1}{2}(-9.8)(1.275183673)^2\Rightarrow s=7.967857665[/tex][tex]\Rightarrow s\approx8[/tex]So, the maxumum altitude for the baseball will be 8 meters, but we have to add the initial 5 feet at which it was launched:
[tex]h\approx8+1.524\Rightarrow h\approx9.491857665[/tex]And taking that to feet we will have:
[tex]h\approx31.141265305118\ldots[/tex]So, the solution must be the last option. [The discrepanc
Related Questions
a laptop was originally sold for %975 the laptop is now on sale for $828.75 what is the percent markdown
Answers
The percent markdown is of the 15% of the price.
What is the percent markdown?We know that the original price is $975, and at the moment is sold by $828.75.
If we define the markdown (as a decimal) as r, then we can write the equation:
$828.75 = $975*(1 - r)
Solving this for r, we get:
($828.75 - $975)/(-$975) = r = 0.15
To write this as a percentage, we just need to multiply this by 100%.
0.15*100 = 15%
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Given the table below, write a linear equation that defines the dependent variable, c, in terms of the independent variable, a.
Answers
For a linear equation, the first step is to find the slope.
Based on the table, I see that every time "t" increases by 1, then "k" increases by 4.
Since we're told k is the dependent variable, the slope will be
[tex]\dfrac{\text{change in }k}{\text{change in }t}} = \dfrac{4}{1} = 4[/tex]
The slope is always [tex]\dfrac{\text{change in dependent variable}}{\text{change in independent variable}}[/tex].
Once you have the slope, you need the vertical (We'd normally call this this y-intercept, but there's no "y" here. You could call it the "k" intercept in this example.)
From the table, we again see that t=0 has k=2, so that 2 is the value we need.
This gives us our equation: k = 4t + 2.
(This all is really just the slope-intercept form with x's now being called "t" and y's now being called "k".)
What is the complement of a 54 1/2 degree angle
Answers
Two angles are complementary if their sum is 90 degrees
Therefore, to get a complement of 54 1/2 degrees, we will have to subtract it from 90 degrees
Let the complement of 54 1/2 be represented by x
[tex]\begin{gathered} x=90-54\frac{1}{2} \\ \\ x=90-\frac{109}{2} \\ \\ x=\frac{180-109}{2} \\ \\ x=\frac{71}{2} \\ \\ x=35\frac{1}{2}\text{ degrees} \end{gathered}[/tex]Therefore, the complement of angle 54 1/2 degrees is angle 35 1/2 degrees
Try It! On Saturday, the vacation resort offers a discount on water sports. To takea surfing lesson and go parasailing costs $130. That day, 25 people takesurfing lessons, and 30 people go parasailing. A total of $3,650 is collected.What is the discounted price of each activity?CHECK ANSWER
Answers
Let the cost of surfing lesson be x and the cost of Parasiling be y
From the question, both surfing lesson and parasailing cost $130
Hnece;
x + y = 130 ---------------------------(1)
From the question, 25 people take surfing lesson and 30 pupil went for parasailing and a total of $3, 650 was collected
Hence;
25x + 30y = 3650--------------------------------(2)
We can now solve equation (1) and (2) simultaneously
Using elimination method,
multiply through equation(1) by 30
30 x + 30 y = 3900 ------------------(3)
subtract equation(1) from equation (3)
5x = 250
divide both-side of the equation by 5
x = 50
substitute x = 50 into equation (1) and then solve for y
x + y = 130
50 + y = 130
subtract 50 from both-side of the equation
y = 130 - 50
y =80
Therefore, the discount price of Surfing lesson is $50 while the discount price for parasailing is $80
I need help with this practice problem solving This subject is trig from my ACT prep guide I will add an additional picture of the answer options
Answers
Connect the points in a smooth curve, approaching the asymptotes located where the tangent function is undefined.
22.2: X's Y'S Match each expression in column A with an equivalent expression from column B. Be prepared to explain your reasoning. А 1.1934) Buty 1. 12(x+y) the w 2. 12(x - y) w 2. (9x + 5y)-(3x + 7y) 3. (9x + 5y)-(3x - 7y) 3.6(x - 2y) 4. 9x - 7: + 3x + 5y 4. 9x + 5y + 3x - 7 5. 9x - 7y + 3x - 5y 5.9x + 5y - 3x + 7y 6.9x - 7y - 3x - 5y 6.9x - 3x + 5y - 7y
Answers
Given data:
The given list.
1) The first expression can be written as,
[tex]\begin{gathered} 9x+5y+3x+7y=12x+12y \\ =12(x+y) \end{gathered}[/tex]2) The second expression can be written as,
[tex](9x+5y)-(3x+7y)=9x-3x+5y-7y[/tex]3)The third expression can be written as,
[tex](9x+5y)-(3x-7y)=9x+5y-3x+7y[/tex]4)The fourth expression can be written as,
[tex]9x-7y+3x+5y=9x+5y+3x-7y[/tex]5)The fifth expression can be written as,
[tex]\begin{gathered} 9x-7y+3x-5y=12x-12y \\ =12(x-y) \end{gathered}[/tex]6)The sixth expression can be written as,
[tex]\begin{gathered} 9x-7y-3x-5y=6x-12y \\ =6(x-2y) \end{gathered}[/tex]Thus, the correct match is 1-1, 2-6, 3-5, 4-4, 5-2, 6-3.
Complete the function table for the given domain, and plot the points on the graph. (t) = -12 + 2.1 + 5 -1 0 1 2 3 Drawing tools Click on a tool to begin draving. EK Select f(x) Point Click on the Graph to place a Point HHHH 6 2 2 10 0
Answers
f(x) = -x^2 + 2x + 5
x -1 0 1 2 3
f(x) 2 5 6 5 2
The box plot shows the average monthly high temperatures in New York City for 12 months. What is the difference between the range and interquartile range of the temperatures data?
Answers
The difference between the range and interquartile range of the temperatures data is equal to 16.
What is a range?Mathematically, range can be calculated by using this formula;
Range = Highest number - Lowest number
Range = 84 - 38
Range = 46.
What is an interquartile range?Mathematically, interquartile range (IQR) is the difference between first quartile (Q₁) and third quartile (Q₃):
IQR = Q₃ - Q₁
Based on the given box and whisker plot (see attachment), we can logically deduce the following quartile ranges:
Third quartile, Q₃ = 48
First quartile, Q₁ = 78
Now, we can calculate the interquartile range (IQR) is given by:
Interquartile range, IQR = Q₃ - Q₁
Interquartile range, IQR = 78 - 48
Interquartile range, IQR = 30
For the difference, we have:
Difference = Range - IQR
Difference = 46 - 30
Difference = 16
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Based on the function F(x) = 2x° +2x² - 4 and the graph of G(x) below, which of the following statements is true? TH O A. F(x) has 3 real roots x 70 G() O B. as x → = G(x) > 0 x → F(x) → O c. as x →-, F(x) — - O D. G(X) has 3 real roots
Answers
We could graph the function F:
[tex]F(x)=2x^3+2x^2-4[/tex]As follows:
As you can see,
[tex]\begin{gathered} as\text{ x}\to\infty,\text{ f(x)}\to\infty \\ as\text{ x}\to-\infty,\text{ f(x)}\to-\infty \end{gathered}[/tex]Therefore, the correct answer is C.
For nitrogen to be a liquid, its temperature must be within 12.78 °F of –333.22 °F. Which equation can be used to find the maximum and minimum temperatures at which nitrogen is a liquid, x?
Answers
The maximum and minimum temperatures at which nitrogen is a liquid is -320.44°F and = -346°F.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the nitrogen to be a liquid, its temperature must be within 12.78 °F of –333.22 °F.
The minimum temperature will be:
= -333.22 - 12.78
= -346°F
The maximum temperature will be:
= -333.22 + 12.78
= -320.44°F
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The formula for calculating the distance, d, in miles that one can see to the horizon on a clear day is approximated by d=1.22radical x, where x is the elevation in feet of a person's eyes. a. approximately how far, to the nearest mile, can a person whose eyes are 600 feet above sea-level see? b. approximately how high, to the nearest foot, would a person's eyes need to be to see 100 miles?
Answers
The expression to calculate the distance a person can see is below, where x is the height in feet of a person's eyes above see-level:
[tex]d=\sqrt[1.22]{x}\lbrack mi\rbrack[/tex]a) A person who is 600 feet height will see:
[tex]d=\sqrt[1.22]{600}=189.30mi[/tex]b) In order to get the height a person needs to be so that he/she could see 100 miles long, we solve the equation for x:
[tex]\begin{gathered} d=x^{\frac{1}{1.22}} \\ d^{1.22}=(x^{\frac{1}{1.22}})^{1.22}=x \\ x=100^{1.22}=275.42ft \end{gathered}[/tex]What is the value??8+(-3)+15-(-40)
Answers
We applied the rules that said:
- If we add a negative number, it is the same as substracting its negative. That is why "+(-3)" is equal to "-3".
- If we substract a negative number is equal to add the negative of this number. That is why "-(-40)" is equal to "+40".
x=72+(m*14)when m=6 to the third power
Answers
The value of x is 3096
Here, we want to find the value of x when m is 6 raised to its third power
We proceed as follows;
[tex]\begin{gathered} m=6^3\text{ = 216} \\ Substitute\text{ this value} \\ x\text{ = 72}+\text{(216 }\times\text{ 14)} \\ x\text{ = }72\text{ + 3024} \\ x\text{ = 3096} \end{gathered}[/tex]The figure below is a net for a right rectangular prism. Its surface area is 396 cm2 andthe area of some of the faces are filled in below. Find the area of the missing faces,and the missing dimension.
Answers
hello
to solve this question, let's add up all the areas from the sides given and equate it to the total area of the prism. Then we can also denote the side with the missing area as x
[tex]\begin{gathered} 396=42+72+42+72+x+x \\ 396=228+2x \\ 2x=396-228 \\ 2x=168 \\ \text{divide both sides by the coefficient of x} \\ \frac{2x}{2}=\frac{168}{2} \\ x=84 \end{gathered}[/tex]now we have established the area of the missing sides as 84cm^2
but then from careful observation, the figure with the missing side have a shape of a rectangle and we can use the formula of area of a rectangle to find the missing side.
[tex]\begin{gathered} a=l\times w \\ a=84\operatorname{cm}^2 \\ l=? \\ w=7\operatorname{cm} \\ 84=l\times7 \\ 84=7l \\ \frac{84}{7}=\frac{7l}{7} \\ l=12\operatorname{cm} \end{gathered}[/tex]from the calculations above, the missing side is equal to 12cm
10<=6-2x<14 solve the inequality
Answers
Having that
10 ≤ 6 - 2x < 14
It meets two statements:
10 ≤ 6 - 2x and 6 - 2x < 14
We are solving each of them separately. We have to remember that we can add or substract any amount both sides of the inequalities and multiply or divide by a positive number both sides.
First statement: 10 ≤ 6 - 2xOn one hand, we want to solve:
10 ≤ 6 - 2x
then
10 ≤ 6 - 2x
↓ adding 2x both sides
10 + 2x ≤ 6
↓ substracting 10 both sides
2x ≤ 6 -10
↓ 6 - 10 = -4
2x ≤ -4
↓ dividing by 2 both sides
2x/2 ≤ -4/2
↓ -4/2 = -2
x ≤ -2
We have that x ≤ -2
Second statement: 6 - 2x < 14For the other hand, we want to solve
6 - 2x < 14
then
6 - 2x < 14
↓ adding 2x both sides
6 < 14 + 2x
↓ substracting 14 both sides
6 - 14 < 2x
↓ 6 - 14 = -8
-8 < 2x
↓ dividing by 2 both sides
-8/2 < 2x/2
↓ -8/2 = -4
-4 < x
We have that -4 < x
Therefore, joining both conclusions, we have that -4 < x and x ≤ -2, then
Answer: -4 < x ≤ -2Instructions: For the following quadratic functions, write the function in factored form and then find the -intercepts, axis of symmetry, vertex, and domain and range. Round to one decimal place, if necessary.
Answers
Factored form: y = (x+1)(x-8)
x-intercept: (-1, 0) and (8, 0)
Axis of symmetry: x = 7/2
Vertex: (7/2, -81/4)
Domain: All real numbers
Range: y ≥ -81/4
Explanations:Given the quadratic equation expressed as:
[tex]y=x^2-7x-8[/tex]Factorize
[tex]\begin{gathered} y=x^2-8x+x-8 \\ y=x(x-8)+1(x-8) \\ y=(x+1)(x-8)\text{ Factored form} \end{gathered}[/tex]The x-intercept is the point where y= 0. Substitute y = 0 into the factored form
[tex]\begin{gathered} (x+1)(x-8)=0 \\ x=-1\text{ }and\text{ }8 \\ The\text{ x-intercept are \lparen-1, 0\rparen and \lparen8, 0\rparen} \end{gathered}[/tex]The axis of symmetry of the equation is given as x = -b/2a where:
a = 1
b = -7
Substitute:
[tex]\begin{gathered} axis\text{ of symmetry:}x=\frac{-(-7)}{2(1)} \\ axis\text{ of symmetry: }x=\frac{7}{2} \end{gathered}[/tex]The vertex form of the equation is in the form (x-h)^2+k where (h, k) is the vertex. Rewrite in vertex form:
[tex]\begin{gathered} y=x^2-7x-8 \\ y=x^2-7x+(-\frac{7}{2})^2-(-\frac{7}{2})^2-8 \\ y=(x-\frac{7}{2})^2-\frac{49}{4}-8 \\ y=(x-\frac{7}{2})^2-\frac{81}{4} \end{gathered}[/tex]The vertex of the function will be (7/2, -81/4)
The domain are the independent values of the function for which it exists. The domain of the given quadratic function exists on all real number that is:
[tex]Domain:(-\infty,\infty)[/tex]The range of the function are the dependent value for which it exist. For the given function, the range is given as:
[tex]Range:[-\frac{81}{4},\infty)[/tex]Five fair tetrahedral (four-sided) dice are rolled at the same time. The values on the faces of each die are 1, 2, 3, and 4.a. What is the theoretical probability of rolling a 1 on all five dice?b. Zavier conducted an experiment in which he rolled five fair tetrahedral dice 50 times. He rolled a 1 on all five dice once. What is the experimental probability of rolling a 1 on all five dice?
Answers
Solution:
The probability of an event is the ratio of number of outcome of the event to the total outcome of events.
Thus;
(a) The theoretical probability of rolling a 1 on all five dice is;
[tex](\frac{1}{4})^5[/tex](b) In the experiment, he rolled five fair tetrahedral dice 50 times. Thus, the experiment probability of rolling a 1 on all five dice is;
[tex]\frac{1}{50}[/tex]Solve the following equation:
-3(5+4x)-7=14
Answers
The value of x is, x = -3.
What is solving an equation?
A General Rule for Equation Solving
Remove parentheses from each side of the equation and combine similar phrases to make it simpler.
To separate the variable term on one side of the equation, use addition or subtraction.
To find the variable, use division or multiplication.
Consider, the given equation
-3(5 + 4x) - 7 = 14
Solving the parenthesis
-15 - 12x - 7 = 14
Simplifying,
-22 - 12x = 14
Adding 22 on both sides,
-22 - 12x + 22 = 14 + 22
-12x = 36
Divide both sides by 12,
-12x/12 = 36/12
-x = 3
Multiply both sides by -1.
-x(-1) = 3(-1)
x = -3
Hence, the value of x is, x = -3.
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List all numbers from the given set that area. natural numbersb. whole numbersd. rational numberse. irrational numbersc. integersf. real numbers{0.1. VT6.0. -2. 15. -3, 98. }a natural numbers =(Use a comma to separate answers as needed. Do not simplify.)b. whole numbers =(Use a comma to separate answers as needed. Do not simplify.)c. integers =(Use a comma to separate answers as needed. Do not simplify)d. rational numbers =(Use a comma to separate answers as needed. Do not simplify.)e irrational numbers =(Use a comma to separate answers as needed. Do not simplify.)f. real numbers =(Use a comma to separate answers as needed. Do not simplify.)
Answers
how long will it take for the population to get to 2552 alligators?
Answers
we have the equation
[tex]P(t)=319(2)^{(\frac{t}{3})}[/tex]For P(t)=2,552
substitute in the given equation
[tex]2,552=319(2)^{(\frac{t}{3})}[/tex]solve for t
[tex]\begin{gathered} 2,552=319(2)^{(\frac{t}{3})} \\ \frac{2,552}{319}=(2)^{(\frac{t}{3})} \end{gathered}[/tex]Apply log both sides
[tex]\begin{gathered} \log \lbrack\frac{2,552}{319}\rbrack=\log \lbrack(2)^{(\frac{t}{3})}\rbrack \\ \log \lbrack\frac{2,552}{319}\rbrack=\frac{t}{3}\cdot\log (2) \end{gathered}[/tex]t=9 yearsthe answer is 9 years from the time of introductionIf 11 people each own of an acre of
2/19
land and they put all their land together
how much land, in acres, would they
Answers
If 11 people each own of an acre of 2/19 land, their land together is area of 22/19 of an acre.
If 11 people each own of an acre of 2/19
The area of land owned by 1 person = 2/9
To find the area of land owned by 11 persons altogether
We have to multiply 11 with the area owned by one person
11 x (2/19)
= 22/19
Therefore, If 11 people each own of an acre of 2/19 land, the they land owned by them altogether is area of 22/19 of an acre.
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John drank 18 fluid ounces of juice. How much is this in cups? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answers
We know that 1 cup is equivalent to 8 fluid ounces. Then, we can establish the following rule of three:
[tex]\begin{gathered} 8\text{ fluid ounces ----- 1 cup} \\ 18\text{ fluid ounces ------ x} \end{gathered}[/tex]Then, by cross multiplying these quantities, we have
[tex]x\times8\text{ fluid ounces= 1 cup}\times\text{ 18 ounces}[/tex]By dividing both sides by 8 fluid ounces, we get
[tex]x=\frac{1\text{ cup}\times18\text{ ounces}}{8\text{ fluid ounces}}[/tex]which gives
[tex]x=\frac{18}{8}\text{ cups}[/tex]Now, we need to convert this simple form to a mixed form, that is,
Then, by simplifying this mixed form, the answer is:
[tex]2\frac{1}{4}\text{ cups}[/tex]A park walkway surrounds a fountain as shown. Find the area of the walkway. Round to the nearest foot.
Answers
The fountain is depicted by the white circle in the picture. The surrounding walkway is depicted by the grey areas.
From the sketch shown above, the semi-circle inscribed in the rectangle is one half of the fountain. We shall calculate the area of the semi-circle and subtract this from the area of the rectangle.
The area of the rectangle is;
[tex]\begin{gathered} \text{Area}=l\times w \\ \text{Area}=30\times42.5 \\ \text{Area}=1275ft^2 \\ \text{The area of the semicircle is,} \\ \text{Area=}\frac{1}{2}(\pi\times r^2) \\ \text{The diameter is 18 ft, and therefore the radius is 9 ft} \\ \text{Area}=\frac{1}{2}(3.14\times9^2) \\ \text{Area}=\frac{1}{2}(3.14\times81) \\ \text{Area}=\frac{1}{2}(254.34) \\ \text{Area}=127.17ft^2 \end{gathered}[/tex]Therefore, the area of the shaded region would be,
Area = 1275 - 127.17
Area = 1147.83
Next step is to calculate the other half of the figure (the right side), as follows;
Observe that the outer semi-circle is the shaded region while the inner one is the white portion.
The area is
[tex]\begin{gathered} \text{Shaded region;} \\ \text{Area}=\frac{1}{2}(\pi\times r^2) \\ \text{Area}=\frac{1}{2}(3.14\times15^2) \\ \text{Area}=\frac{1}{2}(3.14\times225) \\ \text{Area}=\frac{1}{2}(706.5) \\ \text{Area}=353.25ft^2 \\ \text{White region;} \\ \text{Area}=\frac{1}{2}(\pi\times9^2) \\ \text{Area}=\frac{1}{2}(3.14\times81) \\ \text{Area}=127.17ft^2 \end{gathered}[/tex]The area of the shaded region is;
Area = 353.25 - 127.17
Area = 226.38
Therefore the total area of the walkway surrounding the fountain is;
Area = 1147.83 + 226.38
Area = 1374.21
Area = 1,374 feet squared (rounded to the nearest foot)
sally, a journalism student, counted the number of pages in several major magazines. Number of pages Number of magazines 118 4 152 4 169 2 is the number of pages that a randomly chosen magazine had. What is the expected value of X? write your answer as a decimal.
Answers
Let's begin by identifying key information given to us:
4 magazines have 118 pages
4 magazines have 152 pages
2 magazines have 169 pages
The expected value for X (in pages) is given by:
[tex]\begin{gathered} P(118pages)=\frac{4}{10}=\frac{2}{5} \\ P(152pages)=\frac{4}{10}=\frac{2}{5} \\ P(169pages)=\frac{2}{10}=\frac{1}{5} \\ EV(x)=118\times\frac{2}{5}+152\times\frac{2}{5}+169\times\frac{1}{5} \\ EV(x)=141\frac{4}{5}=141.80 \\ EV(x)=141.8 \end{gathered}[/tex]The expected value of X is 141.8 pages
A 104° sector of a circle has an area of 56 square centimeters. Tothe nearest centimeter, what is the diameter of the circle?
Answers
The diameter is 8cm
Explanation:Given the following:
[tex]\begin{gathered} \theta=104^o \\ \\ \text{Area(}A)=\pi r^2=56cm^2 \\ \text{Diameter(D)}=2r=\text{?} \end{gathered}[/tex]From the area of the circle, we can have the value for the radius, r as follows:
[tex]\begin{gathered} \pi r^2=56 \\ r^2=\frac{56}{\pi} \\ \\ r=\sqrt[]{\frac{56}{\pi}}\approx4cm \end{gathered}[/tex]We can now obtain the diameter by multiplying the radius by 2
[tex]D=2r=2\times4=8cm[/tex]#6) long division a. Let P(x) = 8x^3 + 27 and D(x) = 2x + 3
Answers
The functions are given to be:
[tex]\begin{gathered} P(x)=8x^3+27 \\ D(x)=2x+3 \end{gathered}[/tex]To evaluate:
[tex]P(x)\div D(x)[/tex]STEP 1
Divide the leading term of the dividend by the leading term of the divisor. Write down the calculated result in the upper part of the table. Multiply it by the divisor and subtract the dividend from the obtained result:
STEP 2
Divide the leading term of the obtained remainder by the leading term of the divisor. Write down the calculated result in the upper part of the table. Multiply it by the divisor and subtract the remainder from the obtained result:
STEP 3
Divide the leading term of the obtained remainder by the leading term of the divisor. Write down the calculated result in the upper part of the table. Multiply it by the divisor and subtract the remainder from the obtained result:
ANSWER
[tex]\frac{8x^3+27}{2x+3}=4x^2-6x+9[/tex]consider parallelogram JKLM below.use the information given in the figure to find m
Answers
Here, we have a parallelogram JKLM.
Given:
JK = 3x
LM = 3
m∠J = 106°
m∠KMJ = 34°
A parallelogram is a quadilateral that has equal opposite angles and the opposite sides are also equal.
Thus, we have:
• m∠L = m∠J = 106°
m∠L = 106°
• x:
Here, JK is opposite side LM. SInce they are opposite sides, they have equal length.
Thus, we have:
JK = LM
3x = 3
Divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{3}{3} \\ \\ x=1 \end{gathered}[/tex]x = 1
• m∠LKM:
Apply the alternate interior angles theorem. Alternate interior angles are congruent.
∠LKM and ∠KMJ are alternate interior angles. This means they are congruent.
Thus, we have:
m∠LKM = m∠KMJ = 34°
m∠LKM = 34°
ANSWER:
• m∠L = 106°
• x = 1
• m∠LKM = 34°
-5|x+4|-7 describe the transformation.
Answers
Answer:3
Step-by-step explanation:
so you take 41 and divide by 2 and get 5. then take -51 and times by 6 which is 24.then you take seven and multipy by 3 and get 20. so you are left with 5, 24, and 20. Multiply all of them and get 3!!
There are 33.8 fluid ounces in a liter. There are 128 fluid ounces in a gallon. How many litersthere are roughly in a gallon?to. 2b. 3C. 4d. 5Is your estimate greater or less than the exact number of liters in a gallon? Explainhow do you know.
Answers
Answer
Option C is correct.
There are roughly 4 liters in 1 gallon
And the estimate (4 liters in 1 gallon) is greaster then the exact number of liters in a gallon (3.79 liters in 1 gallon).
Explanation
We are given some parameters
33.8 fluid ounces = 1 liter
128 fluid ounces = 1 gallon
We are then told to find the amount of liters that are roughly in a gallon.
To do this, we will put the parameters that are equivalent as fractions on each other
[tex]\begin{gathered} \frac{33.8\text{ fluid ounces}}{1\text{ liter}}=1 \\ \frac{128\text{ fluid ounces}}{1\text{ gallon}}=1 \end{gathered}[/tex]We can write the first relation as an inverse and we will still have the same thing
[tex]\begin{gathered} \frac{1\text{ liter}}{33.8\text{ fluid ounces}}=1 \\ \frac{128\text{ fluid ounces}}{1\text{ gallon}}=1 \\ \text{ Since, 1 }\times1=1 \\ We\text{ can find the relation betw}een\text{ liter and gallon by saying} \\ \frac{1\text{ liter}}{33.8\text{ fluid ounces}}\times\frac{128\text{ fluid ounces}}{1\text{ gallon}} \\ \frac{128}{33.8}\frac{\text{liter}}{\text{gallon}} \\ =\frac{3.79\text{ liters}}{1\text{ gallon}} \end{gathered}[/tex]3.79 liters = 1 gallon
A right approximation will be that
1 gallon = 4 liters
We can then see that the estimate is greater than the exact number of liters in a gallon.
Hope this Helps!!!
Ruth used a spinner to perform 10 to the probably of having the children whyes • Is Ruth's estimated probably representative of the theoretical probaby of having the children were? • Provide the estimated probability from this on and the theoretical probably of having them Respond in the space provide
Answers
Keshawn, this is the solution to part B:
P (blue) = 25% = 1/4
P (brown) = 75% = 3/4
If Ruth performs 10 trials, the theoretical probability would be:
P (blue) = 25% = 2.5/10
P (brown) = 75% = 7.5/10
Upon saying that, the outcome of 1 of having three children with blue eyes isn't a theoretical probability, it is a experimental probability.
Finally, the theoretical probability of having three children with blue eyes is:
P (3 chlildren with blue eyes) = 1/4 * 1/4 * 1/4 = 1/64