Answers
The range of distance from A to C is greater than 12.3 feet and less than 32.1 feet.
What is the Triangle inequality Theorem?To precisely state the dimensions of a triangle's sides, the triangle inequality theorem is a crucial component of geometry.
According to this rule, a triangle's third side must be longer than the sum of its other two sides.
Say, AB, BC, and CA make up three of the sides of the triangle ABC.
The length of (AB + BC) must therefore be longer than CA according to the triangle inequality theorem.
As a result, CA > (AB + BC).
The sum of the lengths of BC and CA must exceed the length of AB.
As a result, AB > (BC + CA).
The sum of the lengths of AB and CA must exceed the length of BC.
Consequently, (AB + CA) > BC.
As per the question:AB = 22.2 feet
BC = 9.9 feet
Taking AB as the longest side of the triangle.
The measure of AB must be less than the sum of AC and BC.
⇒ AC < AB + BC
⇒ AC < 22.2 + 9.9
⇒AC < 32.1 feet
Therefore, the range of distance from A to C is greater than 12.3 feet and less than 32.1 feet.
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Related Questions
Determine the x-intercept from the given Coordinate Pairs. * {(-1,8), (0.6). (5:5).(3,0). 1.5.-17)} O r= 3 b = 6 x = ? = -2
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The x interception is when y = 0
the fouth point is (3,0), in that point y is 0 and x is 3
So the x interception is at x = 3
The answer is the first option x = 3
Adalyn uses 1/5 cup of blue paint for every 2/5 cup of red paint to make purple paint. Enter the number of cups of blue paint Adalyn uses for 1 cup of red paint.
Answers
Given that;
Adalyn uses 1/5 cup of blue paint for every 2/5 cup of red paint to make purple paint.
[tex]\frac{1}{5}\text{ cups of blue paint }\rightarrow\frac{2}{5}\text{ cups of red paint}[/tex]For 1 cup of red paint, the amount of blue paints Adalyn will use is;
[tex]\frac{1}{5}\text{ cups of blue paint }\rightarrow\frac{2}{5}\text{ cups of red paint}[/tex]What is the point-slope form of equation of the line that passes through the point (-1, -4) and has a slope of 3?
Answers
Answer:
y - (-4) = 3(x - (-1)
Step-by-step explanation:
Answer:
y−4=−3(x+1)
Step-by-step explanation:
What's the next term in the sequence of 1, 8, 27, 81, 243?
Answers
The next term in the sequence of 1, 8, 27, 81, 243 is 729.
What is a sequence?
Sequences are ordered collections of numbers, often known as "terms," such as 2,5,8. There are some sequences that adhere to a particular pattern that allows for endless extension. For instance, 2,5,8 adheres to the "add 3" pattern, thus we may now continue the process. There are formulas for sequences that show us where to find any given term.
It might be good to separate each phrase into its component parts to solve this problem:
1, or 3^0, is a factor of 1.
8 is 2^3
27 is 3^3
81 is 3^4
243 is 3^5
The likelihood of the following phrase is 3^6, or 729.
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Could I get help with this problem I have in algebra?
Answers
Answer
Explanation
Cost of a lower deck ticket = 42 dollars
Cost of an upper deck ticket = 75%
ALGEBRA - 30 POINTS
In a volatile housing market, the overall value of a home can be modeled by V(x) = 210x2 – 4400x + 125000, where V represents the value of the home and x represents each year after 2020. Find the vertex and interpret what the vertex of this function means in terms of the value of the home. Show the work you completed to determine the vertex.
Answers
Answer: the vertex is 157x4
Step-by-step explanation:
what is the midpoint of the segment that would be created between points L and N on the graph
Answers
Given:
The figure KLMN on graph.
Required:
what is the midpoint of the segment that would be created between points L and N .
Explanation:
We know the mid point formula
[tex]LN=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]We have L(-2, 3) and N(6, 3)
and
[tex]\begin{gathered} LN=(\frac{-2+6}{2},\frac{3+3}{2}) \\ =(\frac{4}{2},\frac{6}{2}) \\ =(2,3) \end{gathered}[/tex]Answer:
Midpoint is (2,3).
Homework 3.4: Compound InequalitiesScore: 10.38/1811/18 answeredQuestion 6<>04Give the interval that describes the set of values shown above.
Answers
Give the interval that describes the set of values shown above
The interval marked in blue has the following features:
* Starts with a filled blue dot at x=2
* Ends with a filled blued dot at x=4
* Runs from x=2 to x=4 with a blue line
The filled dots indicate that the endpoints are included in the interval
The line indicates that all the values in between the interval are included in the interval
There are two basic forms to indicate an interval with included endpoints:
* A pair of values (the endpoints) comma-separated included in a pair of brackets:
Interval: [2,4]
* The closed interval indicated by inequalities signs:
[tex]2\leq x\leq4[/tex]solve for y = x + 8 for x
Answers
x = y - 8
Which equation that gives the rule for this table.x: 3, 4, 5, 6y: 10, 11, 12, 13A: Y= -x + 7B: Y = x + 7C:Y = 6x + 7OrD: Y= -6 + 7
Answers
To solve this problem we can evaluate te terms in the table in each equation so:
For A) y = -x + 7
we replace (3,10)
[tex]\begin{gathered} 10=-3+7 \\ 10=4 \end{gathered}[/tex]So A is incorrect.
For B) y = x + 7
we replace (3,10), (4,11), (5,12) and (6,13)
[tex]\begin{gathered} 10=3+7=10 \\ 11=4+7=11 \\ 12=5+7=12 \\ 13=6+7=13 \end{gathered}[/tex]So B is the correct answer
Find the area of this circle. Use3.14 for i.7 AtThe area of the circle is aboutfta.(Round to the nearest hundredth as needed.)
Answers
153.86 ft²
Explanation:[tex]\text{Area of a circle = }\pi r^{2}[/tex][tex]\begin{gathered} r\text{ = radius = 7 ft} \\ \pi\text{ = 3.14} \\ In\text{serting into the formula:} \\ \text{Area of the circle = 3.14 }\times7^2 \end{gathered}[/tex][tex]\text{Area of the circle = 153.86 ft}^2[/tex]To the nearest hundredth, Area of the circle = 153.86 ft²
The amount of $In each The amount of $ Total
Answers
Let Lydia invest $x
Half of her stock pays 11% dividend.
So mathematically the amount will be
[tex]\frac{x}{2}\times\frac{11}{100}=\frac{11x}{200}[/tex]With the other half, she pays stocks in 14% interest
So mathematically
[tex]\frac{x}{2}\times\frac{14}{100}=\frac{14x}{200}[/tex]Her total annual interest is $420
So
[tex]\frac{11x}{200}+\frac{14x}{200}=420\Rightarrow25x=84000\Rightarrow x=3360[/tex]She invested $3360 in total
And $1680 in each.
ANGLES what is x,need quick please
Answers
Answer: x = 68
Step-by-step explanation:
Because the 22 degrees and x make up a complementary angle (add up to 90 degrees) we can subtract 22 from 90 to get x.
90-22 = 68
solve for y 10x+8y=4
Answers
Solve the equation.
[tex]\begin{gathered} 10x+8y=4 \\ 8y=-10x+4 \\ y=-\frac{10}{8}x+\frac{4}{8} \\ =-\frac{5}{4}x+\frac{1}{2} \end{gathered}[/tex]So y = -5/4 x +1/2.
Is 4 over 14 simplified and is 15 over 20 simplified and is 21 over 35 simplified
Answers
Solution
For this case we have the following:
[tex]\frac{4}{14}=\frac{2}{7}[/tex]Then the answer is:
2/7
hurry help DUE TONIGHT Based on the figure, which equation is true? Show your work.
Answers
Okay, here we have this:
Considering the provided figure, that we know an angle, the leg opposite a is an angle and we want to know the hypotenuse, we can use the trigonometric ratios since it is a right triangle, so we obtain the following:
The trigonometric ratio that relates an angle, its opposite leg and the hypotenuse is the sine, therefore that is the one we will use, so we have:
[tex]\begin{gathered} \sin (\vartheta)=\frac{Opp}{Hyp} \\ \sin (32)=\frac{8.5}{x} \end{gathered}[/tex]Finally we obtain that the correct answer is the first option (A).
Drag each tile to the correct box Arrange the cylinders in order from least volume to greatest volume. agindur math a diameter of 28 un and a test of 18 units acide with a radius of 13 units and a height of 17 units a cyinder with a diameter of 30 pts and a hught of 14 units onder with a radius of 12 units and a hot 20 units
Answers
Answer:
Explanation:
The volume of a cylinder is given by
[tex]V=\pi r^2h[/tex]Now, to correct the order of the cylinders from least to greatest, we have to calculate the volume of each.
(a). A cylinder with a diameter of 28 units and a height of 18 units.
Diameter is 2 times radius; therefore, r = 14 and the volume is
[tex]V=\pi(14)^2\times18[/tex][tex]V=3529\pi[/tex](b). A cylinder with a radius of 13 units and a height of 17 units.
The volume is
[tex]V=\pi(13)^2\cdot17[/tex][tex]V=2873\pi[/tex](c). A cylinder with a diameter of 30 units and a height of 14 units.
The radius is 15 units; therefore, the volume is
[tex]V=\pi(15)^2\cdot14[/tex][tex]V=3150\pi[/tex](d). A cylinder with a radius of 12 units and a height of 20 units.
The volume is
[tex]V=\pi(12)^2\cdot20[/tex][tex]V=2880\pi[/tex]Hence, from least volume to greatest volume the order is
[tex](b)<(d)<(c)<(a)[/tex]After 4 months of a new nutrition program rashid has lost 16% of his original weight he lost 36lb what was rashids original weight?
Answers
Rashids original weight based on the information illustrated is 225lb.
What was the original weight?From the information given, after the nutrition program rashid has lost 16% of his original weight he lost 36lb.
Let the original weight be given as x.
Therefore, 16% × x = 36
0.16x = 36
Divide through by 0.16
0.16x / 0.16 = 36 / 16
x = 36/0.16
x = 225lb
The weight is 225lb.
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hi i need help as i try with old answer and its wrong
Answers
SOLUTION
The exercise has no question
at a batting cage, each set of baseballs the machine pictures cost $2.50 which inequality represents n, the number of sets of baseballs machine will pitch for no more than $15. 00?
Answers
We have that each set of baseballs cost $2.50, and for the inequality, notice that we cannot spend more than $15. Since each set cost 2.50, then the inequality to represent this situation is:
[tex]5.50n\le15[/tex]Determine whether the relation {(6, –3),
(4, 1), (7, –2), (–3, 1)} is a function. Explain.
Answers
Answer:
A ifs it's not right sorry
A wire of length 22cm is bent in the shape of a circle . find the area of the circle. if the same wire is recent in the form of a square, find it's area which figure encloses more area
Answers
The circle is found to have the more area as compered to the square.
What is termed as the perimeter?A perimeter is a loop that encompasses, encircles, or outlines a two-dimensional shape or length. The circumference of a circle or perhaps an ellipse is its perimeter.For the given question;
The length of the wire is given as 22 cm.
The wire is bent in the circle.
Then, the perimeter of the circle is 22 cm.
Perimeter = 2πr = 22 cm.
Where, π = 3.14 and r is the radius of the circle.
2πr = 22 cm.
r = 11/π 11/3.14
The area of the circle is found as;
Area = πr²
Put the values.
Area = 3.14(11/3.14)²
Area = 38.53 cm².
For the square.
Perimeter = 4 side
22 = 4 side
side = 22/4 = 11/2 = 5.5
Area of square = side²
Area of square = 5.5²
Area of square = 30.25 cm².
Thus, the circle is found to have the more area as compered to the square.
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Miguel bought snacks for his team's practice. He bought a bag of popcorn for $3.33 and a 20-pack of juice bottles. The total cost before tax was $23.33. How much was each bottle of juice?
Answers
The cost of each bottle is $[tex]1[/tex]
Given:
A bag of popcorn costs $[tex]3.33[/tex]Miguel bought [tex]20[/tex]packs of juice bottlesThe total cost before tax was $[tex]23.33[/tex]To find: Cost of each bottle of juice?
It is given that Miguel bought snacks for his team's practice which includes a bag of popcorn, and [tex]20[/tex] packs of juice bottles out of which the bag of popcorn cost him $[tex]3.33[/tex] , and the total cost before tax of all the items costs him $[tex]23.33[/tex]
Now we have to find that how much each bottle of juice costs him as asked in the given question.
Let the bag of popcorn's amount be x and the pack of bottle juice is y
Now according to the linear equation in two variable
[tex]x*1+y*20=23.33[/tex]........(1)
where 1 is the total pack of popcorn bag and [tex]20[/tex] the amount of bottle juice packs
As we know that [tex]x=3.33[/tex] since a bag of popcorn costs him $[tex]3.33[/tex]
Now put the value of x in (1) hence,
[tex]3.33*1+y*20=23.33[/tex]
On further solving we get,
[tex]20y=20[/tex]
On further solving we get,
[tex]y=1[/tex] as the price of every juice of bottle.
Hence a bottle of juice costs him $[tex]1[/tex]
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11x+4<15 or 12x-7>25
Answers
Answer:
Step-by-step explanation:
11x + 4 < 15 or 12x - 7 > 25
-4 -4 +7 +7
11x < 11 or 12x > 32
11 (divide) 11 | 12 (divide) 12
x < 1 or x > 2.7
hope this is right!
Solve using the fractions 5/8 and 1 2/7
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107/56 is the solution of fractions .
What do math fractions mean?
An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.The given fractions are 5/8 and 1 2/7.
We need to find the sum of given fractions.
Now, we can write 1 2/7 as 9/7.
So, 5/8 + 9/7
Here, LCM of 8 and 7 is 56
Then, 35/56 + 72/56
=(35+72)/56
=107/56
Therefore, the sum of the two given fractions is 107/56.
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Find the values of x and y
Answers
Check the picture below.
[tex]13y=20x+3y\implies 10y=20x\implies y=\cfrac{20x}{10}\implies y=2x \\\\[-0.35em] ~\dotfill\\\\ 13y+(8x+y)=180\implies 14y+8x=180\implies \stackrel{\textit{substituting}}{14(\underset{y}{2x})+8x=180} \\\\\\ 28x+8x=180\implies 36x=180\implies x=\cfrac{180}{36}\implies \boxed{x=5}~\hfill \boxed{\stackrel{y = 2(5)}{y = 10}}[/tex]
(Score for Question 1: of 3 points) 1 1. Mahala is standing and fishing on a dock that is 2 - feet above the surface of the water in the pond. Her baited hook is 1.5 feet below the surface of the water. The surface of the water is represented by the 4 rational number 0. Use the number line to graph the distance the dock, point D. is above the water and the hook, point H, is below the water. Make sure you label each point appropriately. Answer: 3 2 -1 0 1 2 3
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graphing the distance of the dock, point D. is above the water and the hook, point H, is below the water.
See the diagram below :
Point D , is above the water =highlited in yellow.
Point H, the hook, is below the water = shown by colour green.
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is divisible by 2". Find P(A). Outcome Probability 1 0.2 2 0.1 3 0.3 4 0.03 5 0.03 6 0.04 7 0.06 0.14 8 0.03 9 0.07 10
Answers
Solution
From the info given the numbers divisible by 2 are:
2,4,6,8,10
And the respective probabilities are:
P(2)= 0.1
P(4) =0.03
P(6)= 0.04
P(8) = 0,14
P(10)= 0.07
And addinf all the values we got:
P(A)= 0.1+0.03+ 0.04+ 0.14 +0.07= 0.38
In a study of bluetits 12 birds were trapped and their masses and wing spans were measured. The data collected are shown in this table. Calculate the estimated standard deviation for the mass of the bluetits, showing your answer to 3 significant figures.
Answers
The standard deviation of the mass of the bluetits to 3 significant figures is 1.30.
What is the standard deviation?Standard deviation is used to determine the variation of a dataset. Standard deviation is the spread of a data from the mean of the dataset. The higher the value of the standard deviation, the greater the spread of the dataset.
In order to determine the standard deviation, take the following steps:
Determine the mean of the mass : (9.9 + 9.8 + 12.2 + 13.3 + 11.8 + 10.2 + 12. 3 + 12.9 + 9.2 + 10.3 + 10.7 + 12.1) / 12 = 11.225
Determine the difference between each value and the mean and then square the result and then find the square root. The answer gotten is the standard deviation. 1.30
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Students in Mrs. McGee's third grade class are working on times tables, and they demonstrate mastery by passing tests. Rebecca has passed 12 tests so far. Her classmate, Marie, has passed 3 tests of them. From now on, Rebecca plans to take and pass 2 tests per week. Meanwhile, Marie plans to do 5 per week. At some point, Rebecca will catch up to Marie. How long will it take? How many tests will each child have passed? In weeks, the children will each have passed tests.
Answers
Solution
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Represent the unknown terms
Let x represents the number of weeks
Let y represents the total number of test passed
STEP 2: Interpret the statements
For Rebecca
[tex]y=2x+12[/tex]For Marie
[tex]y=5x+3[/tex]STEP 2: Find the number of weeks they will pass the same amount of test.
This means that y will be equal to y
[tex]\begin{gathered} y=y \\ 2x+12=5x+3 \\ 2x-5x=3-12 \\ -3x=-9 \\ x=\frac{-9}{-3}=3\text{ weeks} \end{gathered}[/tex]Hence, they will both pass the same number of tests in 3 weeks
STEP 3: Find the amount of tests passed
For Rebecca
[tex]\begin{gathered} 2x+12 \\ x=3 \\ y=2(3)+12=6+12=18 \end{gathered}[/tex]For Marie
[tex]\begin{gathered} y=5x+3 \\ x=3 \\ y=5(3)+3=15+3=18 \end{gathered}[/tex]Both will pass 18 tests in 3 weeks
ANSWER:
In 3 weeks, the children will each have passed 18 tests.
