The range of the distance from A to C is greater than 3.3 feet and less than 29.1 feet.
How to determine the range of distance?The given parameters are
AB = 16.2 feet
BC = 12.9 feet
To determine the range of the third length, we use the triangle inequality theorem
Using this theorem, we have the following inequalities
AB + BC > AC
AB + AC > BC
BC + AC > AB
So, we have
16.2 + 12.9 > AC
16.2 + AC > 12.9
12.9 + AC > 16.2
Solve for AC in the above inequalities
29.1 > AC
AC > -3.3
AC > 3.3
Remove the negative value
29.1 > AC
AC > 3.3
Rewrite as
AC > 29.1
AC > 3.3
This means that the values of AC are between 3.3 and 29.1 feet
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How far does jaylen go if he drive 2 hours at 60 mph
Info given
For this problem we know that Jaylen drive for 2 hours at 60 mph
The velocity is v= 60 mi/hr and the time t= 2 hr
Solution
We can use the definition of distance given by:
[tex]d=vt[/tex]And replacing we got:
[tex]d=60\frac{mi}{hr}\cdot2hr=120mi[/tex]And then the answer would be 120 mi
10. Ariana's iPod battery lasts 6 hours. She listens to her iPod for 2/3 of an hour in theafternoon and another 2 5/6 hours in the evening.a) How much listening time is left on Ariana's iPod?b) What fraction of the battery's power is left? Justify your answer with adiagram.
We have the following:
The first thing is to transform the mixed numbers to decimal numbers, in the following way:
[tex]\begin{gathered} \frac{2}{3}=0.67 \\ 2\frac{5}{6}=2.83 \end{gathered}[/tex]a.
to calculate the remaining time we must subtract the times where music is heard from 6 hours
[tex]6-0.67-2.83=2.5[/tex]Therefore, the answer is 2.5 hours or 5/2 hours battery remaining
b.
To calculate the fraction we must calculate that it represents 2.5 or 5/2 hours in the total, that is, 6 hours
[tex]\frac{\frac{5}{2}}{6}=\frac{\frac{5}{2}}{\frac{6}{1}}=\frac{5\cdot1}{6\cdot2}=\frac{5}{12}[/tex]The diagram is:
A video game system and several games are sold for 504$ . The cost of the game is 3 times as much as the cost of the system . Find the cost of the system and the cost of the games
We get the cost of the system and cost of the games as $126 and $378 respectively.
Given, the price of the video game and several games are sold for $504.
The cost of the game is 3 times as much as the cost of the system.
we need to determine the cost of the system and the cost of the game = ?
Let x = the cost of the games.
Let y = the cost of the system.
therefore, x+y=504
and y = 3x
substitute the value of y.
⇒ x + y = 504
⇒ x + 3x = 504
combine like terms.
⇒ 4x = 504
Divide both sides by 4.
⇒ x = 504/4
⇒ x = 126
The cost of the system is $126.
Use y = 3x substituting 126 for x.
g = 3(126)
g = 378
The cost of the games is $378.
Hence we get the cost of the system and cost of the games as $126 and $378 respectively.
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A pet store has 6 cats. Here are their weights (in pounds).
12, 9, 9, 12, 16, 6
Find the mean weight of these cats.
If necessary, round your answer to the nearest tenth.
pounds
Answer:
mean ≈ 10.7 pounds
Step-by-step explanation:
mean is calculated as
mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{12+9+9+12+16+6}{6}[/tex] = [tex]\frac{64}{6}[/tex] ≈ 10.7 pounds ( to the nearest tenth )
Find the upper quartile of {2,5,13,21,29}
Sort the list in increasing order:
[tex]\mleft\lbrace2,5,13,21,29\mright\rbrace[/tex]The median is 13, therefore the upper quartile Q3 is given by:
[tex]Q3=\frac{21+29}{2}=\frac{50}{2}=25[/tex]Answer:
25
After paying $20,000 for a car, you read that this model has decreased in value 15% per year over the last several years. If this trend continues, how much will the car be worth 5 years from now?
$8860
$8860 is the amount that is reduced after 5 years for the principal amount of $20,000 at a rate of interest 15%.
solution:When interest is compounded on the principal amount invested or borrowed, the interest rate is applied to the new (larger) principal.It's essentially interest on interest, which leads to exponential growth over time.Here ,
Given , P = $20,000
r = 15% = .15%
n = 5
since amount is getting decreased ,
formula of compound interest becomes,
A = [tex]p(1 - r)^{n}[/tex]
here P = principal amount , r = rate of interest and n = number of years.
= 20000(1 - .15)⁵
= 20000 x 0.443
= 8860
A = $8860
So , After paying $20,000 the value decreases by 15% after 5 yrs the value will be $8860.
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3 cm 00 What is the length of AC? A 1.5 cm C 6 cm B 3 cm D 9 cm is Which statement MUST be true? A AD BC В AD - BD CBD - AD D CDAD
The length of AC must be 3 cm letter B
Second question
Both B and C are correct.
**A B C D E F G H I J K L M N O P Q R S T U V W X Y Z**If the code for HTML is JVON.What is the code for COMMIT?
If the code for HTML is JVON, it means that:
letter 8th (H) is letter 10th (J). Letter 20th (T) is letter 22th (V) and so on.
It means that the encoding is taking the letter 2 positions forward.
Hence C=E, O=Q, M=O, I=K, T=V.
The answer is EQOOKV.
Factor the following expression completely:
y² + 6y − 40 =
Answer:
(y+10)(y-4)
Step-by-step explanation:
-40y^2
/ \
10y -4y
In slurfball, a fizzy is worth 2 points and a globbo is worth 5 points. K and W recently played for the surfball game. During the game, K scored eight more Fizzles then the W, but scored five fewer flobbos then the W, together the two teams scored 93 points total. What was the final score?
Using mathematical operations of addition, multiplication, division, and subtraction, the final score was:
K = 42 points
W = 51 points.
What are mathematical operations?
The basic mathematical operations for getting mathematical results from numbers, values, and variables include addition, multiplication, division, and subtraction.
In this situation, we apply these four basic mathematical operations.
Fizzy = 2 points
X = 5 points
Total scores = 93 points
The points in 8 Fizzy = 16 points (8 x 2)
The points in 5 X s = 25 points (5 x 5)
The equation showing the total scores of K = total scores + 16 - 25
= (93 + 16 - 25)/2
= 42 points
The equation showing the total scores of W = total scores - 16 + 25
= (93 - 16 + 25)/2
= 51 points
Hence, Final scores are K = 42 and W = 51.
Thus, applying mathematical operations, the final score shows that K scored 42 points while W scored 51 points, totaling 93 points for the two teams.
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Circuit total capacitance measures .04 microfarad. If the circuit is supplied by an AC power source operating at 2 kHz what is the circuit’s capacitive reactance
The capacitive reactance of the circuit with capacitance of 4 x 10⁻⁸ farad and the AC power source of 2 Khz is X[C] = 1.99 x 10⁻⁷ ohms.
What is Capacitance?The capacitance of a body is defined as the charge holding ability of a body. Mathematically, capacitance is the ratio of charge and potential as follows -
C = dQ/dV
Given is the total capacitance measures .04 microfarad. If the circuit is supplied by an AC power source operating at 2 kHz.
From this we can write -
Capacitance [C] = 0.04 microfarad = 4 x 10⁻⁸ farad.
Frequency of AC supply [f] = 2 KHz = 2 x 10³ Hz
The capacitive reactance is given by -
X[C] = 1/2πfC
X[C] = (1/2 x 3.14 x 2 x 10³ x 4 x 10⁻⁸)
X[C] = 1/(50.24 x 10⁻⁵)
X[C] = 0.0199 x 10⁻⁵
X[C] = 1.99 x 10⁻⁷ ohms
Therefore, the capacitive reactance of the circuit with capacitance of 4 x 10⁻⁸ farad and the AC power source of 2 Khz is X[C] = 1.99 x 10⁻⁷ ohms.
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IM DESPERATE I would like an explanation to go with the answer. THANK YOUOnly #5 and #6
Therefore the original price is $299
[tex]6)\text{ selling price = 152+152}\times\frac{50}{100}=152+76=228[/tex]the selling price is $228
Solve this inequality.70+ 15 <31 – 8
The objective of this excercise is to clear the variable t. We need to pass every term with a t to one side of the inequality and every term without it to the other side:
[tex]7t+15<3t-8[/tex][tex]7t-3t<-8-15[/tex][tex]4t<-23[/tex]then we have:
[tex]t<\frac{-23}{4}[/tex]And finally we have that:
[tex]t<-5.75[/tex]Walter earns $144 by painting his neighbor's shed. He spends 25% of his money on books. He is going to save 50% of the remaining money. How much money will he save?
Answer
Walter saved $54
Explanation
Walter earns $144.
He spent 25% of it on books.
25% of $144 = 0.25 × 144 = $36
Amount left after spending 25% = $144 - $36 = $108
He then saves 50% of the remaining money
50% of $108 = 0.5 (108) = $54
Hope this Helps!!!
(1.57 x 10^5)-(9.5 x 10^4)
(1.57 x 10^5)-(9.5 x 10^4) The answer will be 62000 or Alternative form is 6.2 x 10^4
Given in the question:
(1.57 x 10^5)-(9.5 x 10^4)
To solve the above question:
Now, According to the question:
(1.57 x 10^5)-(9.5 x 10^4)
Factor Greatest Common Factors out :
10^4 (15.7 - 9.5)
Calculate the sum or difference
10^4 x 6.2
Express the number in scientific notation;
6.2 x 10^4
Calculate the power
6.2 x 10000
Calculate the product or quotient
62000
And, Alternative form is 6.2 x 10^4
Hence, (1.57 x 10^5)-(9.5 x 10^4) The answer will be 62000 or Alternative form is 6.2 x 10^4
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what is 10,500,000,000 in scientific notation
Answer:
hope this makes sense
Step-by-step explanation:
1.05 x 10x 10x10x10=10000000000
10500000000
10000000000= 1.05 x 1.05 ×10000000000= 10500000000
10500000000 = 1.05 x10 x10
Work out the volume of the prism below.
Give your answer in cm³.
Answer:
first area is length by width
then our L is 4 and W is 5
=20
and volume is ,area 18 then 18 by 7=126
What is the first step in solving a quadratic equation of the form given below?
(ax + b)² = c
Answer:
take square root on both side
Step-by-step explanation:
Given that point D is at (3,4) and point D' is at (5.-13). What rule shows the translation that occurred?
Answer:
I'm just here for points :3
Step-by-step explanation:
I don't know math
If A=(2,-3,-4) and B(6,7,-4), find ||AB||. Round to 3 decimal places.Type your answer...
The rule we will use is
[tex]\parallel AB\parallel=\sqrt[]{(x2-x1)^2+(y2-y1)^2+(z2-z1)^2}[/tex]x1 = 2 and x2 = 6
y1 = -3 and y2 = 7
z1 = -4 and z2 = -4
[tex]\parallel AB\parallel=\sqrt[]{(6-2)^2+(7--3)^2+(-4--4)^2}[/tex]Now we will find the answer in decimal using the calculator
The answer is 10.77032961
Round it to 3 decimal places, then
[tex]\parallel AB\parallel=10.770[/tex]identify the constant ( s ) in the algebraic expression -3a + 5b - 15
In the expression -3a + 5b - 15;
The constants are; -3, 5 and -15
The variables are; a and b.
What are the constants and variables?
A constant of an Algebraic Expression is simply a value that cannot be changed by inputting another value. For example in the algebraic expression; y³ = 4x³ - 7
The constants here will be 4 and -7 as they cannot be changed
Now, the variables in algebraic expressions are those that can be changed with different values and the equation will still be valid. For example, in the equation y³ = 4x³ - 7, the variables are y and x.
Thus, in our expression -3a + 5b - 15, the constants will be -3, 5 and -15 while the variables would be a and b.
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f(x)= 3× g(x)= 3×+2 -4
We can observe that f(x) is a parent function and g(x) is transformation of f(x).
Specifically, the applied transformations are:
• A vertical shift 4 units downside.
,• A horizontal shift of 2 units left side.
The image below shows the functions
As you can observe, the blue function g(x) was shifted two units left and 4 units down.
Additionally, the functions intercept at (-0.631, 0.5).
Write an equation (any form) for the quadratic graphed below:
y = (1/2)x² + 2x + 2 is the equation of the parabola in the graph.
What is the equation of the parabola?From the graph, the parabola has a vertex at point (-2,0) and passes through point (0,2).
The general equation for a parabola with vertex is (h,k) is;
y = a( x - h)² + k
First we determine 'a' by substituting the given coordinates into the equation.
y = a( x - h)² + k
2 = a( 0 - (-2))² + 0
Solve for a
2 = a(2)²
2 = a( 4 )
a = 2/4
a = 1/2
Now, plug the vertex (-2,0) and a (1/2) into the general equation.
y = a( x - h)² + k
y = (1/2)( x - (-2))² + 0
Simplify
y = (1/2)( x +2) )² + 0
y = (1/2)( x + 2 )²
Expand using FOIL method
y = (1/2)( ( x + 2 )( x + 2 ) )
y = (1/2)( x² + 2x + 2x + 4 )
y = (1/2)( x² + 4x+ 4 )
Apply distributive property
y = (1/2)(x²) + (1/2)4x + (1/2)(4 )
y = (1/2)x² + 2x + 2
Therefore, the equation of the graph is y = (1/2)x² + 2x + 2.
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help me please
thank you
Answer:
Domain: [-6, 2]
Range: [-4, 0]
Function: Yes
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
A relation is a function if each x value corresponds to only one y-value.
Please help urgent 30 points
Answer:
1. How do we transform System A into System B
Answer is First choice with -3 filled in box
-3 x Equation [A1] ⇒ Equation [B1] (first choice; fill in -3)
2. How do we transform System B into System A
answer is the Last choice with 5 filled in the box
5 x Equation [B2] + Equation [B1] => Equation [C1]
In the last choice fill in 5 in the box
Step-by-step explanation:
-3 x [A1] => -3 (-9x - 5y = -2)
=> - 3(-9x) -3(-5y) = 3(-2)
=> 27x + 15y = 6 which is B1
5 x [B2]
=> 5(-4x - 3y) = 5(3)
=> -20x -15y = 15
5 x [B2] + B1
=>
-20x -15y = 15
+
27x + 15y = 6
----------------------
7x + 0 = 21
or 7x = 21 which is C1
Step-by-step explanation:
system A to system B :
-3 × equation A1 -> equation B1
5 × equation B2 + equation B1 = equation C1
Which linear inequality is represented by the graph?
Oy> 2x + 2
Oy²x+1
Oy> 2x + 1
Oy² = x + 2n
Answer:
y>2x+1
Step-by-step explanation:
1. there is 'y=2x+1' graph is represented.
2. the shaded reqion is y>2x+1.
The correct linear inequality represented by the graph is y > 2x + 1. The correct option is C.
What is inequality?An inequality is a mathematical statement that compares two values or expressions and shows their relationship using the symbols < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to).
To see why, note that the line shown in the graph has a y-intercept of 1 and a slope of 2 (i.e., it passes through the points (0,1) and (1,3)).
If we plug in any point above this line, we get a y-coordinate that is greater than 2x + 1. For example, if we plug in the point (2,6), we get:
6 > 2(2) + 1
6 > 5
All points above the line satisfy the inequality y > 2x + 1.
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Supposed to select all statements that are true about the construction
The segment AB is perbenticular to XY.
Here 90 degrees is an interior angle for Arc XB and Arc AY
[tex]90^o=\frac{XB+AY}{2}[/tex][tex]XB+\text{AY}=180^o[/tex]Similarly, 90 degrees is an interior angle for Arc XA and Arc BY
4r+1.1=6.6r-3.84 I can't if they say if both sign are the same
Solution
For this case we have the following equation given:
4r + 1.1 = 6.6r -3.84
We can subtract 4r in both sides and we got:
1.1 = 2.6r -3.84
Then we can add 3.84 in both sides and we got:
2.6 r = 4.94
And then the value of r we got:
[tex]r=\frac{4.94}{2.6}=1.9[/tex]NEED HELP ASAP PLSPLS
Answer:
a= 2
b = 6
c = 2
d = 2
e = 7
f = 2
g = 1
h = 1
R = .3 (repeating)
Step-by-step explanation:
True or False for each one613 rounded to the nearest ten is 610.1,970 rounded to the nearest hundred is 1,900.54,318 rounded to the nearest thousand is 54,000.476,022 rounded to the nearest ten thousand is 470,000.
To round a number to a specific place, look at the number to the right of that place. If the number is less than 5, round down. If it is greater than or equal to 5, round up.
Question 1: 613 rounded to the nearest ten is 610.
The tens digit in 613 is 1. To the right of 1 is 3. Therefore, the approximation of 613 is:
[tex]613\approx610[/tex]THIS STATEMENT IS TRUE.
Question 2: 1,970 rounded to the nearest hundred is 1,900.
The hundreds digit in 1,970 is 9. To the right of 9 is 7. This means that we will round up by adding 1 to 9. Therefore, the approximation will be:
[tex]1970\approx1900+100=2000[/tex]THIS STATEMENT IS FALSE.
Question 3: 54,318 rounded to the nearest thousand is 54,000.
The thousands digit is 4. To the right of 4 is 3. Therefore, the approximation is:
[tex]54318\approx54000[/tex]THIS STATEMENT IS TRUE.
Question 4: 476,022 rounded to the nearest ten thousand is 470,000.
The ten thousands digit is 7. To the right of 7 is 6. This means that we will round up. Therefore, the approximation is:
[tex]476022\approx470000+10000=480000[/tex]THIS STATEMENT IS FALSE.
