Using the triangle rule, the option B can form a triangle.
In the given question,
We have to choose the correct segment from the given segment, which group of segments can form a triangle.
The given options are
A. 3, 10, 14
B. 8, 7, 13
C. 3, 2, 5
D. 20, 7, 13
To check which segment form a triangle we check that sum of two sides is always greater than the third side.
Now checking the first option.
The points is 3,10,14
When we add 3 and 10 we get 13 which is not greater than the 14. So the option A is not form a triangle.
Now checking the second option.
The points is 8,7,13
When we add 8 and 7 we get 15 which is greater than the 13. Similarly when we add 13 and 7 we get 20 which is also greater than the 8. Similarly when we add 8 and 13 we get 21 which is also greater than the 7. So the option B can form a triangle.
Since we get the right answer so we didn't check further option. The way of checking the remaining option is same.
Hence, the option B can form a triangle.
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Mia is buying Ice Blast winter tires at Ryder's Auto Shop. The regular price of one tire is $129.50. The shop is having a sale on winter tires, so each Ice Blast tire is $25 off. Mia buys 4 tires. How much money does she spend on the tires?
Answer:
$418.00
Step-by-step explanation:
Using the declining-balance method, complete the table as shown (twice the straight-line rate): (Enter your answers as a whole dollar amount.) Auto: $26,000 Estimated life: 10 years Residual value: $600 Year Cost Accumulated Depreciation B.O.Y Book Value B.O.Y Depreciation Expense Accumulated Depreciation E.O.Y Book Value E.O.Y 1 A B C D E F 2 G H I J K L 3 M N O P Q R
Using the double-declining-balance method of depreciation, the completion of the table as shown is as follows:
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $26,000 $0 $26,000 $5,200 $5,200 $20,800
2 $26,000 $5,200 $20,800 $4,160 $9,360 $16,640
3 $26,000 $9,360 $16,640 $3,328 $12,688 $13,312
What is the double-declining-balance method?
One of the depreciation methods in use is the double-declining-balance method, however it places more expense in the initial years of an asset's life.
The straight-line rate, which is calculated as the product of 100/estimated useful life multiplied by 2, is doubled in this depreciation technique.
The double rate is applied to the remaining balance at the end of each year for the depreciation expense.
The depreciation expense for the most recent year is calculated as the difference between the ending balance from the prior year and the residual value.
Auto = $26,000
Estimated useful life = 10 years
Residual = $600
Depreciable amount = $26,000 - $600 = 25,400
Straight-line depreciation rate = 100/10 = 10%
Double-declining depreciation rate =10% x 2 = 20%
Depreciation Expense:
1st year = 26000 x 20/100 = 5200
2nd year = 20800 x 20/100 = 4160
3rd year = 16640 x 20/100 = 3328
4th year = 13312 x 20/100 = 2662.40 = 2662
5th year = 10650 x 20/100 = 2130
6th year = 8520 x 20/100 = 1704
7th year = 6808 x 20/100 = 1361.6 = 1361
8th year = 5446 x 20/100 = 1089.2 = 1089
9th year = 4357 x 20/100 = 871.4 = 871
10th year = 3486 x 20/100 = 697.2 = 697
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $26,000 $0 $26,000 $5,200 $5,200 $20,800
2 $26,000 $5,200 $20,800 $4,160 $9,360 $16,640
3 $26,000 $9,360 $16,640 $3,328 $12,688 $13,312
4 $26,000 $12,688 $13,312 $2,662 $15,350 $10,650
5 $26,000 $15,350 $10,650 $2,130 $17,488 $8,520
6 $26,000 $17,488 $8,520 $1,704 $19,192 $6,808
7 $26,000 $19,192 $6,808 $1,362 $20,554 $5,446
8 $26,000 $20,554 $5,446 $1089 $21,643 $4,357
9 $26,000 $21,643 $4,357 $871 $22,514 $3,486
10 $26,000 $22,514 $3,486 $697 $23,211 $2,789
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The recursive formula, an = an-1 - 12 with a0 = 84 describes the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled. Find a5, he amount of water left in the tub after 5 minutes.
_________
The amount of water left in the tub after 5 minutes is; 24 gallons
How to solve recursive formula?The given recursive formula is expressed as;
aₙ = aₙ ₋ ₁ - 12
We are told that a₀ represents the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled.
Thus, when n = 1, we have;
a₁ = a₁ ₋ ₁ - 12
a₁ = a₀ - 12
a₁ = 84 - 12
a₁ = 72
Then;
a₂ = a₁ - 12
a₂ = 72 - 12
a₂ = 60
It will seem that it follows a sequence pattern of;
aₙ = 84 - 12n
Thus;
a₅ = 84 - 12(5)
a₅ = 24 gallons
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100 Points!! Graph h(x) = 32(0.45)x. What is the constant percent rate of change of f(x) with respect to x? Does the graph show growth or decay?
45% growth
45% decay
55% growth
55% decay
The constant percent rate of change of the function is option (d) 55% decay
The constant percent rate of change of the functionThe equation of the function is given as
f(x) = 32(0.45)^x
The above function is an exponential function
An exponential function is represented as
y = ab^x
Where b represents the growth or decay factor
So, we have
b = 0.45
We can see that the value of b is less than 1
This means that the graph would represent a decay
The percent rate of change is then calculated as
Rate = 1 - b
This gives
Rate = 1 - 0.45
Evaluate
Rate = 0.55
Rewrite as
Rate = 55%
Hence, the rate of change is 55% decay
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
The equations that is true for the values x = -2 and x = 2 is x² – 4 = 0 and 4x² = 16.
Equations:
Equation is an an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.
For example, 3x² − 2x + 9 is an algebraic expression.
Given,
Here we have the following equations
x² – 4 = 0
x² = –4
3x² + 12 = 0
4x² = 16
2(x – 2)² = 0
Now, we need to find which of these equations are tur for the values x = -2 and x = 2.
In order to find the true equation, we have to apply the given values on each of these to find which one is correct,
When x = 2 then,
(2)² – 4 = 0 => 4 - 4 = 0 (True)
(2)² = –4 => 4 ≠ -4 (Not true)
3(2)² + 12 = 0 => (3x4) + 12 = 0 => 12 + 12 = 0 => 24 ≠ 0 (Not true)
4(2)² = 16 => (4 x 4) = 16 => 0 = 0 (True)
2(2– 2)² = 0 => 2(0) = 0 = 0 = 0 (True)
Similarly, when we apply the value of x = -1, then we get,
(-2)² – 4 = 0 => 4 - 4 = 0 (True)
(-2)² = –4 => 4 ≠ -4 (Not true)
3(-2)² + 12 = 0 => (3x4) + 12 = 0 => 12 + 12 = 0 => 24 ≠ 0 (Not true)
4(-2)² = 16 => (4 x 4) = 16 => 0 = 0 (True)
2(-2– 2)² = 0 => 2(-4)² = 0 => 32 ≠ 0 = 0 (Not true)
Therefore, the resulting equations are x² – 4 = 0 and 4x² = 16.
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How can you solve 1/2 ÷ 1/3 ?
Answer:
3/2
Step-by-step explanation:
1/2 ÷2/3
1/2x3/2
1x3=3
1x2=2
=3/2
PLEASE HELPP Toshi is going to get a 7% raise after he works at his job for 1 year. If s represents his
starting salary, write an expression that shows how much he will make after his raise. PLEASEE HELP ME ITS THE LAST QUESTION AND I NEED THIS
Answer:
10%
Step-by-step explanation:
Write the equation of the parabola that has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f(x)=a(x-h)²+k.
f(x)=
The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9
How to determine the equation of the parabola?The equation of the function is given as
f(x) = 3x²
Also, we have
Vertex = (5, 9)
The form of the equation is given as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
This means that
Vertex = (h, k) = (5, 9)
Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k
So, we have
f(x) = a(x - 5)² + 9
This also means that
f(x) = -3(x - 5)² + 9
The -3 is gotten from f(x) = -3x²
Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9
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First try was incorrect
Simplify the following expression. Write your answer using positive
exponents.
7^-4/
(7-4)^6
The expression 7⁻⁴/(7⁻⁴)⁶ in simplified form using positive exponents is (7)²⁰ .
In the question ,
it is given that ,
the expression is 7⁻⁴/(7⁻⁴)⁶ .
we need to find the simplified value of the expression .
So ,
= 7⁻⁴/(7⁻⁴)⁶
we know that (xᵃ)ᵇ = (x)ᵃˣᵇ
By using the above property , we get
= 7⁻⁴/(7)⁻⁴ˣ⁶
= 7⁻⁴/(7)⁻²⁴
we know that xᵃ/xᵇ = xᵃ⁻ᵇ
By using the above property , we get
= (7)⁻⁴×(7)²⁴
= (7)²⁴⁻⁴ ... by using the property xᵃ.xᵇ = xᵃ⁺ᵇ
= (7)²⁰
Therefore , The expression 7⁻⁴/(7⁻⁴)⁶ in simplified form using positive
exponents is (7)²⁰ .
The given question is incomplete , the complete question is
Simplify the following expression. Write your answer using positive exponents.
7⁻⁴/(7⁻⁴)⁶
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IxI = 9
Can you please teach me how
to solve this?
Its called ;
Absolute value equations
Answer:
x= +/- 9
Step-by-step explanation:
absolute value is the number's positive value. x could be negative or positive, but its absolute value is positive. absolute value is how far away the number is from 0. if the assignment is on paper, write + above -.
Mrs. Hoeting purchased 1 7 8cups of snozberries. If she eats 1 2cup per serving, how many servings does Mrs. Hoeting have? Justify your answer.
Mrs. Hoeting have approximately 4 times of serving.
Given,
The quantity of snozzberry Mrs. Hoeting purchased = 1 7/8 cups = 15/8 cups
The quantity of snozzberry she eats per serving = 1/2 cups
We have to find the number of servings does Mrs. Hoeting have;
Number of servings = Quantity of snozzberry purchased / Quantity of snozzberry eats per serving
Number of servings = 15/8 ÷ 1/2
Number of servings = 15/8 × 2
Number of servings = 15/4
Number of servings = 3.75 ≈ 4
That is,
Mrs. Hoeting have approximately 4 times of serving.
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What would be the 5 number summary for this data: 18,19,21,23,23,23,24,25,25,31 ?
The 5-number summary of the given data is as follows:
Minimum: 18Quartile Q1: 20.5Median: 23Quartile Q3: 25Maximum: 31What is 5 number summary?A set of descriptive statistics called the five-number summary is used to describe a dataset. When conducting descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.The lower or first quartile of the first group's median is equal to (0 + 1)/2, or 0.5. The median for the second group is (27 + 61)/2, which is 44. This value represents the upper or third quartile. Observations 0 and 63 are the smallest and greatest values. The five-number summary is therefore 0, 0.5, 7.5, 44, 63.So, the data set is:
18,19,21,23,23,23,24,25,25,31Then, the 5-number summary will be:
Minimum: 18Quartile Q1: 20.5Median: 23Quartile Q3: 25Maximum: 31Therefore, the 5-number summary of the given data is as follows:
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In the high school band there are 2 percussionists on the sideline to every 13 marching instruments. If the high school band has 150 total members, then how many percussionists are on the sideline?
Answer:
180 / (13 + 2) =12 bands of 15 students each.
Since 2 from each band are sidelined, then:
12 x 2 = 24 - number of students on the sidelines, so that:
13 x 12 + 24 =180 - total number of students.
14.
DRILLING The volume of a drill bit can be estimated by the formula for a cone, V-hr2, where h is the height of
the bit and r is its radius. Substituting
for h, the volume of the drill bit can be estimated by V=³.
What is the volume of a drill bit with a radius of 3 centimeters?
The volume of a drill bit with a radius of 3 centimeters is of:
16.32 cm³.
How to obtained the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, each instance of the input variable of the function has to be replaced by the value at which we want to find the numeric value.
The volume of a drill bit with a radius of r centimeters is given by the equation presented as follows:
[tex]V = \frac{\sqrt{3}}{9}\pi r^3[/tex]
Hence, for a radius of 3 centimeters, as is the case in this problem, the lone instance of r is replaced by 3, and the volume is obtained as follows:
[tex]V = \frac{\sqrt{3}}{9}\pi (3)^3 = 16.32[/tex]
The unit of the volume is in cubic centimeters, as the radius is measures in centimeters and then it is cubed.
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I need help with my math please
Answer:
41-29=12
756+223=979
821-690=131
eleventh, fifteenth, nineteenth
4
2
use the distributive property to rewite each expression -7(5 - n)
The expression using distributive property becomes 7n - 35
What is distributive property of multiplication?The distributive property is also known as the distributive law of multiplication over addition and subtraction.
The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC. This distributive law is also applicable to subtraction and is expressed as, A (B - C) = AB - AC. This means operand A is distributed between the other two operands.
Using this distributive law, A × (B + C) = AB + AC. to re-write the expression -7(5 - n), A = -7, B = 5 and C = -n
we have -7(5 - n) = (-7 x 5) + (-7 x -n)
which is further simplified as (-35) + (7n) = 7n - 35
In conclusion, the re-written form of -7(5 - n) in distributive form is 7n - 35
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Carlos and his mom went out on a bike ride. They rode 5/8 of a mile to the park and then rode 5/8 of a mile back home. How far did they ride in all?
Using the distance, 5/4 far distance that they ride in all.
In the given question,
Carlos and his mom went out on a bike ride.
They rode 5/8 of a mile to the park and then rode 5/8 of a mile back home.
We have to check how far did they ride in all.
We have to find the total distance that he ride to park and from the park.
We can find the total distance by adding the whole distance that he ride.
Total distance = Distance to the park + Distance back home
Total distance = 5/8+5/8
Since the denominator is same. So
Total distance = (5+5)/8
Total distance = 10/8
Now simplifying.
Total distance = 5/4
Hence, 5/4 far distance that they ride in all.
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Solve the problem.
Find the number of units, x, that produces the maximum profit P, if
C(x) = 20 +52x and
p=72-2x.
A company's profit is determined by its revenue less its cost of operations.Subtract costs from revenue to get the profit function.
Find the number of units ?Let P(x) stand for the profit, R(x) for the revenue, and C(x) for the expense.Profit thus equals P(x) = R(x) -C. (x).The revenue and expense can be modeled as fixed values or as functions,
Profit = Revenue - Cost
We need to find an equation for the revenue R(x).
R(x) = number of units * unit price = x * p(x) = x(72-x) = 72x - x2
Therefore: Profit P(x) = 72x - x2 - (20 + 52x) = - x2 + 20x -20
To find max profit, run the 1st derivative test, so set P'(x) = 0 and solve for x:
P'(x) = -2x + 20
set P'(x) = 0 ----> -2x+20 = 0 ----> -2x = -20 -----> x = 10
The number of units, x, that produces the maximum profit is 10.
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A normal distribution of BMCC MAT51 scores has a standard deviation of 1.5. Find the z-scores corresponding to each of the following values: (Round to 2 decimal places) a. A score that is 1.5 points above the mean. (Hint: "x - mean = 5" is 5 above the mean) z= b. A score that is 1.5 points below the mean. z= c. A score that is 1.36 points above the mean. z= d. A score that is same as the mean. z=
A score that is 1.5 points above the mean is 1, A score that is 1.5 points below the mean is -1, A score that is 1.36 points above the mean is 0.90 and A score that is the same as the mean is 0.
What is normal distribution?A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.
Given that, a normal distribution of BMCC MAT51 scores has a standard deviation of 1.5.
At above 1.5
Z = (μ + 1.5 - μ)/2 = 1
At below 1.5
Z = (μ -1.5 - μ)/2 =-1
At above 1.36
Z = (μ + 1.36 - μ)/2 = 0.90
At same as the mean
Z = (μ - μ)/2 = 0
Hence, A score that is 1.5 points above the mean is 1, A score that is 1.5 points below the mean is -1, A score that is 1.36 points above the mean is 0.90 and A score that is the same as the mean is 0.
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In the spherical triangle
A = 1200
B = 1350
and c = 300.
What is C ?
The value of C be sinC = - 371.932.
Given, the side of the triangle be c = 300
and the angles of the triangle be A = 1200 and B = 1350
Now, using the law of sines, we get
a/sinA = b/sinB = c/sinC = k
sinA/sinB = c/sinC
sin(1200)/sin(1350) = 300/sinC
0.8066/-1 = 300/sinC
sinC = - 371.932
Hence, the value of C be sinC = - 371.932.
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Answer:
- 371.932.
Step-by-step explanation:
Y=-x-7
5y+3x=-13
Solve the system!
Will give brainless if you show work!
Answer:
Step-by-step explanation:
y=-x-7........(1)
5y+3x=-13..........(2)
(2) - 3x(1)=>
5y+3x= -13
3y + 3x = - 21
(-) (-) (+)
-----------------------
2y+0=8
=>y=4
(1)=>
y= -x-7
=>x= -y-7
=>x= -4-7
=>x= -11 .
Answer:
x=-11 & y= 4
Step-by-step explanation:
y=-x-7
5y+3x=-13
y+x=-7—eqn i
5y+3x=-13—eqn ii
multiply eqn i by 5
5y+5x=-35
multiply eqn Ii by 1
5y+3x=-13
put eqn I and Ii together
5y+5x=-35
5y+3x=-13
subtract
2x=-35--13
2x=-35+13
2x=-22
divide both sides by 2
2x/2 = -22/2
x=-11
put x=-11 into eqn i
y+x=-7
y-11=-7
y=-7+11
y=4
graph the linear equation x = -3
SANDBOX Jayden is drawing the top view of a square sandbox on a coordinate plane with vertices at D(1, 1), E(1, 6), F(6, 6) , and G(6, 1) . To move the sandbox so that it is in the shade, he reflects it. The vertices of the image are at D′(1, 1), E′(1, 6), F′(−4, 6) , and G′(−4, 1) . Describe the transformation. Use decimals, if necessary.
reflection in the line x
Reflection is along line x = 1, using plotting of points.
What do you mean by reflection , rotation and translation?
An object can be reversed across a line through reflection without changing its size or shape.
Rotation is the movement of an item around a fixed point while maintaining its original size and shape.
A figure can be translated if it is moved in any direction without altering its size, form, or orientation.
An object is always translated, but it is never turned, flipped, or shrunk.
It is given that Jayden is drawing the top view of a square sandbox on a coordinate plane with vertices at D(1, 1), E(1, 6), F(6, 6) , and G(6, 1) .
On plotting these points on graph paper we get below graph, (1)
Now , to move the sandbox so that it is in the shade, he reflects it and the new vertices of the image are at D′(1, 1), E′(1, 6), F′(−4, 6) , and G′(−4, 1)
On plotting these new coordinates we get below graph (2)
Square box in the second graph shifted to left side of x = 1.
Therefore, reflection is along line x = 1.
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clock has a circumference of 63 in. What is the area of the face of the
The face of a
clock?
Answer:
314
Step-by-step explanation:
1. Divide 63 by pi (equals 20)
2. Divide 20 by 2 which equals 10.
3. Multiply 10 by itself to get the square. which would be 100
4. Multiply 100 by pi
3. Finally A=314
1 point
The value of an automobile decreases each year and is described by the equation (t)- 24 000(0.95)',
where t is the number of years after the car is purchased. Estimate the rate at which the value of the auto
is changing 5 years after it is purchased.
a. -$1250/year
b. -$950/year
C. -$150/year
d. $150/year
The rate of change at which the value of the auto is -950/year.
What is the Rate of Change?
It is said that the rate at which one quantity changes in relation to another is known as the rate of change function.
In simple terms, when calculating the rate of change in one item, the amount of change in another is divided by the comparable amount of change in another.
From the given data of question,
[tex]V(t) = 24000*0.95^{t}[/tex]
Then, by definition, the rate of change =[tex]\frac{d(v(t))}{dt} = \frac{d(24000*0.95^{t} )}{dt}[/tex]
= [tex]24000*0.95^{t}*ln(0.95)[/tex]
For time (t) = 5 years
[tex]\frac{d(v(t))}{dt} = 24000*0.95^{5}*ln(0.95)[/tex]
= 24000*0.7737*(-0.0512)
= -950
Hence, the rate of change of the value of the auto is -950/year.
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Zendaya runs a farm stand that sells blueberries and grapes. Each pound of blueberries sells for $2.50 and each pound of grapes sells for $1.25. Zendaya made $55 from selling a total of 33 pounds of blueberries and grapes. Write a system of equations that could be used to determine the number of pounds of blueberries sold and the number of pounds of grapes sold. Define the variables that you use to write the system.
The system of equation to represent Zendaya blueberries and grapes sells is as follow:
x + y = 33
2.50x + 1.25y = 55
How to represent situation with system of equation?Zendaya runs a farm stand that sells blueberries and grapes. Each pound of blueberries sells for $2.50 and each pound of grapes sells for $1.25. Zendaya made $55 from selling a total of 33 pounds of blueberries and grapes.
The system of equation that can be used to determine the number of pounds of blueberries sold and the number of pounds of grapes sold can be represented as follows:
Therefore,
let
x = number of pounds of blueberries
y = number of pounds of grapes
Hence,
x + y = 33
2.50x + 1.25y = 55
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Find the length of the third side. If necessary, write in simplest radical form.
Answer:
3√5
Submit Answer
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{9^2-(3\sqrt{5})^2}=a\implies \sqrt{81-3^2(5)}=a \\\\\\ \sqrt{81-9(5)}=a\implies \sqrt{81-45}=a\implies \sqrt{36}=a\implies \boxed{6=a}[/tex]
The base of a triangle is represented by the expression 2x-12.The height of the triangle is 8 units more than the length of the base.which expression represents the area of the triangle?
The expression which represents the area of the triangle : [tex]2x^{2}-16x+24[/tex].
Length of base = B = 2x - 12
Height = H = Length of base + 8
= 2x - 12 + 8
= 2x - 4
Area = [tex]\frac{1}{2}(B)(H)[/tex]
= [tex]\frac{1}{2}(2x-12)(2x-4)[/tex]
= [tex]\frac{4}{2}(x-6)(x-2)[/tex]
= [tex]2(x^{2} -8x+12)[/tex]
= [tex]2x^{2}-16x+24[/tex]
Hence, the expression is [tex]2x^{2}-16x+24[/tex].
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On Saturday morning, calls arrive at TicketMaster at the rate of 108 calls per hour. What is the probability of receiving fewer than three calls in a randomly chosen minute?
Exercise 2. Find m∠1 and m∠2
1)
angle 1 is 41
angle 2 is also 41
2)
angle 1 is 124
angle 2 is also 124
