a 204 inch board is cut into two pieces. one piece is five times the length of the other.find the lengths of the two pieces
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When mary began her trip from san jose to la, she filled her car's tank with gas and reset its trip meter to zero. after traveling 324 miles, she stopped at a gas station to refuel; the gas tank required 17 gallons. mary wants a program that calculates and displays her car's gas mileage at any time during the trip. the gas mileage is the number of miles her car was driven per gallon of gas?
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To calculate Mary's car's gas mileage, divide the number of miles driven by the number of gallons of gas used. In this scenario, her car's gas mileage is approximately 19.06 miles per gallon.
Explanation:To calculate Mary's car's gas mileage, we need to divide the number of miles driven by the number of gallons of gas used. In this scenario, Mary traveled 324 miles and used 17 gallons of gas. Therefore, her car's gas mileage can be calculated as:
Gas mileage = Miles driven / Gallons of gas used
Substituting the values:
Gas mileage = 324 miles / 17 gallons
Simplifying the equation:
Gas mileage = 19.06 miles per gallon (rounded to two decimal places)
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Compare methods of solving linear equations and methods of solving linear inequalities. what do they have in common? what is different?
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what fraction 2/3 is found between which pair of fraction on the number line?
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Suppose a and b are 3x3 matrices, with det(a) = 5 and det(b) = 3.
a. det(2a) = ? 4 pts
b. det((ab)-1) = ?
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[tex]\det(\mathbf{AB})^{-1}=\dfrac1{\det\mathbf{AB}}=\dfrac1{\det\mathbf A\det\mathbf B}=\dfrac1{5\times3}=\dfrac1{15}[/tex]
Determine the effective rate for $1 for 1 year at 5.9% compounded quarterly.
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[tex]\bf \qquad \qquad \textit{Annual Yield Formula} \\\\ ~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 5.9\%\to \frac{5.9}{100}\to &0.059\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four times} \end{array}\to &4 \end{cases} \\\\\\ \left(1+\frac{0.059}{4}\right)^{4}-1\implies (1.01475)^4-1 \approx 0.0603 \\\\\\ 0.0603\cdot 100\implies \stackrel{\%}{6.03}[/tex]
Find the distance between points M(6,16) and Z(-1,14) to the nearest tenth.
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rachel's necklace cost 20% more than Tammy's shoes. Bryan' s video game cost 30% more than Rachel's necklace. If Tammy's shoes cost $30.00, what did Brian's video game cost?
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30*20%=6
30+6=36
36*30%=10.80
36+10.80=46.80
hope this helps!
Answer:
46.80
Step-by-step explanation:
Pls brainly I need it so bad I spent 10 minutes of my time to solve this.
Mary having her living room and bedroom painted. Interior Designs USA charges $60.00 to evaluate the space plus $35.00 per hour of labor. Splash of Color charges $55.00 per hour with no initial fee. Which of the following are true? Select all that apply.
If it takes 7 hours to paint the two rooms, Interior Designs USA will charge the least.
Splash of Color will always charge the least.
If it takes more than 5 hours to paint the rooms, Splash of Color will be more cost effective.
If it takes 10 hours to paint the rooms, Splash of Color will charge $200 more than Interior Designs USA.
If it takes 3 hours to paint the rooms, both companies will charge the same amount.
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Answer:
The correct statements are 1, 3, and 5.
Explanation:
Let's calculate the total cost for each company based on the given information:
For Interior Designs USA:
- Evaluation fee: $60.00
- Labor cost per hour: $35.00
- Total labor cost for 7 hours: $35.00/hour × 7 hours = $245.00
- Total cost = Evaluation fee + Total labor cost = $60.00 + $245.00 = $305.00
For Splash of Color:
- Labor cost per hour: $55.00
- Total labor cost for 7 hours: $55.00/hour × 7 hours = $385.00
Now, let's analyze the statements:
1. If it takes 7 hours to paint the two rooms, Interior Designs USA will charge the least. - True. ($305.00 < $385.00)
2. Splash of Color will always charge the least. - False. In this case, Interior Designs USA charges less for 7 hours of work.
3. If it takes more than 5 hours to paint the rooms, Splash of Color will be more cost effective. - True. As we've seen, Splash of Color charges $55.00 per hour, while Interior Designs USA charges $35.00 per hour plus an initial fee.
4. If it takes 10 hours to paint the rooms, Splash of Color will charge $200 more than Interior Designs USA. - False. Let's calculate:
- Interior Designs USA: $60.00 (evaluation fee) + $35.00/hour × 10 hours = $60.00 + $350.00 = $410.00
- Splash of Color: $55.00/hour × 10 hours = $550.00
Splash of Color charges $550.00 - $410.00 = $140.00 more, not $200. Therefore, this statement is false.
5. If it takes 3 hours to paint the rooms, both companies will charge the same amount. - False. Let's calculate:
- Interior Designs USA: $60.00 (evaluation fee) + $35.00/hour × 3 hours = $60.00 + $105.00 = $165.00
- Splash of Color: $55.00/hour × 3 hours = $165.00
They both charge $165.00, so this statement is true.
So, the correct statements are 1, 3, and 5.
Find the roc of the volume of a cube with respect to the length of its side s
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dV/ds = 3s^2.
The roc of the volume of a cube with respect to the length of its side s is 3s².
What is rate of change?
The rate of change of a function is the rate at which the output values change over the input value.
The rate of change of a function is one degree less than the actual function.
The volume of a cube is :
V = s³
The rate of change of volume V with respect to length a will be :
dV/ds = d(s³ )/ds
= 3s²
This means that, a cubic function will have a quadratic rate of change
Hence, The roc of the volume of a cube with respect to the length of its side s is 3s².
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What's the range of 37000 and 45000
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Consider the graph of f(x)=1/x. Which functions result in a vertical compression? Check all that apply.
a. g(x)=1/3x
b. g(x)=3/x
c. g(x)= - 3/x
d. g(x)= - 1/3x
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Hope this helps!
Answer:
A & D
Step-by-step explanation:
1.Find the coordinates of the midpoint of __ given that H (-1,3) and X (7,1).
HX
A.(3,1)
B (0,4)
C(-3,1)
D(-4,0)
2. Find the distance between the points R(0,5) and S(12,3). round the answer to the nearest tenth.
A 10.4
B 16
C 12.2
D 11.8
3. An airplane at T(80,20) needs to fly to both U(20,60) and V(110,85) what is the shortest possible distance for the trip?
A. 165 units
B. 170 units
C. 97 units
D. 169 units
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Answer:
1. (3, 2)
2. Option C. 12.2
3. Option A. 165 units
Step-by-step explanation:
1. The midpoint of two coordinates (x₁, x₂) and (y₁, y₂) is calculate by,
[tex](x, y) = (\frac{x_{1} + x_{2}}{2},\frac{y_{1} + y_{2}}{2})[/tex]
⇒[tex](x, y) = (\frac{-1 + 7}{2},\frac{3 + 1}{2})[/tex]
Thus (x, y) = (3, 2)
Hence, none of given options are true.
2. The distance between two coordinates is calculate by,
[tex]Distance=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2[/tex]
⇒ Distance = 12.16 ≈ 12.2 unit
Hence, option (C) is correct.
3. The distance between T(80, 20) and V(110, 85) is comparatively smaller than T(80, 20) and U(20, 60).
Using the Distance formula,
[tex]Distance=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2[/tex]
Distance between T(80, 20) and V(110, 85) is 71.59 unit
and Distance between U(20, 60) and V(110, 85) is 93.41 unit
So, Airplane firstly go to point V from point T and then point U.
Total shortest distance = 71.60 + 93.40 = 165 unit.
Hence, option (A) is correct.
The mailman delivered a $22 check and 3 - $14 bills today. He also took back 1- $5 bill. What is the total in the mailbox?
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42+22 is 64
64-5= 59
This number represents the number of times the base is used as a factor
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The exponent is the number used in a power to represent the number of times the base is used as a power.
For example: 7^2. The number 2 is the exponent and it indicates that the number 7 (which is the base) is used two times as a factor, this is, 7^2 = 7 * 7.
Othe example: 4^6. The exponent 6 indicates that the base 4 is used 6 times as a factor => 4^6 = 4 * 4 * 4 * 4 * 4 * 4.
What number is 49 less than 78
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Ken watches a marching band. He sees 2 rows of flute players. Six people are in each row. He sees 8 trombone players. How many flute or trombone players does Ken see
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Eight trombone players.
20 total of flute and trombone players.
One tablet contains 575 grams of muscle relaxing medication. How many grams are in 3 1/2 tablets
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All of the following expressions represent the sum of n and itself, except _____.
n + n
2n
n²
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Answer: [tex]n^{2}[/tex]
Step-by-step explanation:
(n + n) represents the definition of the sum of n and itself.
(2n) means two times n, wich is the same as adding n + n.
[tex]n^{2}[/tex] actually represents the multiplication of n two times: [tex]n*n[/tex]
For example, if n=3:
[tex]n+n=3+3=6[/tex]
[tex]2n=2(3)=6[/tex]
[tex]n^{2}=3^{2} =9[/tex]
If there were a million cars in line, bumper to bumper, with a average length of 10.14 feet, how long would that line be in miles? (Round to the nearest mile)
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Hope this helps : )
Let f(x,y)=x2 −y2. find the gradient of f at the point (√2,1). sketch the level curve of f through this point, together with the gradient at that point. g
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Answer:
[tex]\displaystyle \nabla f(\sqrt{2}, 1) = 2\sqrt{2} \hat{\i} - 2 \hat{\j}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Multivariable Calculus
Differentiation
Partial DerivativesDerivative NotationGradient: [tex]\displaystyle \nabla f(x, y, z) = \frac{\partial f}{\partial x} \hat{\i} + \frac{\partial f}{\partial y} \hat{\j} + \frac{\partial f}{\partial z} \hat{\text{k}}[/tex]
Gradient Property [Addition/Subtraction]: [tex]\displaystyle \nabla \big[ f(x) + g(x) \big] = \nabla f(x) + \nabla g(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle f(x, y) = x^2 - y^2[/tex]
[tex]\displaystyle P(\sqrt{2}, 1)[/tex]
Step 2: Find Gradient
[Function] Differentiate [Gradient]: [tex]\displaystyle \nabla f(x, y) = \frac{\partial f}{\partial x} \bigg[ x^2 - y^2 \bigg] \hat{\i} + \frac{\partial f}{\partial y} \bigg[ x^2 - y^2 \bigg] \hat{\j}[/tex][Gradient] Rewrite [Gradient Property - Addition/Subtraction]: [tex]\displaystyle \nabla f(x, y) = \bigg[ \frac{\partial f}{\partial x}(x^2) - \frac{\partial f}{\partial x}(y^2) \bigg] \hat{\i} + \bigg[ \frac{\partial f}{\partial y}(x^2) - \frac{\partial f}{\partial y}(y^2) \bigg] \hat{\j}[/tex][Gradient] Differentiate [Derivative Rule - Basic Power Rule]: [tex]\displaystyle \nabla f(x, y) = 2x \hat{\i} - 2y \hat{\j}[/tex][Gradient] Substitute in point: [tex]\displaystyle \nabla f(\sqrt{2}, 1) = 2\sqrt{2} \hat{\i} - 2(1) \hat{\j}[/tex][Gradient] Simplify: [tex]\displaystyle \nabla f(\sqrt{2}, 1) = 2\sqrt{2} \hat{\i} - 2 \hat{\j}[/tex]∴ the gradient of the given f(x, y) function is equal to <2√2, -2>.
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Topic: Multivariable Calculus
Unit: Directional Derivatives
Which equation has the same solution as 4-2(x-5)-x-19
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The equation 3x - 4 = 2x + 7 has the same solution as 4 - 2(x - 5) = x - 19, with both solutions yielding x = 11.
Let's solve the equation step-by-step: 4 - 2(x - 5) = x - 19
First, expand the left side:4 - 2x + 10 = x - 19Combine like terms:
14 - 2x = x - 19Move all terms involving x to one side:
14 = 3x - 19Move constant terms to the other side:
33 = 3xSolve for x:
x = 11
Now, let's compare this solution to other given equations:
2(x + 5) = -82x + 10 = -8
2x = -18
x = -9 (Not a match)3(x - 3) = 9
3x - 9 = 9
3x = 18
x = 6 (Not a match)x + 2 = 2x - 3
2 = x - 3
x = 5 (Not a match)3x - 4 = 2x + 7
3x - 2x = 7 + 4
x = 11 (Match)
The equation with the same solution as 4 - 2(x - 5) = x - 19 is 3x - 4 = 2x + 7.
Complete question: Which equation has the same solution as 4 - 2(x - 5) = x - 19?
2(x + 5) = -83(x - 3) = 9x + 2 = 2x - 33x - 4 = 2x + 7The area of a square garden is 98 meters squared. How long is the diagonal
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The relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card
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R = 100 - 4x
x= number of lunches bought
R= remaining money on the lunch card
Hope this helps!
Order the fraction from least to greatest.
2/3, 4/9, 5/6, 7/12
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Now we must make all the denominators 36.
(2/3)=(24/36)
(4/9)=(16/36)
(5/6)=(30/36)
(7/12)=(21/36)
So we have the numbers (24/36),(16/36),(30/36), and (21/36).
Since they all have the same denominator, we can compare all the numerators and order hem from least to greatest.
(16/36)<(21/36)<(24/36)<(30/36)
Now that we have the order, we must simplify the numbers back to their original forms.
(4/9)<(7/12)<(2/3)<(5/6)
And that is your answer
2. 7/12
3. 2/3
4. 5/6
an air traffic controller is tracking two planes. To start, playing a is at an altitude of 2814 ft and plan B is just taking off. Plan a is gaining altitude at 30.5 feet per second in playing day is gaining altitude at 80.75 feet per second. How many seconds will pass before the planes are on the same altitude
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The initial altitude is the 'y-intercept'.
The rate of elevation is the slope.
Plane A: y = 30.5x + 2814
Plane B: y = 80.75x
The planes will be at same altitude when the y values are equal.
80.75x = 30.5x + 2814
Solve equation for 'x'.
80.75x - 30.5x = 2814
50.25x = 2814
x = (2814/50.25) = 56
Answer:
It will take 56 seconds before planes are at same altitude.
Answer:
56 seconds will pass.
Step-by-step explanation:
Because its right. :)
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If a production line produces 50 mouse traps every 30 minutes over the course of a 10-hour work day with a half hour break for lunch how many mouse traps are made in a day
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100 traps/ 1 hr times 9.5 hrs = 950
10 hrs - half hr break (30 minutes) = 9.5 hrs of work
so if it is 100 mousetraps per hr...and the hrs worked are 9.5 hrs.....then the number of mousetraps produced are : 9.5 * 100 = 950 mouse traps <==
Solve: 5x - 7x + 6 = -2(x - 3).
A)
0
B)
3
4
C)
2
D)
infinitely many solutions
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Answer:
D) infinitely many solutions
Step-by-step explanation:
The equation reduces to ...
-2x +6 = -2x +6
This is true for all possible values of x, so there are infinitely many solutions.
What is "The sum of m and n"
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Tim bought a pen for $2.25, a pencil for $0.59, a notebook for $6.49, and a highlighter for $1.49. He used a coupon that gave him $5.25 off his entire purchase. How much did he spend in total?
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if y varies directly as x and y=6 when x =-7, find y when x is 4
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When x is 4, y is approximately -3.43.
Explanation:To find y when x is 4, we can use the given information that y varies directly as x. This means that the ratio of y to x remains constant. We can set up a proportion using the initial values of y and x and solve for the unknown value:
6 / -7 = y / 4
By cross-multiplying, we get y = -24 / 7. Therefore, when x is 4, y is approximately -3.43.
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