An equivalent system of equations using the sum of the system and the first equation is:
[tex]x+4y=8\\5x+5y=10[/tex]
What are equations?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal.[tex]3x+5=14[/tex], for example, is an equation in which [tex]3x+5[/tex] and [tex]14[/tex] are two expressions separated by a '=' sign.Given:
[tex]x+4y=8\\4x+y=2[/tex]
Add the above equations to get:
[tex]x+4y+4x+y=8+2\\x+4y+4x+y=10\\5x+5y=10[/tex]
Therefore, an equivalent system of equations using the sum of the system and the first equation is:
[tex]x+4y=8\\5x+5y=10[/tex]
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The correct question is given below:
Create an equivalent system of equations using the sum of the system and the first equation.
x + 4y = 8
4x + y = 2
x + 4y = 8
5x + y = 2
x + 4y = 8
5x + 5y = 2
x + 4y = 8
4x + 5y = 10
x + 4y = 8
5x + 5y = 10
Oltp systems are designed to handle ad hoc analysis and complex queries that deal with many data items.
a. true
b. false
Answer:
b) It is false
In an animated film, a simple scene can be created by translating a figure against a still background. Write a rule for Independent Practice For See Exercises Example 8-9102113124 Extra Practice Skills Practice p. S5 Application Practice p. S28 the translation that maps the rocket from position I to position 2.
The rule of the translation that maps the rocket from position I to position 2 is 4 units right and 4 units up
How to determine the rule for the translation?The translation is added as an attachment
From the attached figure, we have the following corresponding coordinates:
Figure 1 = (0, 0)
Figure 2 = (4, 4)
The rule of translation is calculated as:
(x, y) = T<Figure 2 - Figure 1>
This gives
(x, y) = T<4 - 0, 4 - 0>
Evaluate
(x, y) = T<4, 4>
Hence, the rule of the translation that maps the rocket from position I to position 2 is 4 units right and 4 units up
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Complete question
In an animated film, a simple scene can be created by translating a figure against a still background. Write a rule for the translation that maps the rocket from position I to position 2.
The figure shown is made up of a cone and a cylinder. The height of the cone is 5 ft and its diameter is 12 ft. The height of the cylinder is 20 ft.
Diagram shows a composite shape formed by placing a cone next to a cylinder that share a common circular base. The diameter of the cone is labeled 12 feet, the height of the cone is labeled 5 feet, and the height of the cylinder is labeled 20 feet.
Find the lateral surface area of the cone and the surface area of the sides and bottom of the cylinder.
The lateral surface area of the cone is about Blank ft2. The surface area of the sides and the bottom of the cylinder is about blank ft2. The total surface area of the figure is about blank ft2.
Options for blank 1
A.260
B.188
C. 147
Options for blank 2
A. 980
B. 867
C. 1,508
Options for blank 3
A. 1,168
B. 1,768
C.1,127
D. 1,014
The lateral area of a cone is 147ft².
The total surface area of the cylinder is 867ft².
The total surface area is 1014ft²
What is the lateral surface area of a cone?The lateral area of a cone is defined as the area covered by the curved surface of the cone.
Lateral area of a cone = πr x √(r² + h²)
Where:
r = radius = 12/2 = 6ft h = height = 5ftπ = 3.143.14 x 6 x √(36 + 25) = 147ft²
What is the total surface area of the figure ?
Total surface area of the cylinder : πr(r + 2h),
(3.14 x 6) x (6 + 40) = 867ft²
Total surface area = 867 + 147= 1014ft²
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]m = m \\ \frac{97 - 68}{2 - 1} = \frac{134 - 97}{3 - 2} \\ 29 = 37 \\ this \: function \: is \: non \: linear[/tex]
Since the only two other options are quadratic and given that it must satisfy one of them i will assume the following general form of the function.[tex]f(1) = 68 \: \: \: f(2) = 97 \: \: \: \: f(3) = 134 \\ f(x) = ax {}^{2} + bx + c[/tex]
Substitute in the first function any point.[tex]f(1) = 68 \\ 7.8(1) {}^{2} - 2.9(1) + 67.1 = 68 \\ 7.8 - 2.9 + 67.1 = 68 \\ 72 = 68 \\ this \: is \: false[/tex]
I'm pretty sure something is wrong with the givenChange from rectangular to spherical coordinates. (let ≥ 0, 0 ≤ ≤ 2, and 0 ≤ ≤. ) (a) (5, 5 3 , 10 3 )
The spherical coordinate that is converted from the given rectangular coordinate is (12.62, 46.67°, 35.3°).
Here, the given rectangular coordinate is (5, 5.3, 10.3).
Therefore, the value of 'x' is 5, the value of 'y' is 5.3 and the value of 'z' is 10.3.
We can convert the rectangular coordinate (x, y, z) into spherical coordinate (ρ, θ, Φ) by the below mentioned method.
We know, ρ² = (x²+y²+z²)
Therefore, ρ
= √(x²+y²+z²)
= √[(5)²+(5.3)²+(10.3)²]
= √(25+28.09+106.09)
= √(159.18)
= 12.62
Again, tan θ = (y/x)
Therefore, θ = tan⁻¹(y/x) = tan⁻¹(5.3/5) = tan⁻¹(1.06) = 46.67°
Similarly, cos Φ = (z/ρ)
Therefore, Φ = cos⁻¹(z/ρ) = cos⁻¹(10.3/12.62) = cos⁻¹(0.816) = 35.3°
Here, the spherical coordinate is (ρ, θ, Φ).
Therefore, the required spherical coordinate for the given rectangular coordinate is (12.62, 46.67°, 35.3°).
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What is the circumference of a circle (to the nearest whole number) whose diameter is 12?
Step-by-step explanation:
Circumference = πd
= π × 12
= 37.6991
=38
Answer:38
Step-by-step explanation:
Find the matrix for the linear transformation which rotates every vector in r2 through an angle of −π/3.
The matrix for the linear transformation for which rotates every vector in r2 is [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex].
In this question,
The angle is -π/3 = -60°
Clockwise rotations are denoted by negative numbers.
Matrix for counter-clockwise direction for an angle α is
[tex]\left[\begin{array}{cc}cos\alpha &-sin\alpha \\-sin\alpha &cos\alpha \end{array}\right][/tex]
Then, matrix for clockwise direction for an angle α
Put α = -α in the above matrix,
⇒ [tex]\left[\begin{array}{cc}cos(-\alpha) &-sin(-\alpha) \\-sin(-\alpha) &cos(-\alpha) \end{array}\right][/tex]
⇒ [tex]\left[\begin{array}{cc}cos\alpha &sin\alpha \\sin\alpha &cos\alpha \end{array}\right][/tex]
Now substitute α = 60°
Then matrix becomes,
⇒ [tex]\left[\begin{array}{cc}cos60 &sin60 \\sin60 &cos60 \end{array}\right][/tex]
⇒ [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex]
Hence we can conclude that the matrix for the linear transformation for which rotates every vector in r2 is [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex].
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help help help help me pleaseeeeeeeee
The ticket price which will maximize the student's council is: C. $3.10.
What is price?Price can be defined as an amount of money which is primarily set by the seller of a product, and it must be paid by a buyer to the seller, so as to enable the acquisition of this product.
Based on the information provided about Valley High School student council, we can logically deduce the following data:
Total number of students = 420 students.Lowest ticket price = $2.00.Increase in ticket price = $0.20.Attendance = 20 fewer students How to determine the ticket price?Mathematically, the equation which model the profit is given by:
Profit = price × number of tickets sold
P(x) = (2 + 0.2x)(420 - 20x)
P(x) = 840 + 84x - 40x - 4x²
P(x) = -4x² + 44x + 840.
For any quadratic equation with a parabolic curve, the axis of symmetry is given by:
Xmax = -b/2a
Xmax = -44/2(-4)
Xmax = -44/-8.
Xmax = 5.5
Ticket price for maximum profit is given by:
Ticket price = 2 + 0.2x
Ticket price = 2 + 0.2(5.5)
Ticket price = $3.10.
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Ileana received a statement on her certificate of deposit showing that her investment had returned $5,084 over its life. if the certificate of deposit pays a simple interest rate of 4.1% and her initial investment was $15,500, how long had the money been invested? please help me! i'm dying!
Ileana have to invest for 8 years :
What is Simple interest?Simple interest is a simple and straightforward formula for figuring out how much interest will be charged on a loan. Simple interest is calculated by dividing the daily interest rate by the principle and the number of days between payments.
How do you calculate simple interest?The principal amount must be multiplied by the time, interest rate, and time period in order to calculate simple interest. Simple Interest = Principal x Interest Rate x Time is the written formula.
Given Data:Principal amount = $15,500
interest = $5,084
Time = ?
Rate = 4.1% simple interest
Solution:to find the simple interest :
I = [tex]\frac{(p*t*r)}{100}[/tex]
Then:
Time = [tex]\frac{I*100}{P*R}[/tex]
= [tex]\frac{(5084*100)}{(15500*4.1)}[/tex]
= [tex]\frac{508400}{63,550}[/tex]
= 8 years
Ileana have to invest for 8 years
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Can anyone please help me with these 3 math questions? its very urgent ‼️
i don’t understand where to start..
The unit rate of Mikayla and brie is 0.16 miles per minutes and 0.25 miles per minutes respectively.
Brie runs faster.
Unit rateMikayla
2 miles in 12 1/2 minutes
Unit rate = miles / minutes
= 2 ÷ 12 1/2
= 2 ÷ 25/2
= 2 × 2/25
= 4/25
= 0.16 miles per minutes
Brie
5 miles in 22 1/4 minutes
Unit rate = miles / minutes
= 5 ÷ 22 1/4
= 5 ÷ 89/4
= 5 × 4/89
= 20/89
= 0.25 miles per minutes
Brie runs fasterLucy
4 4/5 pounds for $18.50
Unit rate = pounds / price
= 4 4/5 ÷ 18.50
= 24/5 ÷ 18.50
= 24/5 × 1/18.50
= 24/92.50
= $0.26 per pound
Sophie
3 1/2 pounds for $14.75
Unit rate = pounds / price
= 3 1/2 ÷ 14.75
= 7/2 ÷ 14.75
= 7/2 × 1/14.75
= 7/29.5
= $0.24 per pound
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Sea World's dining card offers a choice of a three main entrees, a choice from five sides and a choice from four desserts. How many different meals can be selected?
Powers of 10 and Exponents (number 4 is a 10 incase u can’t see of the ripped page.)
Answer:
below
Step-by-step explanation:
2) 10², the second power of ten
3) 10⁴, the fourth power of ten
4) 1000
5) 400
6) 90,000
7) 10
8) 100,000
9) 50
10) 7000
11) 8
12) 24 x 10⁴
13) 93,000,000
Answer + Step-by-step explanation:
A data set contains three points, and two of the residuals are 7 and -3. What 7
is the third residual?
The data set in discuss which contains three points and two of the residuals are 7 and -3 would have its third residual as; -4.
What is the third residual if the data set characterized as having 2 of its three residuals to be; 7 and -3?According.tinthe task content, the data set in discuss has three points and consequently should have three residuals.
Additionally, two of the three residuals have been given and on this note, it follows that the third residual must have a value such that the algebraic sum of all residuals is 0.
Hence, we have; -3 + 7 +x = 0;
x = 3-7 = 4.
Ultimately, the third residual is; -4.
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The external and the internal radii of a hollow cylindrical metallic vessel 56 cm long are 10.5 cm and 10.1 cm respectively. Find the cost of the metal contained by the vessel at Rs 2 per cubic cm. Also, find the cost of polishing it's outer surface 20 paisa per square cm.
The total cost of polishing it's outer surface 20 paisa per square cm exists Rs. 738.58.
How to estimate the cost of polishing metallic vessel outer surface 20 paisa per square cm.?External radius of the hollow cylinder = 10.5 cm
Internal radius of the hollow cylinder = 10.1 cm
Height of the hollow cylinder = 56 cm
Cost to Polish Outer Surface: 20 paisa/sq. cm.
Surface Area of Hollow Cylinder = Circumference [tex]*[/tex] height
Surface area of hollow cylinder = 2 π r h
= 2 π (10.5 cm) 56 cm
= π (21)(56)
= 3692.64 [tex]cm^2[/tex] (Using π ≈ 3.14 rounding to 2 digits)
Total Cost of metallic cylinder [tex]$= 3692.64 cm^2 * 20 paisa/cm^2[/tex]
= 73,852.8 paisa
= Rs. 738.58
Therefore, the total cost of polishing it's outer surface 20 paisa per square cm exists Rs. 738.58.
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Which car has "best" car combination of mpg and hp, where mpg and hp must be given equal weight?
The mpg and hp is print(paste("The car with the best combination of mpg and hp is",rownames(myCars[myCars$combination==max(myCars$combination),])))
MPG is an abbreviation for 'miles-consistent with gallon and it is used to give you an indication of the fuel financial system of a vehicle or industrial vehicle. It helps you to work out how reasonably-priced or high-priced an automobile might be to run.
As for a new vehicle, an awesome MPG is around 50 to 60. Having this stepped forward gasoline economy facilitates minimizing going for walks fees and cheaper avenue tax due to decreased CO2 emissions. consistent with What car's featured blog, here are a number of the most gasoline-green automobiles in the marketplace nowadays.
The gas economic system of a car relates to the space traveled via an automobile and the quantity of fuel fed on. intake can be expressed in terms of the volume of gasoline to travel a distance, or the gap traveled according to the unit quantity of gasoline consumed.
The car has the “best” combination of mpg and hp, where mpg and hp must be given equal weight.
#sum the scaled values of mpg and hp and add a new column called combination
myCars$combination<-scale(myCars$hp)+scale(myCars$mpg)
#Which car has the best combination of mpg and hp?
print(paste("The car with the best combination of mpg and hp is",rownames(myCars[myCars$combination==max(myCars$combination),])))
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A circle is described by the equation x2 y2 14x 2y 14 = 0. what are the coordinates for the center of the circle and the length of the radius?
Answer:
length is (-7,-1) and radius is 6
Step-by-step explanation:
We are given the expression of the equation of a circle that is
x2 + y2 + 14x + 2y + 14 = 0.
Using completing the squares:
x2 + y2 + 14x + 2y + 14 = 0(x+7)^2 + (y+1) ^2 = -14 + 49 + 1(x+7)^2 + (y+1) ^2 = 36 center thus is at (-7,-1) and the radius is equal to square root of 36 equal to 6.
7
of the trains are arriving late due to a train strike.
Write down the ratio of on-time trains to late trains.
15
Answer:
15:7
Step-by-step explanation:
you put the numbers in order first the number of on time trains to off time trains
1,615×10 to the 2 power
simplifying 1,615×10 to the 2 power would give 161500
Simplifying the index form
Index notation is known as a way of representing numbers (constants) and variables (e.g. x and y) that have been multiplied by themselves a number of times.
Index notations, or indices are use to simplify expressions or solve equations involving powers.
For instance;
8 × 8 × 8 × 8
8 is multiplied by itself 4 times
In index form , it is written as 8 ^4, that is, 8 to the 4 power
From the information given, we have to simply 1,615×10 to the 2 power
It can be written as;
= 1, 615 × 10 × 10
= 1, 615 × 100
= 161500
Thus, simplifying 1,615×10 to the 2 power would give 161500
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The law of Cosines Is......
Answer: [tex]\Large\boxed{C.~21}[/tex]
Step-by-step explanation:
The goal of the question
Find the value of 2abcosC
Given information
a = 4
b = 3
c = 2
Given formula (Law of Cosine)
[tex]c^2=a^2+b^2-2abcosC[/tex]
Substitute values into the formula (Leave 2abcosC as it is)
[tex](2)^2=(4)^2+(3)^2-2abcosC[/tex]
Simplify the exponents
[tex]4=16+9-2abcosC[/tex]
Simplify by addition
[tex]4=25-2abcosC[/tex]
Add 2abcosC on both sides
[tex]4+2abcosC=25-2abcosC+2abcosC[/tex]
[tex]4+2abcosC=25[/tex]
Subtract 4 on both sides
[tex]4 + 2abcosC-4=25-4[/tex]
[tex]\Large\boxed{2abcosC=21}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
C
Step-by-step explanation:
a² + b² - 2abcosC = c² ( subtract a² + b² from both sides )
- 2abcosC = c² - a² - b² ( multiply through by - 1 )
2abcosC = a² + b² - c²
a, b, c are the sides opposite vertices A, B, C
here a = 4 , b = 3 , c = 2 , then
a² + b² - c²
= 4² + 3² - 2²
= 16 + 9 - 4
= 25 - 4
= 21
A quantity h varies directly with w and inversely with p. when w = 4 and p = 6, h = 2. what is the constant of variation?
The value of the constant of variation is 3.
The correct option is C.
What is variation?Direct variations occur when variables in a variation vary proportionately, that is, when they both increase or decrease at the same time. As a result, you can write X Y symbolically if X and Y are in direct variation. The variables alter disproportionally in inverse or indirect variations.
According to the given information:
Let the constant of variation be k
A quantity h varies directly with w and inversely with p
That is,
h∝ w/p
Introducing the constant of variation, k, we get
h = k(w/p)
Also, from the give information,
w = 4
p = 6
h = 2
Putting the parameters into the relation, we get
2 = K x 4/6
6 x 2= 4K
K = (6 x 2)/4
K = 3
Hence, the value of the constant of variation is 3.
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I understand that the question you are looking for is:
A quantity h varies directly with w and inversely with p. If h = 2, w = 4, and p = 6. What is the constant of variation?
A. 1/2
B. 4/3
C. 3
D. 12
Answer:
C
Step-by-step explanation:
The verified user said so
Question #1) x4 = 256 solve for x
In the given equation the value of x is 4.
According to the statement
we have given that the a equation and we have to solve that equation for x and find the value of the x.
So, For the value of x in given statement:
The given equation is
x⁴ = 256
we know that the 2 changes into the square root after rearrangement in the equation so, the equation become
(x²)² = 256
Now,
(x²) = √256
Then equation becomes
(x²) = 16
This is because the square root of the 256 is 16.
Now another square changes into square root then
x = √16
And
x = 4
So, In the given equation the value of x is 4.
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i dont understand the math can pls help
Answer: 46.7 in/3
Step-by-step explanation:
Talia buys a 6-ounce container of macadamia nuts for $5.94 what is the unit price per ounce?
Answer:
$0.99 or 99 cents
Step-by-step explanation:
Since 6 ounces is worth $5.94, divide 5.94 by 6 to get the unit price. This is $0.99 or 99 cents.
It took Sandra 5 hours to drive to her father's house and back. She lives 120 miles from the city where her father lives. What was her per hour driving rate for the trip?
What is the solution to this system of equations?
4x + 5y = 7
3x – 2y = –12
The solution is
The solution to the system of equations is (-2, 3)
Rhombus A B C D is shown. All sides are congruent. Lines are drawn from point A to point C and from point D to point B and intersect at point E at the center.
The area of rhombus ABCD is 120 square units.
AE = 12 and BD = x – 2. What is the value of x and the length of segment BD?
x =
BD = units
Answer:
x = 22
BD = 20 units
Step-by-step explanation:
The formula for the area of a rhombus can be used with the given values to write an equation that can be solved for x and for BD.
Area of a rhombusThe formula is ..
A = 1/2(d1)(d2) . . . . where d1 and d2 are the lengths of the diagonals.
Using the given values, we have ...
120 = 1/2(12)(x-2)
SolutionDividing by 6, we find ...
20 = x -2 = BD
22 = x . . . . . . . . add 2
The value of x is 22.
The length of BD is 20.
Answer:
x=12
BD=10
Step-by-step explanation:
Rashon walked 10 miles in 4 hours. if he walked the same distance every hour, how far did he walk in one hour? write your answer in feet if 1 mile equals 5280 feet.
Answer:
Step-by-step explanation:
Miles per hour: [tex]\frac{10miles}{4hrs} = 2.5\frac{miles}{hour}[/tex]
Feet per hour:
[tex]2.5\frac{miles}{hours} (\frac{5280ft}{1mile} )[/tex]
[tex]=13,200\frac{ft\\}{hr}[/tex]
Write the following in interval notation
x < 8
Answer:
Yup Yup
Step-by-step explanation:
yessah
Inequalities help us to compare two unequal expressions. The given inequality x<8 can be written in the interval notation as x=(-∞,8).
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
Continuous sets of real numbers can be represented using interval notation by the numbers that bound them. When written, intervals resemble ordered pairs in several ways. They do not, however, intend to indicate any particular location. Instead, they serve as a concise approach to expressing an inequality or a set of inequalities.
The given inequality x<8 can be written in the interval notation as,
x = (-∞,8)
Hence, The given inequality x<8 can be written in the interval notation as x=(-∞,8).
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Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(x) = x e5t2 − 4t dt 4 g'(x) =
The derivative of the given equation is [tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex].
According to the statement
we have given that the statement and we have to find the derivative of that term.
So, We know that the
The given equation is
[tex]g(t) = \int\limits^x_4 {e^{5t^{2} - 4t} } \, dt[/tex]
Now find the derivative of that term
We find the derivative of the given term is with the help of the FTC.
And then
[tex]\frac{dg(x) }{dt} = {e^{5x^{2} - 4x} } \, \frac{dx}{dx}[/tex]
Then the equation become is
[tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex]
So, this is the derivative of the given equation.
So, The derivative of the given equation is [tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex].
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I NEED HELP WITH THIS ASAP! Find x and y
Answer: D
Step-by-step explanation: a^2+b^2=c^2
so use y value for b2 and 6 square root 3 as a and check with it.
