Final answer:
The system of equations has infinitely many solutions because they represent the same line. The solution can be written in terms of the parameter t as (x, y) = ((3 + 6t)/5, t).
Explanation:
The student's question involves determining the type of solution a system of two linear equations has and finding the solution if it exists. The given system of equations is:
5x - 6y = 3
10x - 12y = 6
Notice that the second equation is just the first equation multiplied by 2. This means the system has infinitely many solutions because the two equations are actually the same line. To find these solutions in terms of a parameter t, we can solve the first equation for x as follows:
Choose t to represent y (i.e., let y = t).
Substitute y = t into the first equation to get 5x - 6t = 3.
Solve for x to find x = (3 + 6t)/5.
Therefore, the solutions to the system can be expressed as (x, y) = ((3 + 6t)/5, t), where t is any real number.
What is the largest whole number that will round up or down to 500 if we're rounding to the nearest hundred?
Answer:
549
Step-by-step explanation:
The next larger whole number, 550, will round up to 600.
The largest whole number that rounds to 500 is 549 when rounding to hundreds.
A company manufactures cell phones. In August, a random sample of 125 cell phones was inspected, and 3 phones were found to be defective. The company manufactured 8,000 cell phones in August. Based on the results from the sample, about how many cell phones are expected to be defective?
Answer:
192
Step-by-step explanation:
To find how many phones are expected to be defective, we need to represent the values in a fraction.
[tex]\dfrac{x}{8000}=\dfrac{3}{125}[/tex]
x = number of defective phones
Now we can solve this using algebra.
To get the value of x we need to multiply both sides by 8000 to leave x alone.
[tex]x=\dfrac{3}{125}(8000)[/tex]
[tex]x=0.024(8000)[/tex]
[tex]x=192[/tex]
So around 192 cell phones are expected to be defective out of 8000 phones.
Answer:
192
Step-by-step explanation:
Phil is 23 years older than Keith. In two years Phil will be twice as old as Keith will be. How old is Keith in years?
Answer:
44 years old
Step-by-step explanation:
The deifference between their ages is always the same. So 23x2=46
but that is in 2 years so we -2 from 46 =44
Answer:
44
Step-by-step explanation:
What is the simplest form of the radical expression 3 sqrt 24 - 2 sqrt 54 + 2 sqrt 18
Please show all of your work.
Answer:
[tex]6\sqrt{2}[/tex]
Step-by-step explanation:
we have
[tex]3\sqrt{24} -2\sqrt{54}+2\sqrt{18}[/tex]
we know that
[tex]\sqrt{24}=\sqrt{2^{3}3}=2\sqrt{6}[/tex]
[tex]\sqrt{54}=\sqrt{3^{3}2}=3\sqrt{6}[/tex]
[tex]\sqrt{18}=\sqrt{3^{2}2}=3\sqrt{2}[/tex]
Substitute
[tex]3(2\sqrt{6}) -2(3\sqrt{6})+2(3\sqrt{2})[/tex]
[tex](6\sqrt{6}) -(6\sqrt{6})+(6\sqrt{2})[/tex]
[tex]6\sqrt{2}[/tex]
When simplifying the square roots in the expression 3sqrt(24) - 2sqrt(54) + 2sqrt(18), we find that the simplified solution is 6sqrt(2).
Explanation:To simplify the radical expression 3 sqrt 24 - 2 sqrt 54 + 2 sqrt 18, we first need to break down each square root into its simplest form. In order to do this, we look for perfect-square factors (numbers like 4, 9, 16, 25 that have an integer as a square root) within each number:
3sqrt(24) = 3sqrt(4*6) = 6sqrt(6)
2sqrt(54) = 2sqrt(9*6) = 6sqrt(6)
2sqrt(18) = 2sqrt(9*2) = 6sqrt(2)
Because the sqrt(6) terms are like terms we can combine those, and then include the sqrt(2) term:
6sqrt(6) - 6sqrt(6) + 6sqrt(2) = 6sqrt(2).
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The temperature at a point (x, y, z) is given by t(x, y, z) = 200e−x2 − 3y2 − 7z2 where t is measured in °c and x, y, z in meters. (a) find the rate of change of temperature at the point p(4, −1, 4) in the direction towards the point (5, −5, 6).
Looks like the temperature is given by
[tex]t(x,y,z)=200e^{-x^2-3y^2-7z^2}[/tex]
We have gradient at any point [tex](x,y,z)[/tex]
[tex]\nabla t(x,y,z)=200e^{-x^2-3y^2-7z^2}(-2x,-6y,-14z)[/tex]
Then the rate of change of [tex]t[/tex] at [tex]p[/tex] in the direction of (5, -5, 6) is given by
[tex]\nabla t(4,-1,4)\cdot\dfrac{(5,-5,6)}{\|(5,-5,6)\|}=\left(-\dfrac{400}{e^{131}}(4,-3,28)\right)\cdot\dfrac{(5,-5,6)}{\sqrt{86}}=-\dfrac{40600}{e^{131}}\sqrt{\dfrac2{43}}[/tex]
which is very nearly 0.
The rate of change of temperature at the point p(4, -1, 4) in the direction towards the point (5, -5, 6) can be found by computing the gradient vector at p, obtaining a unit direction vector towards the other point, and calculating their dot product.
Explanation:To find the rate of change in the direction towards the point (5, -5, 6), we need to compute the gradient vector of the temperature at point p(4, -1, 4), and then calculate the directional derivative in the direction towards the other point.
First, we calculate the partial derivative of t with respect to x, y, and z. These derivatives give us the gradient vector ∇t at point p. The gradient vector represents the direction of the steepest incline at p and its magnitude gives the rate of increase of t.
Next, we need to find the unit vector in the direction towards point (5,-5,6) from p. Subtracting the coordinates of p from the other point gives us the direction vector. Normalizing this vector gives us the unit direction vector.
Finally, the rate of change of temperature at p in the direction towards the other point is given by the dot product of ∇t at p and the unit direction vector. This is known as the directional derivative of t at p in the mentioned direction.
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If you were to create a histogram from the data shown in this stem-and-leaf plot, how many data points would be contained in the bar from 95-105?
A) 3
B) 4
C) 5
D) 6
Answer:
the answer is A, 3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Stem Leaf Plot : A special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).
So, In the Given Stem leaf plot the numbers are :
100,101,90,93,94,94,95,81,86,87,89,70,72,76,69,56,58,49
Arrange in ascending order
49,56,58,69,70,72,76,81,86,87,89,90,93,94,94,95,100,101
Now we are supposed to find how many data points would be contained in the bar from 95-105
49,56,58,69,70,72,76,81,86,87,89,90,93,94,94,95,100,101
So, we can see there are 3 data points are contained in bar from 95 -105.
Hence 3 data points are contained in bar from 95 -105.
Two particle with charges q and −q are fixed at the vertices of an equilateral triangle with sides of length
a. if k = 1/4π 0, the work required to move a particle with charge q from the other vertex to the center of the line joining the fixed particles is:
Answer:
k(qq)/r^2 times the length of the distnace
Step-by-step explanation:
Force times distance. The Electrical force is the only thing you have to find first.
The work required to move a particle with charge q from the other vertex to the center of the line joining the fixed particles is -kq^2/a.
Explanation:To find the work required to move a particle with charge q from the other vertex to the center of the line joining the fixed particles, we need to calculate the electrostatic potential energy. The potential energy is given by the equation:
U = kqQ/r
where U is the potential energy, k is the electrostatic constant, q and Q are the charges, and r is the distance between the charges.
In this case, we have two charges of magnitude q and -q at the vertices of an equilateral triangle. The distance from the center of the triangle to each charge is a/2, where a is the length of the side of the triangle. Therefore, the potential energy is:
U = (1/4πε0)q(-q)/a
where ε0 is the permittivity of free space. Simplifying the expression, we get:
U = -kq2/a
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A hot air balloon is flying above Groveburg. To the left side of the balloon, the balloonist measure the angle of depression to the Groveburg soccer fields to be 20° 15'. To the right side of the balloon, the balloonist measures the angle of depression to the high school football field to be 62° 30'. The distance between the two athletic complexes is 4 miles.
What is the distance from the balloon to the football field?
Answer:
The answer is 1.4 miles ⇒ answer (d)
Step-by-step explanation:
* Let the balloon is at the vertex A, and the soccer fields
at vertex B and the football field at vertex C
∴ m∠B = 20° 15' = 20.25°
∴ m∠C = 62° 30' = 62.5°
∴ m∠A = 180 - 20.25 - 62.5 = 97.25°
∵ BC = 4 miles
* By using the sin Rule:
∵ AC/sin(B) = BC/sin(A)
∴ AC = (BC)(sinB)/sin(A)
∴ AC = [4 × sin(20.25)] ÷ sin(97.25) = 1.395 ≅ 1.4 miles
∴ The distance from the balloon to the football filed = 1.4 miles
Answer:
1.4
Step-by-step explanation:
Consider the equation 5 + x = n. What must be true about any value of x if n is a negative number? Explain your answer. Include an example with numbers to support your explanation.
Answer:
x < 5
Step-by-step explanation:
Any value of x must have a bigger negative number than 5. In this case, formally you say that all x values must be LESS than 5 only.
Answer:
Step-by-step explanation:
Line A is represented by the equation given below: x + y = 3 What is most likely the equation for line B, so that the set of equations has infinitely many solutions? 3x + 3y = 3 3x + y = 3 x + y = 9 3x + 3y = 9
Answer:
3x + 3y = 9
Step-by-step explanation:
Multiplying the given equation by 3 gives you ...
3(x + y) = 3(3)
3x + 3y = 9 . . . . . . matches the last choice
This is an equation for the same line as the given equation, so the lines will have infinitely many points in common (infinitely many solutions).
Answer:
3x + 3y = 9
Step-by-step explanation:
Equivalent expression
Answer:
The answer is C. 9^-2
Step-by-step explanation:
Don’t know but not the first one
The height of a pyramid is 15 inches. The pyramid's base is a square with a side of 5 inches. What is the pyramid's volume?
Answer:
The pyramid's volume is [tex]125\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the pyramid is equal to
[tex]V=(1/3)Bh[/tex]
where
B is the area of base of pyramid
h is the height of the pyramid
Find the area of the base B
[tex]B=5^{2}=25\ in^{2}[/tex] -----> is a square
[tex]h=15\ in[/tex]
substitute the values
[tex]V=(1/3)(25)(15)=125\ in^{3}[/tex]
Can someone help me please I’m struggling so much. let me know if the things that I put already are right
your calculations for volume (pi x r^2 × h) and surface area (2 × pi × r (h+r)) are correct. However your ratio are incorrect. From the formulas the ratio of surface area to volume would be r×h:2(h+r)
What's the sum of −62 and its opposite?
The sum of any negative number and its opposite is 0. So your answer is 0.
The sum of any negative number and its opposite is equal to 0.
look at the picture for the question
Please answer
Answer:
[tex]\large\boxed{D.\ 12x^2-29x+14}[/tex]
Step-by-step explanation:
Use FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex](3x-2)(4x-7)=(3x)(4x)+(3x)(-7)+(-2)(4x)+(-2)(-7)\\\\=12x^2-21x-8x+14\qquad\qquad\text{combine like terms}\\\\=12x^2+(-21x-8x)+14=12x^2-29x+14[/tex]
Type the correct answer in the box
Answer:
[tex]w=V/(lh)[/tex]
Step-by-step explanation:
Let
l------> the length of the base of the prism
w------> the width of the base of the prism
h------> the height of the prism
we know that
The volume of the prism is equal to
[tex]V=lwh[/tex]
Solve for w
That means-------> isolate the variable w
so
Divide both sides by (lh)
[tex]V/(lh)=lwh/(lh)[/tex]
Simplify
[tex]w=V/(lh)[/tex]
Help with this question, please!! I need serious help on this question!
Answer:
[tex]\large\boxed{d_2=15\ cm}[/tex]
Step-by-step explanation:
The formula of an area of a kite:
[tex]A=\dfrac{d_1d_2}{2}[/tex]
d₁, d₂ - diagonals
We have A = 120 cm² and d₁ = 16 cm. Substitute:
[tex]\dfrac{16d_2}{2}=120[/tex]
[tex]8d_2=120[/tex] divide both sides by 8
[tex]d_2=15\ cm[/tex]
Wendy can ride her bike 0.7 miles in 6 minutes how many miles can she ride in 2.5 hours
Wendy can ride 17.5 miles in 2.5 hours
Answer:
17.5 miles
Step-by-step explanation:
[tex]\frac{miles}{min} = \frac{miles}{min} \\\\\\[/tex]
Convert hours to minutes
60 minutes = 1 hour
[tex]2.5*60=150[/tex]
2.5 hours = 150 minutes
[tex]\frac{0.7}{6} = \frac{x}{150} \\\\\\[/tex]
Cross multiply
[tex]0.7*150=6*x\\105=6x\\\frac{105}{6} =x\\17.5=x[/tex]
oop please help quick!!
In the space below, provide the larger of the two positive integers that add to 10 and have the largest possible product.
Answer:
5
Step-by-step explanation:
The integers 5 and 5 sum to 10 and have the largest possible product.
___
The two numbers will be x and (10-x). Their product is x(10-x), which describes a downward-opening parabola with zeros at x=0 and x=10. The maximum (vertex) of that parabola is halfway between the zeros, at x=5. Both integers have the same value: 5. Their product is 25.
If there is a requirement the integers be distinct, then 6 and 4 are the integers of choice. Their product is 24.
samantha purchased an automobile for 4,200. her state charged 4% tax for the car, $47 for the license plate, and $35 for the state safety and emission inspection. how much does samantha need to pay for the extra charges , not including the price of the car
The amount that need to be pay is $250.
The calculation is as follows;= 4% of 4,200 + $47 + $35
= $168 + $47 + $35
= $250
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Samantha needs to pay a total of $250 in extra charges, which includes $168 for the state tax, $47 for the license plate, and $35 for the state safety and emission inspection.
Explanation:Calculation of Extra Charges for Automobile PurchaseTo determine how much Samantha needs to pay in extra charges for her automobile purchase, we need to calculate each component separately and then sum them up. Firstly, we calculate the state tax by multiplying the purchase price by the tax percentage:
Tax = Purchase Price × Tax Rate
Tax = $4,200 × 0.04 = $168
Next, we add the fixed costs for the license plate and state safety and emission inspection:
Total Extra Charges = Tax + License Plate Fee + Inspection Fee
Total Extra Charges = $168 + $47 + $35 = $250
Therefore, Samantha needs to pay $250 in extra charges, not including the price of the car.
Please people
Find the function h(x) = f(x) ∘ g(x) if f(x) = x(2 - x) and g(x) = 3^x.
A. h(x) = 0
B. h(x) = -3^2x
C. h(x) = 2(3^2x)
D. h(x) = 3^x (2 - 3^x)
Answer:
D
Step-by-step explanation:
Function composition substitutes more than just values or constants. It substitutes functions inside another function. Solve each expression by starting inner most and working to outermost. The expression f(x) ∘ g(x) means f(g(x)).
Let f(x) = x(2 - x) and g(x) = 3^x.
Begin by substituting g(x) in for x in f(x).
[tex]f(g(x)) = (3^x)(2-(3^x))[/tex]
The solution is D.
Identify the graph of the equation. What is the angle of rotation for the equation?
xy=-2.5
Answer:
It is B. hyperbola, 45 degrees.
SteIt is p-by-step explanation:
If we rotate the standard form x^2 - y^2 = 1 through 45 degrees we get xy = 1/2.
xy = -2.5 comes from x^2 - y^2 = -5 being rotated 45 degrees.
Answer:
The correct option is b
Step-by-step explanation:
The given equation is
[tex]xy=-2.5[/tex]
It can be written as
[tex]xy+2.5=0[/tex] .... (1)
The general forms of conic is
[tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex] .... (2)
From (1) and (2), we get
[tex]A=0,B=1,C=0,D=0,E=0,E=2.5[/tex]
[tex]B^2-4AC=1-4(0)(0)=1>0[/tex]
Since the value of B²- 4AC > 0, then it is hyperbola.
The formula form angle of rotation is
[tex]\tan 2\theta=\frac{B}{A-C}[/tex]
[tex]\tan 2\theta=\frac{1}{0-0}[/tex]
[tex]\tan 2\theta=\infty[/tex]
[tex]\tan 2\theta=\tan (90^{\circ})[/tex]
[tex]2\theta=90^{\circ}[/tex]
[tex]\theta=45^{\circ}[/tex]
The angle of rotation is 45°. Therefore the correct option is b.
You roll a die and flip three coins. The number of possible outcomes in the sample space is.
Answer:
48
Step-by-step explanation:
We assume that the die and coins are non-bias.
If you roll a die once, you have 6 possible outcomes (anything from 1-6).
If you flip 3 coins once, you have 2 possible outcomes for each coin (either heads or tails). Multiply those 3 possibilities (2x2x2), you get 8.
Multiply 8 with 6, and you get 48 possible outcomes in sample space.
*In the sample space shown below, do the same combinations to all roll die outcomes to get the whole sample space (i.e., 2TTT, 3TTT, 4TTT etc.).
Determine the relationship between the quantities of the given graph.
D
The time worked is directly proportional to the wages. This means as the wages increase, the hours of work increases.
What is the total surface area of this square pyramid?
Answer:
The total surface area of this square pyramid is [tex]297\ mm^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of a square pyramid is equal to
[tex]SA=b^{2} +4[\frac{1}{2}(b)(h)][/tex]
we have
[tex]b=9\ mm[/tex] ----> the length side of the square base
[tex]h=12\ mm[/tex] ----> the height of the triangular faces
substitute the values
[tex]SA=9^{2} +4[\frac{1}{2}(9)(12)]=297\ mm^{2}[/tex]
Carla has two lengths of ribbon. One ribbon is 2 feet long. The other ribbon is 30 inches long. Which length of ribbon is longer?
Answer:
The length of 30 inches is longer
Step-by-step explanation:
we know that
[tex]1\ ft=12\ in[/tex]
Convert the length to inches
[tex]2\ ft=2(12)=24\ in[/tex]
therefore
[tex]30\ in>24\ in[/tex] ------> [tex]30\ in>2\ ft[/tex]
The length of 30 inches is longer
A triangular sail has a perimeter of 25 m. Side a is 2 m shorter than twice side b, and side c is 3 m longer than side b. Find the length of each side.
We know that perimeter of the triangle its a+b+c=25
a=2b-2
b=b
c=b+3
Now we can substitute it into the formula
2b-2+b+b+3=25
4b+1=25 /-1
4b=24 /:4
b=6 - its b side
a=2*6-2
a=12-2=10 - its a side
c=6+3=9 - its c side
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Simplify 13 2
the 2 is tiny so I think it's 13 to the power of 2
Answer: 169
Step-by-step explanation:
You just multiply 13 by 13
When simplifying 13 to the power of 2, you multiply 13 by itself, resulting in 13 x 13, which equals 169. This is known as squaring a number.
The question you've asked involves exponents, which is a way to express repeated multiplication of the same number. When you write 13 with a tiny 2 next to it, you're indicating that 13 should be multiplied by itself once, which is what squaring a number means. In other words, 13 to the power of 2 is 132, which is 13 × 13.
Let's simplify 132:
Multiply 13 by itself: 13 × 13.Calculate the product: 169.So, 132 equals 169. This process is using an integer power, which involves multiplying the base (in this case, 13) by itself as many times as indicated by the exponent (in this case, 2). This can apply to any number, where for example 53 (5 cubed) equals 5 × 5 × 5, which is 125.
What is the solution set?
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[̲̅T̲̅][̲̅h̲̅][̲̅e̲̅]
[̲̅A̲̅][̲̅t̲̅][̲̅t̲̅][̲̅a̲̅][̲̅c̲̅][̲̅h̲̅][̲̅m̲̅][̲̅e̲̅][̲̅n̲̅][̲̅t̲̅] ❣
❣❣... ℏ✺℘ḙ !т ℏḙℓ℘ṧ ʏ✺ṳ...❣❣
Answer:
The possible solution that is obtained from the system of equation are:
(1,3) and (6,13)
Step-by-step explanation:
We are asked to find the solution set of the given system of equation as:
[tex]y=x^2-5x+7-----------(1)[/tex]
and [tex]y=2x+1--------(2)[/tex]
We know that the solution of the system of equations is the possible set of x and y-values that satisfy both the equations.
Or we may say the point of intersection of the graph that is obtained from both the equations.
We solve the system by substitution method as:
We put the value of y from equation (1) in equation (2) to obtain:
[tex]x^2-5x+7=2x+1[/tex]
which is further written by combining the like terms as:
[tex]x^2-5x-2x+7-1=0\\\\x^2-7x+6=0\\\\x^2-6x-x+6=0\\\\x(x-6)-1(x-6)\\\\(x-1)(x-6)=0[/tex]
Hence, we get the possible values of x as:
x=1 and x=6
Also the value of y when x=1 is:y=2×1+1=2+1 ( Putting the value of x in equation (2))
y=3
when x=6 we have the value of y as:y=2×6+1
y=13
Hence, the possible solutions are:
(1,3) and (6,13)