Answer:
One solution which is x = 2
Step-by-step explanation:
Equations like these most often won't have more than one solution unless they are the exact same equation.
If the equation was x + 1 = x + 1, it would have infinitely many solutions because both sides are the same.
Equations with absolute value and quadratic equations most often have 2 solutions have there is a negative answer and a positive answer.
a car travels 120120 miles from aa to bb at 3030 miles per hour but returns the same distance at 4040 miles per hour. the average speed for the round trip is closest to:
The Average Speed of car for the round trip is 346.28 km/ hr.
Average Speed is calculated by dividing the total distance that something has travelled by the total amount of time it took it to travel that distance.
If a car travels a distance d at rate r₁ and return the same distance at rate r₂, then,
Average Speed = total distance ÷ total time
= 2d ÷ d/r₁ + d/r₂
= 2d ÷ r₂d + r₁d / r₁r₂
= 2r₁r₂ / r₁ +r₂
∴ x = 2× 3030×4040/ 3030 +4040
= 2448240 ÷ 707
= 346.28 km/hr
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-2( y-4 ) + 8y + 2 < 16
Answer: y<1
Step-by-step explanation:
A piece of notebook paper measures 8 1/2 inches by 11 inches. Which of the following metric approximations is the same?
2 m x 2.8 m
3 cm x 4 cm
22 cm x 28 cm
30 m x 40 m
austin prepared 20 kilograms of dough after working 4 hours. how much dough did austin prepare if he worked for 5 hours? solve using unit rates.
Answer:
Answer: 9 hours. If austin prepared 20 kg of dough in 5 hours, this means he can prepare 4kg of dough an hour. This is because 20/5=4.
The points given in the table lie on a line. Find the slope of the line.
x –1 2 5 8
y 3 –1 –5 –9
Answer:
Slope = -4/3 or -1.33 in decimal form
Step-by-step explanation:
To find the slope divide the rise by the run. The rise would be the difference between the 2 y points (y2-y1) divided by the run (x2-1x)
Here the rise is (-9-3 = -12) and the run is (8-(-1) = 9) So -12/9 is -4/3 in fraction form and -1.33 in decimal form.
A slice of pizza has 1,200 calories. If 520 calories are from fat, what percentage of calories are fat?
Answer:
43.33%
Step-by-step explanation:
x : 100 = 520 : 1200
x = (520 * 100)/1200
x = 520/12
x = 43.333333%
f a national survey finds candidate A leads candidate B by 5 percent in the upcoming election and the margin of error in the survey is 3 percent, it means that:
candidate A leads candidate B by anywhere between 2 and 8 percentage points.
If the margin of error for the electoral poll is 3%, then candidate A has an advantage over candidate B of between 2 and 8 points.
Define the term margin of error?Your results will deviate by how many percentage points from the actual population value, according to your margin of error.
It is considered as a very small percentage that is allowed for error in calculations.
As the question stated-
A candidate would receive more or fewer points than the margin of error, which is the number of points.In this scenario, if one candidate has 5% more voting intentions than the other, it suggests that he is likely 5 points in front.The candidate is leading by three points, more or less, if the margin of error is three percent.This leads us to the conclusion as candidate A is 2 or 8 points ahead of voter intentions.This suggests that if the margin of error for the electoral survey is 3%, candidate A is leading of candidate B by 2 to 3 percentage points.
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The complete question is-
If a national survey finds candidate A leads candidate B by 5 percent in the upcoming election and the margin of error in the survey is 3 percent, it means that-
candidate A leads candidate B by exactly 5 percentage points. candidate A leads candidate B by anywhere between 2 and 8 percentage points. candidate A leads candidate B by exactly 3 percentage points.Which shows the following expression after the negative exponents have been eliminated? startfraction a cubed b superscript negative 2 baseline over a b superscript negative 4 baseline endfraction, a not-equals 0, b not-equals 0 startfraction a cubed b superscript negative 4 baseline over a b superscript negative 2 baseline endfraction startfraction a b superscript 4 baseline over a cubed b squared endfraction negative startfraction a cubed b superscript 4 baseline over a b squared endfraction startfraction a cubed b superscript 4 baseline a b squared endfraction.
Which shows the following expression after the negative exponents have been eliminated
[tex]a^{2} b^{2}[/tex]
Given the algebraic expression:
[tex]\frac{a^{3}b^{-2} }{ab^{-4} }, a\neq 0, b\neq 0[/tex]
We are required to eliminate the negative exponents and find the resulting expression.
Using the Negative Exponent Law of Indices: [tex]x^{-y} = \frac{1}{x^{y} }[/tex]
Using the Division Law of Indices: [tex]\frac{t^{x} }{t^{y} } = t^{x-y}[/tex]
Therefore:
[tex]\frac{a^{3}b^{-2} }{ab^{-4} } = a^{3-1}.b^{-2-(-4)}\\ \\ Simplifying\\ \\a^{3-1}.b^{-2-(-4)} = a^{2}b^{-2+4}\\ \\ =a^{2} b^{2}\\\\Therefore:\\\\\frac{a^{3}b^{-2} }{ab^{-4} } =a^{2} b^{2}\\[/tex]
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A table represents a relation that is also a function if it shows that every ____ value is assigned to _____ one ___ value
A table represents a relation that is also a function if it shows that every input value is assigned to exactly one output value
What is function?A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain. For all values of a and b, f = (a,b)|If every element in set A has exactly one and only one image in set B, then the relation is said to be a function.A function is a relation from a non-empty set B such that its domain is A and it never has the same first member in two different ordered pairs.To learn more about function, refer to
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Write an equation of a line
that passes through the
point (-5, 1) and is
perpendicular to y = -x - 3
A) y = x + 6
B) y = -x - 5
C) y = -x-4
D) y = x + 4
E) y = x - 6
From perpendicular line, we have m1
Knowing m1 * m2 = -1 for perpendicular lines gives us
-1 *m2 = -1
m2 = 1
Using y-b = m(x-a) with the point provided gives
y-1 = 1(x--5)
y = x+6
Therefore (A) is the correct answer
Please help. 10 points.
The new circle be made with double radius of the given circle.
Also, the circumference of the new circle is double of the given circle and the Area of the new circle is Four times of the given circle.
Given, a circle
If the radius of the given circle is 'r'
then, the radius of the new circle '2r'
Now, the Circumference of the new circle be,
C' = 2π(2r)
As, the Circumference of the given circle be,
C = 2πr
On dividing, we get
C'/C = 2
C' = 2C
So, the circumference of the new circle is double of the given circle.
Now, the Area of the new circle be,
A' = π(2r)²
As, the Area of the given circle be,
A = πr²
On dividing, we get
A'/A = 4
A' = 4A
So, the Area of the new circle is Four times of the given circle.
Hence, the new circle be made with double radius of the given circle.
Also, the circumference of the new circle is double of the given circle and the Area of the new circle is Four times of the given circle.
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The volume V of a sphere varies in direct proportion to the cube of its radius .
What change in volume reduces the radius by 10% ?
There will be no change in volume reducing the radius by 10%.
What is Direct Proportion?
The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. Since the other variable is reversed in this case, the inversely proportional relationship is really represented by the same symbol.
For instance, if x and y are two quantities or variables that are intimately linked to one another, we can say x y. The ratio of x and y becomes equal to a constant when the proportionality sign is removed, for example, x/y = C, where C is a constant. In contrast, x and y are represented as x 1/y or xy = C in the case of inverse proportion.
Let the radius be r then
The volume of every sphere is,
[tex]\mathrm{V}=4 \pi \frac{\mathrm{r}^3}{3}[/tex]
In the given question, It is given:
The volume V of a sphere varies in direct proportion to the cube of its radius.
That means:[tex]\mathrm{V}[/tex] ∝ [tex]r^{3}[/tex]
That means:[tex]4 \pi \frac{\mathrm{r}^3}{3} = kr^{3}[/tex]⇒[tex]4 \pi \frac{\mathrm{1}}{3} = k[/tex]
So, The equation is independent of radius.
Hence, There will be no change in volume reducing the radius by 10%.
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the mean monthly electric bill for 43 residents of the local apartment complex is $69. what is the best point estimate for the mean monthly electric bill for all residents of the local apartment complex?
The best point estimate for the mean monthly electric bill for all residents of the local apartment complex is $69.
It is given that the mean monthly electric bill for 43 residents of the local apartment complex is $69.
That means the sample mean X for 43 residents is $69.
And we know that the sample mean, X is the best point estimate of the population mean, μ.
Therefore the best point estimate for the mean monthly electric bill for all residents of the local apartment complex is $69.
The point estimate for the population mean is the sample mean. Point estimate is the one value that is used to estimate the population parameter. It is also known as the unbiased estimate of the population mean is the sample mean.
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Alizay sold 15 shirts priced equally for Rs.2800. She spent Rs. 14,000 of her earned amount on shopping and Rs. 7500 on buying grocery. How much is she left with?
The amount of money left with Alizay after shopping is Rs 17700 .
Alizay sold shirts for Rs. 2800.
She sold 14 shirts.
Cost earned from selling 14 shirts = 14 × 2800 = Rs. 39200
Spent on shopping =Rs. 14000
Spent on Grocery = Rs. 7500
Total amount spent = Rs.(14000+7500) = Rs. 21500
Amount of money left = Rs 39200 - Rs 21500 = Rs 17700
Therefore she is left with Rs 17700 .
In the case of a single variable, there is only one viable response. This particular case, in which the variable is accurately referred to as the "unknown," is one to which the term linear equation sometimes relates implicitly.
The Cartesian coordinates of a point on the Euclidean plane can be used to understand each solution in the scenario with two variables. A linear equation's solutions define a line in the Euclidean plane, and each line is the collection of all solutions to a linear equation with two variables.
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Derek Jeter, the short stop for the New York Yankees, a major league baseball team, played in 159 games in 2012 and hit 15 home runs. If he plays a total of 1272 games in his career, approximately how many home runs will he hit?
[A] Write a proportion that is defined by this situation.
[B] Explain how the cross product is used to solve the problem.
[C] Answer the question.
a. The the proportion that would be used is: 159/15 = 1272/x
b. See explanation for the cross product below.
c. Approximately 120 home runs will be hit.
What is a Proportion?A proportion can be defined as an equation that involves comparing two equal ratios that are equivalent to each other or set equal to each other.
a. To write a proportion that defines the situation described above, let x represent the number of runs he will hit in his career.
Therefore, we would have the following proportion:
159:15 = 1272:x
or
159/15 = 1272/x
b. Using the cross product, we can find the value of x as shown below:
159 × x = 1272 × 15
159x = 19,080
Divide both sides by 159
159x//159 = 19,080/159
x = 120
c. The number of runs he will hit in his career is: 120.
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what is the smallest possible perimeter, in units, of a triangle whose side-length measures are consecutive integer values?
If a triangle whose sides length measures are consecutive integers, then the smallest possible perimeter is 9 units
If a, b and c are the sides of the triangle
Then it will be
a + b > c
b + c > a
c + a > b
Given that the side length of the measures are consecutive integer
Smallest consecutive integer is 1, 2 and 3
But
1 +2 > 3
3 = 3
Therefore it will not be the sides of the triangle
Next smallest consecutive integers are 2, 3 and 4
Then,
2+3 > 4
5 > 4
3+4 > 2
7 > 2
2+4 > 3
6 > 3
This will be the sides of the triangle
The perimeter of the triangle is the sum of sides of the triangle
The perimeter = 2 + 3 + 4
= 9 units
Hence, if a triangle whose sides length measures are consecutive integers, then the smallest possible perimeter is 9 units
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Find the surface area of the prism.
Answer:
312 m^2
Step-by-step explanation:
Start by separating the shapes.
you will get:
2 triangles with the dimensions 6m x 8m
1 rectangle with the dimensions: 9m x 8m
1 rectangle with the dimensions: 6m x 9m
1 rectangle with the dimensions: 10m x 9m
1) find the area of every shape
2 triangles with the dimensions 6m x 8m -----> 48m^2 and 48 m^2
1 rectangle with the dimensions: 9m x 8m ----> 72m^2
1 rectangle with the dimensions: 6m x 9m ----> 54 m^2
1 rectangle with the dimensions: 10m x 9m ---> 90m^2
2) add everything up
48m^2 + 48 m^2 + 72m^2 + 54 m^2 + 90m^2 =
312m^2
I inserted a picture so it can be more clear. This is for Algebra 2, Unit 2
The inverse function of f(x) = 3x-4 when x = -1 will be 1.
According to the question,
We have the following function:
f(x) = 3x-4
Now, to find its inverse we will convert this function into a linear equation:
y = 3x-4
Now, we will change variable from x to y and y to x:
x = 3y-4
Now, we have to find the value of y, which will be the inverse of the given function:
Moving 4 from the right hand side to the left hand side will result in the change of signs:
x+4 = 3y
3y = x+4
Dividing by 3 on both the sides:
y = (x+4)/3
Now, we have:
[tex]f^{-1} (x)[/tex] = (x+4)/3
Putting the value of x = -1:
(-1+4)/3
3/3
1
Hence, the inverse function of f(x) = 3x-4 when x = -1 will be 1.
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In a farm composed of cows and chickens, there are total of 13 heads and 42 feet. How many cows are there?.
In a farm composed of cows and chickens, there are total of 13 heads and 42 feet.
Let 'h’ represent the number of hens the farmer has.
Let 'c’ represent the number of cows the farmer has.
Assume that all hens have two legs and all cows have four.
There are a total of 42 legs. So
2h + 4c = 42 (1)
There are 13 animals in total.
h + c = 13 (2)
Now that we have our system of equations, we can solve by either substitution or elimination.
Elimination
(2) x 2
2h + 2c = 26 (3)
(2)—(3)
2c = 6
c=3
From (2):
c + h = 13
3+h = 13
h= 10
Therefore, the farmer has 3 cows and 10 hens.
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Substitution
3x + 5y = 5
Y = -x -2
Find ( x , y )
As per the substitution method, the value of (x , y) is (-15/2, 11/2)
Substitution method:
Substitution method is the process of solve one equation for one of the variables. And substitute (plug-in) this expression into the other equation and solve. Then resubstitute the value into the original equation to find the corresponding variable.
Given,
Here we have the following expression.
3x + 5y = 5
Y = -x -2
Now, we need to find the value of x and y.
According to the substitution method, let us consider
3x + 5y = 5 -------------------(1)
Y = -x -2 ---------------------(2)
Now, we have to apply the value of y as -x - 2 in equation (1), then we get,
=> 3x + 5(-x - 2) = 5
When we expand it then we get,
=> 3x - 5x - 10 = 5
Simplify the expression,
=> -2x - 10 = 5
=> -2x = 5 + 10
=> -2x = 15
Then the value of x is,
=> x = -15/2
If the value of x is -15/2. then the value of y is calculated by using the equation (2),
=> y = -(-15/2) - 2
=> y = 15/2 - 2
=> y = (15 - 4)/2
=> y = 11/2
Therefore, the value of (x, y) is (-15/2, 11/2).
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What is the image of (-1,-1) after a dilation by a scale factor of 5 centered at the origin
Answer:
If the plot point was dilated by a scale factor, it would be multiplying the scale factor with each X and Y. Therefore it would be (-5,-5)
The image of (-1, -1) after the dilation by a scale factor of 5 centered at the origin is (-5, -5).
To find the image of (-1, -1) after a dilation by a scale factor of 5 centered at the origin, we can apply the formula for dilation in the coordinate plane.
The formula for dilation with a scale factor of k centered at the origin is (k * x, k * y), where (x, y) is the original point.
In this case, the original point is (-1, -1), and the scale factor is 5. Applying the dilation formula, we have:
Image = (5 * (-1), 5 * (-1))
= (-5, -5)
This means that the point (-1, -1) is dilated by a factor of 5, and its position is shifted five times farther from the origin in both the x and y directions.
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calculate the amount of goodwill that would be recorded by brave for this acquisition. (be careful to count your zeros in your answer since this is a big number!)
Purchase consideration less fair value of net assets is goodwill (Purchase Consideration-Fair Value of Net Assets) $690,000,000
What does "goodwill" mean?
Goodwill cannot be purchased or sold on its own; rather, it is a premium over fair value that is paid during a transaction. Other intangible assets include things like licenses or patents that are independent purchases or sales. While most intangibles have a set useful life, goodwill has an unlimited lifespan.
Estimating goodwill
The extra payment made as purchase consideration over the acquiree's net assets' fair market value is referred to as goodwill.
The calculation looks like this:
(Millions of Dollars)
Cost of the purchase: $ 900,000,000
Fair value of net assets is less.
True Cost of the Assets
$15,000,000 in supplies
$200,000,000 in intangible assets
$20,000,000 for property, plant, and equipment
Total $235,000,000
True Cost of Liabilities
$5,000,000 in current liabilities
$20,000,000 in Notes Payable
Total $25,000,000
Goodwill (Purchase Consideration-Fair Value of Net Assets) (Purchase Consideration-Fair Value of Net Assets) $690,000,000
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Which system of linear equations has no solution?
Which system of linear equations has no solution?
A. 2x+3y=6
−2x−3y=−6
B. 2x+3y=6
4x+6= 8
C. 2x+3y=6
3x−2y=−6
Which system of linear equations has no solution?
D. 2x+3y=6
10x+15y=30
Answer:
Below
Step-by-step explanation:
A Both are the same line
**** B If that is 4x + 6 y = 8 the lines are parallel ===> no solution***
C Intersecting lines
D same line
Carrie works as a library assistant in Orpington Library. She earns $9. 75 per hour. How much will
she get paid, if she puts in 40 hours of work in a week?(Tutors please explain how You do your division,multiplication,etc)
Carrie will be paid $390 if she puts in 40 hours of work in a week.
The total amount of time of work = 40 hours.
As we are stated that the earnings for 1 hour is $9.75, so, we will perform multiplication to find the earnings for the time she worked. We are performing multiplication because the amount will increase as the number of hours increases.
Performing calculation now.
Amount earned in a week = 9.75 × 40
Performing multiplication on Right Hand Side of the equation to find the amount earned in a week
Amount earned in a week = $390
Thus, the amount paid to Carrie in a week is $390.
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AB has endpoints A (2, 3) and B(5,-2). Determine the endpoints of the image of AB after a reflection in the line y = z.
The endpoints of the image of AB after a reflection in the line y = z are A'(2, -3) and B'(5, 2).
What is endpoints of the graph?
On a graph, an endpoint is the place where a figure comes to an end. A genuine line has no terminal because it goes on indefinitely in both directions. A ray is a figure that resembles a line and only extends in one direction infinitum. It is one type of line. The endpoint of a ray is on the side that is not extending.
(x, y) → (x, -y), x-coordinate stays as is and y-coordinate changes its sign to opposite.
We have given points:
A(2, 3) and B(5,-2).
The image of AB will have coordinates:
A'(2, -3) and B'(5, 2)
The endpoints of the image of AB after a reflection in the line y = z are A'(2, -3) and B'(5, 2).
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registrants at a large convention are offered 6 sightseeing tours on each of 3 days. in how many ways can a person arrange to go on a sightseeing tour planned by this convention?
The registrants would be able to see the 6 sightseeing tours in 18 ways.
Here it is given that the convention has organized the 6 sightseeing tours on 3 days each.
This implies that the 6 sightseeing tours are available on all three days.
Hence, the registrants would be able to book the tour on any of the one days.
Hence, on day 1
the registrants will be able to tour in ways
On day 2
the registrants would again be able to tour in 6 ways,
Similarly on day 3, they will again be able to tour in 6 ways.
Since they need to choose either of the days given, the total number of ways to tour will be
no.of ways for day 1 + no. of ways for day 2 + no. of d6ays for day 3
= 6 + 6 + 6
= 18 ways
Hence, they can go on a sightseeing tour in 18 ways.
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The median house price in Dallas, Texas is $405,000. Property tax is 3%. How much does a homeowner pay in property tax?
Answer:
Step-by-step explanation:
I believe the tax would be $ 12,150
Enter the ratio of students who chose
alternative to the total number of students.
Answer:
1 : 4
Step-by-step explanation:
the ratio of
alternative : total
= 15 : 60 ( divide each part by 15 )
= 1 : 4
What score is a 12 out of 30?.
If qr = 20 in., rs = 7 in., and sq = 24 in., what is pn? 3 in. 7 in. 20 in. 24 in.
The value of PN is 20 in.
What are congruent triangles?
Congruent triangles are triangles in which all the sides and all the angles are congruent.
These triangles can appear identical when moved, rotated, flipped, and turned. They coincide if moved in a different direction.
In the diagram, two congruent triangles are given ΔPMN ≅ ΔQSR.
So by CPCTC (corresponding parts of congruent triangles are congruent)
In ΔPMN and ΔQSR
PN=QR=20 in.
PM=SQ=24 in.
MN=RS= 7 in.
If two triangles are said to be congruent then all corresponding parts must be equal.
So, the value of PN is 20 in.
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Answer:
C. 20 in
Step-by-step explanation:
