Answer:
r = ±4.
Step-by-step explanation:
The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants. To write the equation 2r^2 - 32 in this form, you can subtract 32 from both sides to get 2r^2 - 32 = -32, and then divide both sides by 2 to get r^2 - 16 = -16. Finally, you can add 16 to both sides to get r^2 = 0, which is the standard form of a quadratic equation.
So, the equation 2r^2 - 32 = 0 can be written as the quadratic equation r^2 = 16, which has two real roots, r = ±4.
703 divided by 58
With remainder
HATS Bill ha h hat. If he buy 8 more hat, then multiplie hi total by 3 he would till have fewer hat than Jim. Jim ha 45 hat. Write and olve an inequality that repreent thi ituation. How many hat doe Bill have?
Inequality: _
_(
__) _
_ 45
Solution: h
_
_ __
Bill has 6 hats in total.
According to the question
In order to solve the issue, an inequity that depicts Bill and Jim's condition and their hat collections must be eliminated. Jim has 45 hats, Bill has a certain amount. According to the issue, even if Bill purchases 8 additional hats and increases his total by 3, he would still possess fewer hats than Jim.
Let's use the variable "x" to represent Bill's total number of hats.
We are aware that when Bill purchases 8 additional hats, his total will be x + 8.
The result of multiplying this new sum by three is 3(x + 8).
This number is less than 45, thus we can create an inequality since we know that:
3(x + 8) < 45
Extending the sentence on the left:
3x + 24 < 45
24 is subtracted from both sides:
3x < 21
by 3 and dividing both sides:
x < 7
The least positive integer solution to this inequality is 7, as x, the number of hats Bill owns, must be a positive integer. Bill thus needs six hats.
The difference between Jim and Bill is that Jim has 45 hats, but Bill owns less than 7, even after purchasing 8 additional hats and multiplying the total by 3.
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Bill has 6 hats in total.
According to the question
In order to solve the issue, an inequity that depicts Bill and Jim's condition and their hat collections must be eliminated. Jim has 45 hats, Bill has a certain amount. According to the issue, even if Bill purchases 8 additional hats and increases his total by 3, he would still possess fewer hats than Jim.
Let's use the variable "x" to represent Bill's total number of hats.
We are aware that when Bill purchases 8 additional hats, his total will be x + 8.
The result of multiplying this new sum by three is 3(x + 8).
This number is less than 45, thus we can create an inequality since we know that:
3(x + 8) < 45
Extending the sentence on the left:
3x + 24 < 45
24 is subtracted from both sides:
3x < 21
by 3 and dividing both sides:
x < 7
The least positive integer solution to this inequality is 7, as x, the number of hats Bill owns, must be a positive integer. Bill thus needs six hats.
The difference between Jim and Bill is that Jim has 45 hats, but Bill owns less than 7, even after purchasing 8 additional hats and multiplying the total by 3.
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the function g is given by g(x)=1x2−4x 5. the function h is given by h(x)=2x2−8x 10x2−4x 6. if f is a function that satisfies g(x)≤f(x)≤h(x) for 0
By the sandwich's theorem,
the limit of the function f(x) at x→2 is 1.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
Given:
The functions;
g(x) = 1/{x²-4x + 5},
and h(x) = {2x²-8x +10}/{x²-4x+6}
If f is a function that satisfies g(x) ≤ f(x) ≤ h(x) for 0 < x < 5.
To find the limit at x→2.
[tex]\lim_{x \to \2} g(x) =[/tex] 1/{2²-4(2) + 5} = 1
[tex]\lim_{x \to \2} h(x) =[/tex] {2(2)²-8(2) +10}/{(2)²-4(2)+6} = 1
By the sandwich's theorem,
the limit of the function f(x) at x→2 is 1.
Therefore, 1 is the limit.
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Aiden spends $18 on a souvenirs during a school trip to New York City. This is 45% of the money he brings on the trip. How much money does Aiden bring on the trip? Show your work
Aiden brings money about $40 on the trip.
Aiden's Trip Money CalculationLet's call the amount of money Aiden brings on the trip "x".
According to the problem, $18 is 45% of x, so we can set up an equation:0.45x = 18
To find the total amount of money Aiden brings, we can solve for x by dividing both sides of the equation by 0.45:
x = 18 / 0.45
x = 40
So Aiden brings $40 on the trip.The subject of mathematics that the problem is related to is algebra. Algebra is the branch of mathematics that deals with symbols and the rules for manipulating those symbols to solve equations and study relationships between variables. In this problem, we use algebraic equations and operations to find the value of the unknown variable x, which represents the amount of money Aiden brings on the trip.
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solve for x:3^x+1 = 9^x.1/27
Answer:
9^(x)=(1)/(27)
Step-by-step explanation:
On a team, 9 girls and 5 boys scored a total of 51 points. The difference between the number of points scored by the 9 girls and the number of points scored by the 5 boys is 21 . Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and each boy.
The number of points scored by each girl is 4 and each boy is 1 point.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
9 girls and 5 boys scored a total of 51 points.
The difference between the number of points scored by the 9 girls and the number of points scored by the 5 boys is 21 .
Each girl scored the same number of points and each boy scored the same number of points.
Let x be the number of points the 9 girls scored.
=> 51 - x is the number of points the 5 boys scored.
We have x + 21 = 51 - x
or x - 21 = 51 - x.
=> 2x = 30 or 2x = 72
=> x = 15 or x = 36
We reject x = 15
as 15 is not a multiple of 9
So x = 36,
each girl scored 36/9 = 4 points.
and,
=> 41 - (36) = 5,
each boy scored 5/5 = 1 points.
Hence, the number of points scored by each girl is 4
and each boy is 1 point.
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What are the solution(s) to the system?
y=x²-2x +4
y = 3x + 10
The solution to this system is (x,y)=(10/3, 20/3 + 4).
What is equation?An equation is a mathematical statement that describes the relationship between two or more variables. It is a statement that states the equality of two expressions. Equations can be used to describe anything from the motion of a pendulum to the growth of a population. They are used in all areas of mathematics, physics, and other sciences. Equations are written using symbols, such as = (equal to), > (greater than), and < (less than).
The solution to this system of equations is the set of values that make both equations true at the same time. To solve this system, we can use the substitution method. First, we solve for one of the variables in one equation, then substitute that value into the other equation.
For this system, we will solve for x in the second equation. We can do this by subtracting 3x from both sides, which gives us 10 = 3x. We then divide both sides by 3, which gives us x = 10/3.
Next, we substitute 10/3 into the first equation and solve for y. We can do this by replacing x with 10/3, which gives us y = (10/3)² -2(10/3) + 4. Simplifying this equation gives us y = 20/3 + 4.
Therefore, the solution to this system is (x,y)=(10/3, 20/3 + 4).
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At what point/s do the following function and their inverses intersect? A.f(x) =3x-8 B.g(x) = √x+2 C.h (x=x³
f(x) =3x-8 and g(x) = √x+2 are the function and their inverses intersect.
A function is a mathematical representation that maps one set of values to another set of values. The inverse of a function is a reflection of the original function over the line y=x, where the input and output are reversed.
For the function f(x) = 3x - 8, the inverse can be found by switching the input and output values, then solving for x.
In this case, we have
=> y = 3x - 8 and x = (y + 8)/3.
The two functions will intersect when the input value is equal to the output value, or when
=> 3x - 8 = (y + 8)/3.
Solving for x, we find that x = 4. This is the only intersection point between the two functions.
For the function g(x) = √x + 2, the inverse can be found by switching the input and output values, then solving for x.
In this case, we have
=> y = √x + 2 and x = y² - 2.
The two functions will intersect when the input value is equal to the output value, or when
=> √x + 2 = y² - 2.
Solving for x, we find that x = 4. This is the only intersection point between the two functions.
Therefore option (a) and (b) is correct.
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1. Researchers who were interested in the types of movies pre-
ferred by children of different age groups asked students in the
sixth grade and in the eighth grade if they would prefer to see
an animated feature like The Lion King or an action feature like
The Avengers. The results are summarized in the table:
Sixth Grade
Eighth Grade
Animated Action
45 35
40 60
Which proportions represent the conditional distribution of
grade for children who preferred an action feature?
A) 0. 194 and 0. 333
B) 0. 368 and 0. 632
C) 0. 40 and 0. 60
D) 0. 444 and 0. 556
E) 0. 529 and 0. 471
Sixth grade students prefer action movie is 0.194 & Eight grade students prefer action movie is 0.333
Given that the information below:
Sixth grade students prefer animated movie - 45
Eight grade students prefer animated movie - 40
Sixth grade students prefer action movie - 35
Eight grade students prefer action movie - 60
Total sixth grade students - 80
Total eight grade students - 100
Total students prefer animated movie - 85
Total students prefer action movie - 95
Proportion of sixth grade students prefer action movie =
Sixth grade prefer action movie/Total students
= 35/180 = 0.194
Proportion of eight grade students prefer action movie =
Eight grade prefer action movie/Total students
= 60/180 = 0.333
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7(2y)= Complete the tatement uing the pecified property. Aociative Property of Multiplication
The statement using the specified property i.e Associative Property of Multiplication will be 14y.
One's identity property is its capacity for multiplication.
7(2y)
The phrase is given as follows:
7(2y)
=14y
The one has the multiplication property, which says:
Any number or expression that is multiplied by one doesn't alter in any way.
The result is: 1xa=a
The identification property is another name for this particular attribute.
The general rule is shown as follows:
Examples include
1 * 2 = 2
1 * x = x
1 * ab = ab
and so forth
So, the property of multiplying by one is an identity property.
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Willow purchased a new
car. Her loan, including
interest, is $12,720. How
much are her monthly
payments if she has 60
monthly payments to
make?
Answer:
$212
Step-by-step explanation:
Giorgi paid 1 GEL and 25 tetris for 5 erasers and 2 rulers, Tornike paid 1 GEL and 5 tetris for 2 erasers and 3 rulers.
Let's say the price of an eraser is x white, the price of a ruler is y white. To find these prices
The requried price of an eraser and ruler is given as 0.15 Tetris and 0.25 Tetris respectively.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
1 GEL and 25 tetris = 1.25
1 GEL and 5 tetris = 1.05
We can set up two equations to find the unknown values of x and y:
1.25 = 5x + 2y - - - - - -(1)
1.05 = 2x + 3y - - - - - (2)
To solve the system of equations, we can substitute the value of y in the first equation using the second equation:
y = (1.25 - 5x) / 2
Substituting this value of y in the second equation:
1.05 = 2x + 3((1.25 - 5x) / 2)
x = 0.15
Now,
Put x = 0.15 equation 1,
e get
y = 0.25
Thus, the requried price of an eraser and ruler is given as 0.15 Tetris and 0.25 Tetris respectively.
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At a school event, adults are seated in groups of exactly 15 and children are seated in groups of exactly 8. If there are the same number of adults as children, what is the minimum number of adults attending?
Answer:120
Step-by-step explanation:
LCM of 8 and 15
Find the lengths of the diagonals of rectangle $WXYZ$ . $WY=14x+10$ $XZ=11x+22$
The lengths of the diagonals of rectangle is 66 units
How to determine the valuesThe properties of a rectangle is given as;
A rectangle is a known as a quadrilateralThe opposite sides are parallel and equal to each other Interior angle is equal to 90 degreesSum of all the interior angles is equal to 360 degreesThe diagonals bisect each other at right angleDiagonals have the same lengthFrom the information given, we have that;
$WY=14x+10
$XZ=11x+22
Since the diagonals are of the same length, we have;
WY = XZ
14x + 10 = 11x + 22
collect like terms
14x - 11x = 22 - 10
subtract the like terms
3x = 12
Make 'x' the subject of the formula
x = 4
WY = 54 + 10 = 66
XZ = 66
Hence, the values are 66
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What is the Formula for Percent Error and How is it Calculated?
A percent error calculation is used to determine how close a measured value is to a true value.
How percent error is calculated?Percent error (percentage error) is defined as the difference between an experimental and theoretical value divided by the theoretical value and multiplied by 100.The formula of percent error is :Percentage Error = ((Estimated Number – Actual Number)/ Actual
number) x 100.
The percentage error tells us how much a small number of unavoidable errors affect our experimental results. It is calculated by subtracting the actual value from the observed value. Small percentage errors indicate that you are near the accepted or true value.Consider the example, assume you guessed there were 230 gumballs in the image, but there were actually 311 gumballs. The percentage error is the difference between your guess (230) and the actual number (311) expressed as a percentage of the actual number (311).To learn more about percent error refer to :
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the type of reasoning used to prove a conjecture is called
Answer:
deductive reasoning
Step-by-step explanation:
Carlos's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=61+7.6xy=61+7.6x, where yy represents the expected quiz score and xx represents hours spent on homework that week. What is the meaning of the xx-value when y=92y=92?
When y = 92, the value of x is approximately 4.07 hours. This means that if a student spends approximately 4.07 hours on their homework each week, we would expect their quiz score to be 92.
What is the linear equation?
Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.
If y = 92, we can solve for x by substituting 92 for y in the equation y = 61 + 7.6x:
92 = 61 + 7.6x
7.6x = 92 - 61
7.6x = 31
x = 31 / 7.6
x = 4.07
Therefore, when y = 92, the value of x is approximately 4.07 hours. This means that if a student spends approximately 4.07 hours on their homework each week, we would expect their quiz score to be 92.
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pls help this is urgent hurry
The value of m∠ABC in the triangle ABC is 55°
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
From the diagram:
m∠ABC + m∠ABD = 180° (sum of angles on a straight line)
Substituting gives:
(6x + 5) + m∠ABC = 180
m∠ABC = 175 - 6x
m∠ABC + m∠BAC + m∠ACB = 180 (angle in a triangle)
Substituting:
(3x) + (x + 45) + (175 - 6x) = 180
2x = 40
x = 20
m∠ABC = 175 - 6x = 175 - 6(20) = 55°
m∠ABC is equal to 55°
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What are the Types of Corresponding Angles Based on their Sum?
Their total determines which angles are equivalent. Alternative Corresponding Angles Parallel Corresponding angles
What is meant by Corresponding Angles?Whenever a transversal line crosses two parallel lines, corresponding angles are created. Examples of comparable angles that can be found in daily life include the opening and closing of a lunchbox, completing a Rubik's cube, and endless parallel railroad tracks.Corresponding objects are ones that show up at the same location in two related circumstances. In the example below, angles are a common cause. Given that they are in the same spot in the two related shapes, angle A on the left and angle K on the right are equivalent. As we say, A is equivalent to K.Angles that match up are congruent. Corresponding pairs are all angles that are situated in the same location with respect to the parallel and transversal lines.To learn more about Corresponding Angles, refer to:
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Need help ASAP. Congruent Triangles Gina Wilson all things algebra
The answers for all triangle problems are:
x = 2°∠S = 36°x = 26°; ∠P = 116°; ∠Q = 21°; ∠R = 43°∠J = 44°; ∠K = 81°; ∠L = 51°x = 11°; ∠B = 108°; ∠C = ∠D = 36°10. ΔABC is a equilateral triangle, then:
∠A = ∠B = ∠C = 8x - 44
3 (8x - 44) = 180
24x - 132 = 180
24x = 48
x = 2
11. ΔRST is an isosceles triangle, then:
∠R = ∠T
15x - 31 = 9x + 11
6x = 42
x = 7
∠S + ∠R + ∠T = 180°
∠S + 2∠T = 180°
∠S + 2( 9x + 11) = 180°
∠S + 2(9(7) + 11) = 180°
∠S + 2 (63 + 11) = 180°
∠S + 2 (74) = 180°
∠S = 180 - 144
∠S = 36°
12. Based on the given data:
∠P = 5x - 14
∠Q = x - 5
∠R = 2x - 9
Since ΔPQR is a triangle, then:
∠P + ∠Q + ∠R = 180°
(5x - 14) + (x - 5) + (2x - 9) = 180°
8x - 28 = 180°
8x = 208
x = 26
∠P = 5x - 14 --> 5(26) - 14 = 116°
∠Q = x - 5 --> (26) - 5 = 21°
∠R = 2x - 9 --> 2(26) - 9 = 43°
13. ΔJKL is a triangle, where:
∠J = ∠L - 7
∠K = 2∠L - 21
∠J + ∠K + ∠L = 180
(∠L - 7) + (2∠L - 21) + ∠L = 180°
4∠L - 28 = 180°
4∠L = 208
∠L = 51°
∠J = ∠L - 7 --> (51) - 7 = 44°
∠K = 2∠L - 21 --> 2(51) - 21 = 81°
14. In a triangle ΔBCD:
BD = BD
∠B = 13x - 35
∠C = 5x - 19
∠D = 2x + 14
Since BC = BD; then:
∠C = ∠D
5x - 19 = 2x + 14
3x = 33
x = 11
∠C = ∠D = 2x + 14 --> 2(11) + 14 = 36°
∠B + ∠C + ∠D = 180°
∠B + 36° + 36° = 180°
∠B = 108°
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A box contains 5 plain pencils and 5 pens. A second box contains 3 color pencils and 1 crayon. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected?
The probability that a plain pencil from the first box and a color pencil from the second box are selected is 3/8.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
A box contains 5 plain pencils and 5 pens.
A second box contains 3 color pencils and 1 crayon.
One item from each box is chosen at random.
The probability that a plain pencil from the first box and a color pencil from the second box are selected,
= 5/10 x 3/4
= 3/8
Therefore, the probability is 3/8.
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what is the probability that a subject, with a true cholesterol level of 196, takes the test twice (assume independent) and both tests classify the subject incorrectly?
The probability that a subject, with a true cholesterol level of 196, takes the test twice and both tests classify the subject incorrectly depends on several factors.
The factors that matter, such as the accuracy of the test, the threshold for normal cholesterol levels, the population being tested, and the distribution of cholesterol levels in that population. Without more information, it is not difficult to determine the exact probability.
However, it is generally unlikely for a test to classify a subject's cholesterol level incorrectly twice in a row, especially if the test has a high level of accuracy. Cholesterol levels in a population tend to follow a normal distribution, making it unlikely for a single subject to have significantly different readings on two separate tests.
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Please help me find the x and y
the values of x and y will be 60 and 25 respectively.
What are parallel lines?Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.
Given, ∠2y + 25 and ∠3y are alternate interior angles
Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.
Thus,
2y + 25 = 3y
y = 25
And since, When two lines intersect each other, then the opposite angles, formed due to the intersection, are called vertical angles or vertically opposite angles. Also, a pair of vertical angles are always congruent.
thus,
∠x + 15 = ∠3y
x + 15 = 3y
x + 15 = 75
x = 60
therefore, the values of x and y will be 60 and 25 respectively.
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please help I was thinking it was 7 but I'm not sure
Answer:
2 people should go
Step-by-step explanation:
if more than 2 people go it would be over $500 for food, hope this helps and stay positive :)
Use polar coordinates to find the volume of the given solid. Below the paraboloid z = 8 - 2x 2 - 2y 2 and above the xy-plane.
The volume of the solid is approximately 54.8 cubic cm.
What do you mean by integration?Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.
There are two main types of integration: definite and indefinite integration. Definite integration involves finding the exact area between a curve and the x-axis over a specified interval. Indefinite integration involves finding the general antiderivative of a function, which is a function that, when differentiated, will yield the original function.
The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.
The paraboloid z = 8 - 2x² - 2y² can be written in polar coordinates as z = 8 - 2r². The volume of the solid can be found by using the double integral of the height of the paraboloid over the region defined by the polar coordinates.
In polar coordinates, the region is defined by 0 <= r <= √4 and 0 <= θ <= [tex]\frac{\pi }{2}[/tex]The volume of the solid is given by:
V=[tex]\int\limits \int\limits {(8-2r^{2} )} r\, dr dy[/tex]
= [tex]\int\limits^0_\frac{\pi }{2} {} \, dx\int\limits^0_\sqrt{4} \,}(8-2r^{2})r }dr[/tex]
= [tex]\int\limits^0_\frac{\pi }{2} dx[ {4r^{2} -\frac{2}{3}r^{3} }] \,[/tex] from 0 to sqrt(4)
= [tex]\frac{\pi }{2} [4(4)-(\frac{2}{3}4^{\frac{3}{2} } ][/tex]
= [tex]\frac{\pi }{2}[16-\frac{2}{3}(16^{\frac{1}{2} } )][/tex]
= [tex]\frac{\pi }{2}[16-8({\frac{2^{} \frac{1}{2} }{3} }) ][/tex] cubic cm
So the volume of the solid is approximately 54.8 cubic cm.
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True or False : the null space of a is the solution set of the equation ax = 0.
The statement is True: the null space of a is the solution set of the equation ax = 0.
What is null space?The collection of all solutions to the homogeneous equation makes up a matrix's null space. Any matrix's null space contains the zero vector at all times. The null space is denoted as Null A.
We know that The null space of an m × n matrix A, written as Nul A, is the set of all solutions to the homogeneous equation Ax = 0.
Hence, the statement is True: the null space of a is the solution set of the equation ax = 0.
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4.5a−1.5(a+5) what expression is equivelant to it
3a+5
3a-7.5
6a+5
6a-7.5
Answer:
3a - 7.5
Step-by-step explanation:
4.5a−1.5(a+5)
4.5a - 1.5a - 7.5
3a - 7.5
So, the answer is 3a-7.5
Yolanda uses the data in the table to predict that if all 4,220 students at her school vote for a new school mascot, about 886 students will vote for Barracudas. Do you agree? Explain.
Yolanda's prediction that the number of students who would vote for Barracudas, is agreeable.
Why is the prediction plausible ?The sample of students who took the survey on the new school mascot was 691 students and out of these, 144 said they would like a Barracudas. In percentage terms, this is:
= 144 / 691 x 100 %
= 21 %
If all the students voted, then the number of students out of the 4, 220 students at the school that would vote for Barracudas is:
= Percentage to vote Barracuda x Number of students
= 21 % x 4, 220
= 886 students
So Yolanda's prediction is viable.
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
750=y²-5y is the equation that can be used to solve for y, the length of the room.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that the area of a rectangular room is 750 square feet.
The width of the room is 5 feet less than the length of the room.
Let y be the length of the room
Width=y-5.
Area=Length×Width
750=y(y-5)
750=y²-5y
Hence, 750=y²-5y is the equation that can be used to solve for y, the length of the room.
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How can you find the slope of the line that passes through the points (0,0) and (2,4)? Explain
Answer:
2
Step-by-step explanation:
Let ( x1, y1) represent the first point (0,0) and (x2, y2) represent the second point (2,4). Slope (m) (y2 - y1) / ( x2 - x1)= (4 - 0) / (2-0) =2