Answer:
3a - 2b = -3
Step-by-step explanation:
= (3) (3) - (6) (2)
= 9 - 12
= -3
Answer:
Step-by-step explanation:
3(3)- (6)2
9-12
-3
Ethan buys a video game on sale. if the video game usually costs $39.99, and it was on sale for 20% off, how much did ethan pay? round to the nearest cent.
Answer:
If the video game that Ethan bought usually costs $39.99, and it was on sale for 20% off, then the discount on the game would be $39.99 x 20/100 = $8.00. To determine the final price of the game after the discount, we can subtract the discount from the original price of the game, which gives us:
Final price = $39.99 - $8.00 = $31.99
Therefore, Ethan paid $31.99 for the video game that was on sale. This can be rounded to the nearest cent to give us a final answer of:
Final price = $31.99 ≈ $32.00.
Therefore, Ethan paid $32.00 for the video game that was on sale.
Step-by-step explanation:
Which graph increases most rapidly from its vertex?
Answer:
f(x) = 5x^(2)-3
Step-by-step explanation:
graph each equation
translate (x , y) ( x - 5, y - 3); reflect over the line x = 0 ( the x- axis); rotate 180 defgrees clockwise about the orgin
The vertices of the image of triangle ABC after the transformations are given as follows:
A'(4,-2), B'(4,2), C'(0,-1).
How to obtain the vertices of the image of triangle ABC?The vertices of triangle ABC are given as follows:
A(1,1), B(1,5), C(5,2).
The first transformation is the translation defined as follows:
(x,y) -> (x - 5, y - 3).
Hence the translated vertices are given as follows:
A'(-4, -2), B'(-4, 2), C'(0, -1).
The second transformation is the reflection over the x-axis, hence the rule is:
(x,y) -> (x, -y).
Then the vertices of the translated and reflected triangle are given as follows:
A'(-4, 2), B'(-4,-2), C'(0,1).
The final transformation is the rotation of 180º clockwise around the origin, for which the rule is of:
(x,y) -> (-x,-y).
Then the vertices of the image, after all the transformations, are given as follows:
A'(4,-2), B'(4,2), C'(0,-1).
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Can someone please help???
The measurement of <B is 121 degree.
What is Angle Sum Property?The sum of a triangle's three internal angles is 180 degrees, as stated by the angle sum Property of a triangle.
According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees.
Given:
let the measure of <A be x.
So, m<G= x- 9
and, m<B = 4x- 15
Using Angle Sum Property
m<A+ m<B+ m<G= 180
x+ 4x- 15 + x- 9 = 180
6x - 24 = 180
6x = 180+ 24
x= 204/6
x= 34
So, m<A = 34
m<B= 4(34) - 15 = 121
and, m<G = 34 - 9= 25 degree.
Hence, the measure of <B is 121 degree.
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How do you solve a function easy?
Function can be solved easily by f(x)= mx + c.
function
A function produces one output per input. Learn about function notation, tables of values, and more.
Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
A function is uniquely represented by the set of all pairs (x, f (x)), called the graph of the function, a popular means of illustrating the function. When the domain and the codomain are sets of real numbers, each such pair may be thought of as the Cartesian coordinates of a point in the plane.
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What is the solution to the system of equations y 3x 2 5x 2y 15?
The solution of the system of equations y = -3x - 2 and 5x + 2y = 15 is (-19, 55)
The first equation is
y = -3x - 2
The second equation is
5x + 2y = 15
To solve this problem we have to use the substitution method
Substitute the value of y = -3x - 2 in the second equation 5x + 2y = 15
5x + 2(-3x -2) = 15
5x - 6x - 4 = 15
-x - 4 = 15
-x = 15 + 4
-x = 19
x = -19
Substitute the value of x in the first equation
y = -3x - 2
y = -3(-19) - 2
= 57 - 2
= 55
Therefore, the solution of the system of equation is (-19, 55)
I have solved the question in general, as the given question is incomplete
The complete question is
What is the solution to the system of equations
y = -3x - 2 and 5x + 2y = 15
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Solve using elimination. –x − 7y = –20 –6x − 7y = –15
Answer:
x = −1 and y = 3
Multiply the second equation by -1, then add the equations together.
(−x−7y=−20)
−1(−6x−7y=−15)
Becomes:
−x−7y=−20
6x+7y=15
Add these equations to eliminate y:
5x=−5
Then solve5x=−5for x:
5x=−5
5x/5 = -5/5
x = -1
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
−x−7y=−20
Substitute−1 for x in −x −7y = −20:
−(−1)−7y=−20
−7y+1=−20(Simplify both sides of the equation)
−7y+1+−1=−20+−1(Add -1 to both sides)
7y = -21
-7y/-7 = -21/-7
y=3
Yaritza runs a farm stand that sells peaches and grapes. Each pound of peaches sell for $2.50 and each pound of grapes sells for $3.75. Yaritza made $225 from selling a total of 75 pounds of peaches and grapes. Graphically solve a system of equations in order to determine the number of pounds of peaches sold, x, and the number of pounds of grapes sold, y.
The amounts of each substance are given as follows:
Peaches: 45 pounds. Grapes: 30 pounds.How to solve the system of equations graphically?The graphic solution of a system of equations is given by the point of intersection of the equations that compose the system.
The variables that define the system in this problem are given as follows:
Variable x: number of pounds of peaches sold.Variable y: number of pounds of grapes sold.Yaritza sold a total of 75 pounds of peaches and grapes, hence:
x + y = 75.
Each pound of peaches sell for $2.50 and each pound of grapes sells for $3.75, and she made $225, hence:
2.5x + 3.75y = 225.
As given by the image at the end of the answer, the intersection of these two equations in the graph is given as follows:
(45, 30).
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A vegetable distributor knows that during the month of august, the weights of its tomatoes are normally distributed with a mean Of 0.62 lb and a standard deviation of 0.15.
A ) What percent of the tomatoes weight less than 0.77 lb?
B ) In a shipment of 8000 tomatoes can be expected to weight more then 0.32 lb?
C ) in a shipment of 3500 tomatoes how many tomatoes can be expected to weight from 0.32 lb to 0.92 lb
In a shipment of 3500 tomatoes can be expected to weight from 0.32 lb to 0.92 lb is 3340. When A vegetable distributor knows that during the month of august, the weights of its tomatoes are normally distributed with a mean Of 0.62 lb and a standard deviation of 0.15.
Define mean and standard deviation.A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean. The standard deviation measures the degree of dispersion of a set of data. Each data point is compared to the average of all the data points, and standard deviation gives a determined value that indicates whether the data points are clustered together or dispersed. The standard deviation of a normal distribution indicates how far values deviate from the mean.
Given,
A vegetable distributor knows that during the month of august, the weights of its tomatoes are normally distributed with a mean Of 0.62 lb and a standard deviation of 0.15.
Normal variable of x = 0.32
Z = X - mean/ standard deviation
Z = 0.32 - 0.62/0.15
Z = -2
Now, normal variable of x = 0.92
Z1 = X - mean/ Standard deviation
Z1 = 0.92 - 0.62/ 0.15
Z1 = 2
Required area,
P(-2 ≤ z ≤ 2)
2P(0 ≤ z ≤2 )
2 × 0.4772
0.9542
Weight of 3500 tomatoes
3500 × 0.9542
3340
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How do you choose an infinitive in a sentence?
We choose an infinitive in a sentence; It is "to + 1st form of verb" in the case of the infinitive, "1st form of the verb + -ing", and "1st form of the verb + both the first and third form of the verb" in the case of gerunds.
In the given question we have to explain how we choose an infinitive in a sentence.
The verb form called as an infinitive can be used as a noun, adjective, or adverb. They can be helpful when talking about activities without actually performing the activity because they are typically created by adding the word to before the underlying verb.
It is "to + first form of the verb" in the case of the infinitive, "1st form of the verb + -ing" that serves as a noun, and "1st form of the verb + both the 1st and 3rd form of the verb" in the case of gerunds that the first form with –ing. "To do" is the infinitive in this sentence.
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45% of the children in a school have a dog, 30% have a cat, and 18% have a dog and a cat. a) what percent of those who have a dog also have a cat? b) what percent of those who have a cat also have a dog?
(a) the percent of those who have a dog also have a cat is 40% .
(b) the percent of those who have a cat also have a dog is 60% .
In the question ,
it is given that ,
the percent of children who have a dog = 45% ,
the percent of children having cat = 30%
the percent of children having dog and cat = 18% ,
Part(a)
the percent of children that have a dog also have a cat is
= (number of children that have dog and cat)/(number of children having dog)
= 18/45
= 0.4 = 40% .
Part(b)
the percent of children that have a cat also have a dog is
= (number of children that have dog and cat)/(number of children having cat)
= 18/30
= 0.6 = 60% .
Therefore , the required percent for part(a) is 40% and part(b) is 60% .
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the edges of a regular pentagon are colored red, blue, or green at random, so that each edge has an equally likely chance of being painted with any given color. what is the probability that in the resulting coloring, no two adjacent edges have the same color?
The probability that in the resulting coloring, no two adjacent edges have the same color is 1/24.
It is given that the edges of a regular pentagon are colored res, blue or green at random, so that each edge has an equally likely chance of being painted with any color.
So you can't have 0 reds.
You can have 1 red and there are 2 scenarios for that.
You can have 2 reds and there are 8 scenarios for that.
You can't have 3+ reds.
In total there are 10 scenarios that work.
Therefore there are 3⁵ - 3 total cases.
i.e there are 240 total cases.
So the probability that no two adjacent edges have the same color is,
total scenarios/total cases = 10/240 = 1/24.
Therefore the probability that no two adjacent edges have the same color is 1/24.
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Write an equation of a line in lope intercept form that pae through (1,5) and i parallel to y=4x2
The equation of the line is y = 4x + 9
Given,
The points; (x₁, y₁) = (1, 5)
The line is parallel to, y = 4x - 2
Here,
The line given is in the Slope Intercept Form
y = mx + b
y = 4x - 2
Parallel Lines have the same slope
So,
Slope, m = 4
Then,
y = 4x + b
Since it passes through point p(1, 5) we can use these coordinates to solve for b
5 = -4 + b
Solve for b
9 = b
Therefore, the equation of the line;
y = 4x + 9
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Solve the equation 4x + 7y = 11 for y.
y equals the quantity 4 times x plus 11 end quantity over 7
y equals the quantity negative 4 times x plus 11 end quantity over 7
y equals negative 4 times x plus 11 over 7
y equals negative 4 over 7 times x plus 11
The solution is Option B.
The value of y of the equation 4x + 7y = 11 is y equals the quantity negative 4 times x plus 11 end quantity over 7
y = ( -4x + 11 ) / 7
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given by
4x + 7y = 11 be equation (1)
On simplifying the equation to solve for y , we get
Subtract 4x on both sides of the equation , we get
7y = 11 - 4x
Divide by 7 on both sides of the equation , we get
y = ( 11 - 4x ) / 7
So , on simplifying the equation , we get
y = ( -4x + 11 ) / 7
Therefore , the value of y is ( -4x + 11 ) / 7
And , y equals the quantity negative 4 times x plus 11 end quantity over 7
Hence , The value of y of the equation 4x + 7y = 11 is y equals the quantity negative 4 times x plus 11 end quantity over 7
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Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score between 68 and 82.
68.26% of students out of 500 would score between 68 and 82 if the mean is 75 and standard deviation is 7.
What is meant by standard deviation?A low standard deviation suggests that values are often close to the mean (also known as the anticipated value) of the collection, whereas a large standard deviation suggests that values are dispersed over a wider range.
Standard deviation, often known as SD, is most frequently represented in mathematical texts and equations by the lower case Greek letter (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.
Given,
Mean μ=75
σ=7
By using normal distribution,
P(68<x<82)=P(((68-μ)/σ)<z<((82-75)/7))
P(-1<z<1)
P(z<1)-P(z< -1)
By using z-table, we get
=0.8413-0.1587
=0.6826
P(68<x<82)=0.6826≈68.26
P(68<x<82)=68.26%
Therefore, 68.26% of students out of 500 would score between 68 and 82 if the mean is 75 and standard deviation is 7.
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Which of the following equations has the solutions shown in the graph?
-5-4-3-2
7
n
2
w
+
&
a.
y=x²-3x+ 2
b. y=x²+2x-3
1 23 4
C. y=x²+x-6
d.
y=x²-x-6
Answer: can you provide the graph so i can give an answer?
Step-by-step explanation:
the formula gives the length of the side, s, of a cube with a surface area, sa. how much longer is the side of a cube with a surface area of 1,200 square inches than a cube with the surface area of 768 square inches? in. in. in. in.
The difference between the two lengths is 2.8284 inches
What is cube?
The six square faces of a cube, which has six sides that are all the same length, make it a solid object in three dimensions. One of the five platonic solids, it is additionally referred to as a regular hexahedron. Twelve edges, eight vertices, and six square faces make up the form. Given that the three-dimensional object is a square with equal-length sides, the lengths of the cube's length, breadth, and height are all the same. The edge, which is regarded as the edge's bounding line, divides a cube's faces along a shared border.
Cube's surface area is equal to 6 * (sides)2 where side2 = surface area / 6 and side = sqrt (surface area / 6)
The cube's 1200 square inch surface area is as follows:
side = (surface area / 6)
side = sqrt(1200/6)
size equals 14.1421 inches.
Using the 768-square-inch cube as an example:
side = (surface area / 6)
side = sqrt(768 / 6)
dimension is 11.3137 inches.
Hence the difference between the two lengths is 2.8284 inches
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solve for e: -4b+1=8+2e
Answer:
-2b - 7/2
Step-by-step explanation:
solve for e: -4b+1=8+2e
-4b + 1 = 8 + 2e
-4b + 1 -8 = 2e
-4b - 7 = 2e
-2b - 7/2 = e
What is the equation of a line that is perpendicular to Y =- 3x 2?
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. The equation of a line that is perpendicular to Y = -3x^2 is: X = -3y^2/2
The equation of a line that is perpendicular to a given line is found by changing the sign of the slope of the given line and taking the reciprocal of the slope.
The slope of the given line Y = -3x^2 is -3, so the slope of the line perpendicular to it is 3.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Therefore, the equation of a line that is perpendicular to Y = -3x^2 is: x = 3y + b
We can now solve for the y-intercept, b, by substituting the point (0,0) into the equation:
x = 3y + b
0 = 3(0) + b
b = 0
Therefore, the equation of a line that is perpendicular to Y = -3x^2 is: x = 3y^2/2
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The histogram summarizes the percentage of people in each state and the District of
Columbia who identify as Hispanic or Latino. Use the drop-down menus to describe the
distribution of percentages shown in the histogram.
Is the answers that I chosen are correct? Pls Help Me
Answer:
skewed to the right
40.1
49.9
Step-by-step explanation:
the largest possible range is the largest number from the largest margin minus the smallest number from the smallest margin
(49.9-0=49.9
the smallest possible range is the smallest number from the largest margin minus the largest number from the smallest margin
(45.0-4.9=40.1)
carla believed that her teammates on the track team were faster than she was, so she began putting in extra practices in order to become just as fast as them. this is an example of . a. compensation b. rationalization c. regression d. displacement please select the best answer from the choices provided a b c d
Carla's behavior of putting in extra practices to become faster can be seen as an example of (Option A.) compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.
Carla began putting in extra practices in order to become just as fast as them. This is an example of: Option A. CompensationCarla's behavior of putting in extra practices to become faster can be seen as an example of compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.
By engaging in extra practices, Carla is attempting to compensate for her lack of speed and improve her performance. This is different from rationalization, which is the act of making excuses for one's behavior, or from regression, which is the act of reverting to a younger age in response to a stressful situation.
Finally, displacement is the act of redirecting one's emotions or anger onto another person or object.
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let f be a function of two variables that has continuous partial derivatives and consider the points a(8, 3), b(12, 3), c(8, 10), and d(14, 11). the directional derivative of f at a in the direction of the vector ab is 4 and the directional derivative at a in the direction of ac is 15. find the directional derivative of f at a in the direction of the vector ad. (round your answer to two decimal places.) 18.16 incorrect: your answer is incorrect.
Therefore the directional derivative of f at a in the direction of the vector ad is grad F( x, y ) ×ad(u) =64/10
What is directional derivative ?Any function's rate of change at a given location in a fixed direction is known as its directional derivative. Any derivative is thought of in this way: as a vector form. It provides information on the function's immediate rate of variation.
Here,
The terms "directional derivative" and "gradient of a function" must be used in order to respond to this question.
Grad F(x, Y) = 64/10 ad(u)
A function's gradient is a vector with the following definitions:
Grad f(x,y) is equal to f(x,y)/x I + f(x,y)/y j.
where the definition of the directional derivative in the direction of ab is
Grad f(x,y) = Uab(u), where Uab is a unitary vector pointing in the direction of ab.
Consequently, Uab (u) = Uab/|ab|
If f (x,ydirectional )'s derivative in the direction of vector ab is 5, then.
A (7, 3), B (12, 3), and vector ab is then:
ab = [ 12 - 7 , 3 - 3 ] ⇒ ab = [ 5 , 0 ] as well as |ab| = (5)2 (0)2 |ab| = 5
a unitary vector in the direction of ab is:
ab(u) = 5×i/ 5 and according to equation (1)
δf(x,y) / δx × i × 5 × i / |5| = 5
δf(x,y) / δx × i × 5 × i = 25
δf(x,y) / δx = 5 then f( x,y ) = 5 × x + ????
We go on to calculate the component on j of f(x,y)
Following the same procedure
ac = ( 7 , 7 ) - ( 7 , 3 ) ⇒ ac = [ 0 , 4 ] |ac| = √(4)² + (0)²
|ac| = 4
In the direction of ac(u), the unitary vector is:
ac/|ac| = 4 × j / 4
Then :
j / 4 + f(x,y) / y = 4
16 is equal to f(x,y) / y j + 4 j.
both f(x,y) = -4y & f(x,y) / y = - 4
f(x,y) = 5 × I + 4 × j
Finally:
((15 - 7, 9 - 3)) as the vector ad ⇒ ad = ( 8 , 6 ) ( 8 , 6 )
a unitary vector in the direction of
ad(u) = (8 ×i + 6 ×j) / √ (8)² Plus (6)
² ⇒ ad(u) = (8 ×i + 6 ×j) /√ (8)² + (6) ²
ad(u) = (8 ×i + 6 ×j) /10
Currently, we have f (x, y) = 5 I + 4 j and ad(u) = 8 I + 6 j /10.
We can calculate the directional derivative of f(x,y) in the direction of ad with the use of equation (1)
grad F( x, y ) ×ad(u) = ( 5 × i + 4 × j ) × ( 8 ×i + 6 ×j ) /10
grad F( x, y ) ×ad(u) = 4 + ( 24/10)
grad F( x, y ) ×ad(u) =64/10
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If a rectangle is 11 feet long and 5 feet wide, what is its area in square feet?.
Answer: 55 square feet
Step-by-step explanation:
To find area:
Length * Width
11 * 5 = 55
Answer: 55 sq. feet
explanation : 5 x 11 is 55, so 55 square feet
How do you find the slope and y-intercept of a graph?
The slope and y-intercept of a graph can be determined by examining the equation of the line.
The slope is the coefficient of the x-term (the number next to x in the equation) and the y-intercept is the number that the line crosses the y-axis (the constant in the equation). For example, if the equation of a line is y = 2x + 5, then the slope is 2 and the y-intercept is 5. To graph the line, you can use the slope and y-intercept. Start at the y-intercept and move up or down the number of units indicated by the slope. For example, if the slope is 2, move two units up or two units down and plot a point. Repeat this process until the graph is complete.
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Simply the following expression. Show your work: 2(0.6x + 3/4 x + y)
Answer:
2.7x +2y
Step-by-step explanation:
Why because u distribute the 2 to get 1.2x + 1.5x + 2y. CBL and get
2.7x +2y
100 POINTS HELP ME PLEASE ILL GIVE BRAINLIEST ASAP
Answer:
B
Step-by-step explanation:
Do old total minus the new total to get the difference then divide by old to total.
The correct answer would be (B).
write the standard form of the equation of each line given the slope and y-intercept
slope= -¼ y-intercept = 0
slope= -1 y-intercept = -2
slope = -1 y- intercept= -1
slope= -2 y-intercept= 0
Kiran's aunt plans to bike 10 miles.
1. How long will it take if she bikes at an average rate of 8 miles per hour?
Answer:
1.25 hours (1 and 1/4 hours)
Step-by-step explanation:
Kiran;s aunt bikes at an average rate of 8 miles/hr. Assuming it is an average day, we can determine the time it will take her to bike 10 miles by dividng the miles by her average speed:
(10 miles)/(8 miles/hr)
The miles cancel and the hr comes to the top:
(10/8) hours or 1.25 hours 1 and 1/4 hours
Kiran's aunt takes 1.25 hours to cover the distance of 10 miles at the average speed of 8 miles per hour.
What is speed?In unit time, the distance covered by any object is called speed.
In mathematical term, Speed is express as S = D/T,
where S=speed, D=distance, T= time.
Given that,
Distance that Kiran's aunt plans to bike = 10 miles.
The average speed of bike = 8 miles per hour.
To find the time taken by Kiran' aunt to cover 10 miles distance,
Use Formula
Time = Distance / speed
Time = 10 / 8
Time = 1.25
The time taken by Kiran's aunt to cover 10 miles distance is 1.25 hours.
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Write and simplify an expression for the area of a rectangle where the length is three more than twice the width.
Answer:
a = 2[tex]w^{2}[/tex] + 3w
Step-by-step explanation:
Area = length time width
A= (2w + 3) w
a = 2[tex]w^{2}[/tex] + 3w
It takes a cyclist 44 minutes to cycle a distance of 11 km. (a) How long will it take him to cycle a distance of (i) 45 km,
Answer:180 minutes
Step-by-step explanation: