Answer: p²+2pq+q²
Step-by-step explanation:
squaring a binomial works like this:
(p+q)² = (p+q)(p+q)
try the FOIL method: multiply the first, outside, inside, and last numbers/variables to distribute properly
F: (p)(p) = p²
O: (p)(q) = pq
I: (q)(p) = pq
L: (q)(q) = q²
then add them all together
q²+pq+pq+q²
and combine like (identical) terms
q²+2pq+q²
it's 2pq because they're being added, not multiplied.
hope this helps!
1. Which of the following is equivalent to 5a³ + 4a³??
O (5+4) a³+3
O (5+4) a³
(5.4) a³+3
O (5.4) a³
ہے
The equivalent to 5a³ + 4a³ is (5+4) a³, according to the question.
What do you mean by Equivalent ?
Equivalent refers to the mathematical notion that distinct terms and expressions having a similar value are treated equally.
According to the given question,
We have the given options are:
O (5+4) a³+3
O (5+4) a³
O (5.4) a³+3
O (5.4) a³
Now, we will find the equivalent,
5a³ + 4a³
Then, we will taking common factor from the given equation:
5a³ + 4a³
= a³(5+4)
So that is same as (5+4)a³.
Therefore, the equivalent to 5a³ + 4a³ is (5+4) a³.
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fast as you can. point slope form. algebra 1)
Answer: Y=mx+b
Step-by-step explanation:
If you roll a fair die, what is the probability you will roll a 5 or a number less than 3?
Answer:
1/2
Step-by-step explanation:
Since 5 is one of the six possible numbers available, rolling a 5 is a 1/6 probability.
Since rolling a number less than 3 means rolling a 1 or 2, rolling a 1 or 2 is a 2/6 probability.
Add those probabilities up since you can get either of those outcomes and you get 1/6+2/6=3/6
3/6=1/2
Michael is building a skateboard
ramp. The ramp needs to include a
right angle to be safe. If the side
lengths are 10 feet, 2.5 feet, and 10.5
feet, will the ramp be safe? Prove
your answer with an inequality.
Given that the side lengths of the ramp are 10 feet, 2.5 feet, and 10.5 feet.
We know that for making a right angle A Pythagoras triplet must follow
So, a² + b² = c²
Where a, b, c are the lengths of the triangle and a, b <=c
So, on applying the above formula
We have,
2.5² + 10² = 10.5²
6.25 + 100 = 110.25
But 106.25 is not equal to 110.25
So all these sides are not good for making the ramp safe.
There are three types of the triangle based on angle -
1. Acute angled triangle
2. Right-angled triangle
3. Obtuse angled triangle
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the table shows the number of stickers three friends have, Hannah has fewer stickers than Marco but more stickers than Addison. how many stickers could Hannah have?
Find the inverse of the following function. f(x) 8√ x for x > 0
Answer: The inverse of a function is found by switching the positions of the input and output values in the function. For example, if the function is f(x) = 2x, the inverse would be f<sup>-1</sup>(x) = x/2.
In the case of the given function, f(x) = 8√ x, the inverse can be found by switching the positions of the input and output values. This gives us f<sup>-1</sup>(x) = √ x/8. This means that if x is the input value, the output value will be √ x/8. Note that the domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function. In this case, the domain of f<sup>-1</sup>(x) is [0, ∞) and the range is [0, ∞), since these are the range and domain of the original function.
Here is the complete inverse function:
f<sup>-1</sup>(x) = √ x/8 for x > 0.
Triangle OPQ is shown below with line RS passing through points R and S:
R
S
If triangle OPQ is dilated about the center of the triangle to create triangle O'P'Q', what can you
conclude about segments RS and R'S'? (6 points)
Segment O'Q' is perpendicular to segment R'S'.
Line RS is parallel to line R'S'.
Line RS is perpendicular to line R'S:
Point P' passes through line RS.
Dilation is a type of transformation. So it can concluded that: Line RS is parallel to line R'S'.
Transformation is a method required to either increase or decrease the size of a given object, or change its orientation. Types of transformation are dilation, translation, rotation and reflection.
Dilation is a process in which the size of a given shape or figure is reduced or increased appropriately to form an image.
Two lines are said to be perpendicular when the measure of angle between is a right angle. While two or more lines are said to be parallel is the measure of angle between them is that of a straight line.
Thus, the appropriate statement that would be concluded considering the conditions in the question is line RS is parallel to line R'S'.
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Zehra owns a bakery and is getting ready for the Thanksgiving rush. She needs to stock up on pumpkin pie filler to be able to meet demand, so she begins buying a constant number of cans of pumpkin pie filler per week. After 5 weeks, she has 29 cans. After 9 weeks, she has 57 cans. How many cans is she buying per week?
Based on the rate of change, Zehra is buying 7 cans per week.
What is the rate of change?The rate of change gives the ratio between the change in one quantity to the change in another quantity.
Linear relationships have a constant rate of change and the rate of change is usually represented as the slope or gradient.
For instance, the number of cans changed from 29 to 57, a difference of 28, as the number of weeks changed from 5 to 9, a difference of 4.
The rate of change can be expressed as 28/4 or 7.
The number of cans after 5 weeks = 29
The number of cans after 9 weeks = 57
The change in weeks = 4 (9 - 5)
The change in the number of cans = 28 (57 - 29)
The rate of change = 7 (28/4)
Thus, we can conclude that Zehra buys 7 cans weekly.
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If f(x) = 3x-1 and g(x) = x^2+2, what is (f ° g)(x)?
Answer:
(f ○ g)(x) = 3x² + 5
Step-by-step explanation:
substitute x = g(x) into f(x) , that is
(f ○ g)(x)
= f(g(x))
= f(x² + 2)
= 3(x² + 2) - 1
= 3x² + 6 - 1
= 3x² + 5
A quadrilateral with vertices A(-2, 2), 8(-3, 6), C(-7, 7), and D(-4, 1) is rotated 180° about the origin. Which of
the vertices is NOT correct?
A quadrilateral with vertices A(-2, 2), 8(-3, 6), C(-7, 7), and D(-4, 1) is rotated 180° about the origin is Coordinates of D' (-6,3).
What is quadrilateral?
A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners. The angles at the vertices of a quadrilateral ABCD are ∠A, ∠B, ∠C and ∠D. A quadrilateral has the following sides: AB, BC, CD, and DA.
When any figure is rotated 180° in the counterclockwise direction, then the coordinates of the vertices is changed into its opposite sign.
(x, y) → (-x, -y)
The coordinates of the vertices of quadrilateral ABCD is changed when it is rotated 180 degrees counterclockwise about the origin as,
A (7,-7) → A'(-7,7)
B (4,-10) → B' (-4,10)
C (1.5, -2.5) → C' (-1.5, 2.5)
D (6, -3) → D'(-6,3)
So the coordinates of D' will be (-6,3).
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if a point is characterized as having both a nonzero x and y coordinate and oppositely signed coordinates, then the point must be in which of the labeled quadrants in the standard xy coordinate plane?
The labeled quadrants in the standard xy coordinate plane is Quadrant II
What is Quadrants?
The intersection of the x-axis (the horizontal number line) and the y-axis in the cartesian system divides the coordinate plane into four equal pieces (the vertical number line). Because each of these four areas occupies a quarter of the entire coordinate plane, they are collectively referred to as quadrants.
Concept:
The x and y coordinates are both positive in quadrant I. In quadrant II, the x and y coordinates are oppositely positive. The x and y coordinates are both negative in quadrant III. The x-coordinate is positive and the y-coordinate is negative in quadrant IV.
The origin, or the point where the x- and y-axes connect, is where both the x and y coordinates are zero (0, 0).
The point is in the first quadrant if both x and y are positive. If both x and y are negative, the point will be in the second quadrant. In the third quadrant if both x and y are negatives, the point is located.
The labeled quadrants in the standard xy coordinate plane is Quadrant II
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▲DEF has vertices D (-2 ,1 ), E (2,4), and F (3,1) and is dilated by a factor of 3 using the point (1,1) as the point of dilation. The dilated triangle is names ▲D'E'F'.
If your answer is useless then don't answer because last time someone typed random stuff and I was left answerless.
The dilated triangle is names ▲D'E'F' ,
Vertex D' → ( -8, 1)
Vertex E' → (4, 10)
Vertex F' → (7, 1)
What is dilation ?
Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation. An image that retains the original shape is created by this alteration. The size of the form does differ, though. A dilatation should either enlarge or decrease the initial form. By using the phrase "scaling factor," this transition is described.
Enlargement is the name given to a dilatation that results in a larger image.
Reduction is what happens when a dilatation results in a smaller picture.
According to question
Since the center of dilation is not at the origin, we can use the following formula in order to find the coordinates of the vertices of the triangle D'E'F':
[tex]D_{(O,k)}(x,y) = (k(x-a) +a, k(y-b) +b)[/tex]
Where "O" is the center of dilation at (a,b) and "k" is the scale factor.
In this case you can identify that:
(a,b) = (1,1)
k = 3
Therefore, susbtituting values into the formula shown above, you get that the coordinates ot the resulting triangle D'E'F, are the following:
Vertex D' → [tex](3(-2-1) +1, 3(1-1) +1) = (-8, 1)[/tex]
Vertex E' → [tex](3(2-1) +1, 3(4-1) +1) =(4,10)[/tex]
Vertex F' →[tex](3(3-1) +1, 3(1-1) +1) =(7,1)[/tex]
hence the vertex of ▲D'E'F' are (D' → ( -8, 1), E' → (4, 10), F' → (7, 1).)
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If a plane can travel 480 miles per hour with the wind and 380 miles per hours against the wind, find the speed of the wind and the speed of the plane in still air
Answer:
Step-by-step explanation:
I am not super sure about this one
2
Write the answer in each blank.
Of these numbers
745 281 578 170
is the smallest
is the largest
Enter the measurement of the vehicle part.
Answer:
2 1/4
Step-by-step explanation:
I know bc its basic math
suppose that CDE IS ISOSCELES WITH THE BASE ED suppose also that m<E=(2x+37) and m<D=4x+23)
find the degrees measure of each angle in the triangle
Answer:
the measure of angle a is 51.43 degrees, the measure of angles C and E is also 51.43 degrees. The measure of angle D is 77.14 degrees.
Step-by-step explanation:
Since CDE is an isosceles triangle with the base ED, the two angles at C and E are equal. Let's call this angle a. This means that the angles at D and E are also equal and have a measure of 180 - 2a.
We know that the measure of angle D is 4x + 23. Since the angles at D and E are equal, the measure of angle E is also 4x + 23. Therefore, the measure of angle a is 2x + 23.
To find the measure of each angle in the triangle, we need to use the fact that the sum of the angles in a triangle is 180 degrees. Since we already know the measure of angle D and angle E, we can use this information to find the measure of angle C.
Since the sum of the angles in the triangle is 180 degrees, we can write the following equation:
a + (180 - 2a) + (180 - 2a) = 180
Solving for a, we get:
a = 180 - 2(180 - 2a)
a = 360 - 4(180 - 2a)
a = 360 - 720 + 8a
a = -360 + 8a
7a = 360
a = 51.43 degrees
Since the measure of angle a is 51.43 degrees, the measure of angles C and E is also 51.43 degrees. The measure of angle D is 4x + 23, as given in the problem statement.
you walk to the subway station for your morning commute. given that you always leave your apartment at the same time, there is a probability of 1/2 that you will wait 3 minutes for the train and a probability of 1/2 that you will wait 7 minutes for the train. find the expected value of your wait time
To find the expected value of your wait time, we need to multiply the value of each possible outcome by its probability and then add up all the products. In this case, there are two possible outcomes: waiting 3 minutes or waiting 7 minutes.
The probability of waiting 3 minutes is 1/2, and the probability of waiting 7 minutes is also 1/2. Therefore, the expected value of your wait time is:
(3 minutes * 1/2) + (7 minutes * 1/2) = 5 minutes
So, on average, you can expect to wait about 5 minutes for the train.
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Which of the following represents the least value?
1/3 of 1,212
1/5 of 1,212
25% of 1,212
30% of 1,212
Answer:
1/5 of 1,212
Step-by-step explanation:
Note that 25% = 1/4 and 30% = 3/10.
The least value is achieved when we take the smallest fraction, which is 1/5.
Answer:
1/5 of 1212 is the smallest value
Step-by-step explanation:
if we convert 25% to a fraction we have 1/4
if we convert 30% to a fraction we have 3/10
now we convert each of the four fractions into equivalent fractions using lowest common denominator of 60
1/3 = 20/60
1/5 = 12/60
1/4 = 15/60
3/10 = 18/60
the smallest fraction is 12/60, or 1/5
therefore 1/5 of 1212 is the smallest value
A) Q''(−5, 6), R''(−2, 1), S''(1, 5)
B) Q''(7, 11), R''(10, 16), S''(13, 12)
C) Q''(−5, 2), R''(−2, 7), S''(1, 3)
D) Q''(13, 2), R''(10, 7), S''(7, 3)
The correct answer is C.
Identify the rate of decay r (as a percent) of the exponential function f(x) = 0.3(0.82)^x
a. r = 30%
b. r = 18%
c. r = 70%
d. r = 82%
Answer:
b. r = 18%
Step-by-step explanation:
0.3(0.82)^x:
0.3(0.82)^x:
The 0.82 is getting affected since it is raised to the power of x
Hence, for every iteration of x, the object is becoming 82% of itself.
100%-82%=18%
r = 18% ==> b
Option B is correct, 18% is the rate of decay of the exponential function f(x) = 0.3(0.82)ˣ
What is a function?A relation is a function if it has only One y-value for each x-value.
The exponential function f(x) = 0.3(0.82)^x can be written in the form f(x) = a(b)ˣ, where a = 0.3 and b = 0.82.
In an exponential function of the form f(x) = a(b)ˣ
the base b represents the rate of change.
If b is between 0 and 1, then the function represents exponential decay. The rate of decay r can be found using the formula:
r = (1 - b) x 100%
In this case, b = 0.82, so the rate of decay is:
r = (1 - 0.82) x 100%
= 0.18 x 100%
= 18%
Hence, option B is correct, 18% is the rate of decay of the exponential function f(x) = 0.3(0.82)ˣ
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Increasing Functions
30
27.5
25
20
175
15
10
y = 2
(y=x
y = 2x
Consider the graph shown, which func
the other functions?
4x A
{x B
C
D
y=2
y=z²
y = 2x
cannot be determined
Which function will eventually surpass
Answer:
b
Step-by-step explanation:
i know ..
Sam is using these numbers to make a new
number.
12
1
1
4
7
He can only use brackets, +, -, x, ÷ once.
He cannot use any number more than once.
He cannot use powers.
He cannot put numbers together
e.g. he cannot use '147'.
What is the biggest number he can make?
Show how he can make this number.
Answer:
87
Step-by-step explanation:
12x7+4-1/1
Answer: 741
Step-by-step explanation:
The biggest number Sam can make is 741. He can make this number by using the brackets and the division symbol: (12 + 1 + 1) / 4 = 741.
If 1.5 liters of washing up liquid is 2.70$ find the cost of 1 liter
The cost of one liter of washing up liquid would be = $1.8
What is liters?Liters is a variable that is can be used to denote the measurement of a liquid.
The quantity of the washing up liquid that was given= 1.5 liters.
The cost of 1.5 liters of washing up liquid =$2.70
If 1.5 L = 2.70
1 L = X
Make X the subject of formula;
X = 1× 2.70/1.5
X = $1.8
Therefore, the cost of one liter of washing up liquid would be = $1.8
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Solve 945 divided by 9 =
O 105
O 105 2/9
O 105 5/9
O 105 8/9
GIVING BRAINLIEST
945 divided by 9 = 105.
What is divided?
In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each. The division sign, ",÷" or occasionally "/," is used in computer code.
If the sum of the digits is not divisible by 9, then 945 is not divisible by 9.
The sum of the digits is calculated as follows:
9 + 4 + 5 = 18
18 is divisible by 9
[tex]\frac{945}{9}$$[/tex]
Write the problem in long division format
[tex]9 \longdiv { 9 4 5 }[/tex]
Divide 9 by 9 to get 1
[tex]$$\begin{gathered}91 \\\frac{1}{945} \\\frac{9}{04}\end{gathered}$$[/tex]
Divide 4 by 9 to get 0
[tex]$$\begin{gathered}910 \\\frac{10}{945} \\\frac{0}{45}\end{gathered}$$[/tex]
Divide 45 by 9 to get 5
[tex]$$\begin{gathered}9105 \\\frac{9}{045} \\\underline{4} \\\frac{45}{0}\end{gathered}$$[/tex]
The solution for Long Division of [tex]$\frac{945}{9}$[/tex] is 105
105
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what is the z-score of a value 20 from a binomial distribution with 50 trials and probability 0.76 of success? round your answer to three decimal places. incorrect answer:
z-score of a value is -5.96
What is z-score in binomial distribution?
The Z score represents the number of standard deviations above or below the mean. The Z score of the mean is 0 by definition.
What is Probability?
The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.
Given,
A random variable, let's call it X, has parameters that fit the Binomial distribution: n (number of trials) = 50 and p (success probability) 0.76.
We must ascertain the z-score (Z) of the value 20 = that this random variable X has chosen.
Now, for a random variable, say X, its z-score (Z) is defined as ,
Z = (X - mean of X)/ Standard deviation of X
A binomial random variable with the parameters once more n and p, its mean is given as np and its standard deviation is given as [tex]\sqrt{n*p*(1-p)}[/tex]
The standard deviation of X is provided as [tex]\sqrt{50*0.76*0.24}[/tex] = [tex]\sqrt{9.12}[/tex] = 3.0199933 while the mean of X is given as 50*0.76 = 38.
Therefore, the required z-score (Z) for X = 20, is given as,
Z = 20-38/3.0199933
Z= -5.9602781238
Z= -5.96 that is the necessary z-score.
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Graph Y= -1/4 x + 6.
The x-intercept and y-intercept of the line will be at (24, 0) and (0, 6). And the line is drawn below.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
The linear equation is given below.
y = -(1/4)x + 6
Convert the equation into intercept form, then we have
y = -(1/4)x + 6
4y = - x + 24
x + 4y = 24
x / 24 + y / 6 = 1
The x-catch and y-capture of the line will be at (24, 0) and (0, 6) and the line is drawn underneath.
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y= 1/2x + 1
y=-x + 7
Answer: point form: (4,3) equation form: x=4 y=3
Step-by-step explanation:
a) Shashwat obtained an average marks of 15 in 3 subjects. When the marks obtained in another subject is also included, the average marks is increased by 1. Find the marks obtained in the fourth subject.
The mark obtained in the fourth subject is 19
How to determine the mark obtained in the fourth subject?From the question, we have the following parameters that can be used in our computation:
Average marks in 3 subjects = 15
Average marks in 4 subjects = 15 + 1
When the number of subjects is increased by 1, we have the following equation
Average = Sum of subjects/Number of subjects
Substitute the known values in the above equation, so, we have the following representation
15 + 1 = (3 * 15 + Score in 4th subject)/4
So, we have
16 = (3 * 15 + Score in 4th subject)/4
Evaluate the products
16 = (45 + Score in 4th subject)/4
So, we have
45 + Score in 4th subject = 64
Subtract 45 from both sides
Score in 4th subject = 19
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How can we use the formula M= 58h + 135 to determine the mile marker that Sam passed at hour 6
Sam passed the marker of 483 miles, in 6 hours.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
An expression is given as M = 58h + 135. shows how many miles the same has traveled for h hours,
To evaluate the mile marker that sam passed at 6 hours, substitute the value with h in a given expression.
M = 58×6 +135
Simplifying the above expression gives the mile marker
M = 483 miles
Thus, the required miles are 483.
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What does y equal, in this picture with 30 60 90 triangles?
The value of y= 5.49≈ 5.5cm
What is 30-60-90 traingle?
The 30-60-90 triangle is cut straight through the middle along its altitude, like one half of an equilateral triangle. Its name is derived from its three angles of 30 degrees, 60 degrees, and 90 degrees. Any triangle with angles of 30-60-90 will look like this: The hypotenuse is always twice as long as the shortest leg, and the length of the long leg can be calculated by multiplying the short leg by the square root of three. The shortest leg is across from the 30-degree angle.
By 30-60-90 triangle rule,
Side across 60° angle = x
Hypotenuse side = 2x= 15
Side across 30° angle = x√3
By solving,
2x= 15
x= 7.5cm
So side across 60° angle= 7.5 cm
Side across 30° angle = 7.5×√3
= 7.5× 1.732= 12.99≈ 13cm
As the figure given us square so,
13= 7.5+y
y= 13-7.5
y= 5.5 cm
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