Answer:
Therefore, the fully factorised form is 5a(1 + 3b).
Step-by-step explanation:
5a + 15ab as 5a(1 + 3b) by taking out the common factor of 5a from both terms.
Select the statement that best justifies the conclusion based on the given information. If x + 5 = 15, then x = 10.
The Subtraction property of equality justifies the conclusion based on the given information.
Subtraction Property of Equality Definition:The subtraction property of equality states that when the same number is subtracted from both sides of an equality, then the two sides of the equation still remain equal. In simple words, we can say that when a number is subtracted from one side of an equation, the same number must be subtracted from the other side of the equality.
if a = b
then;
a-c = b-c
We have:
If x + 5 = 15
By subtraction property of equality:
Subtract 5 from both sides we have;
x = 10
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At a circus, 135 clowns are getting into cars. Blue cars hold 20 clowns and red cars only hold 15. There are a total of 8 cars. How many of each are there?
find the domain and range of each f(x)^ * = 1 + x ^ 2
The function f(x)* = 1 + x^2 is defined for all real numbers x, so the domain is all real numbers, or (-∞, ∞).
How to explain the domainIn determining the function's output values, one must consider its collection of feasible results to extract the range. Reviewing f(x)* exhibits a minimum value of 1 due to x^2 being perpetually non-negative, while adding another factor merely preserves positivity.
Concurrently as x skyrockets, so too does the value of f(x)* given that approaching infinity generates infinitely larger powers than any constant coefficient subordinated by it. Consequently, the overall range of f(x)* becomes [1, ∞), enwrapping all feasible solutions equivalent or superior to 1.
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31. There are two gears that are connected to each other. One gear has 20 teeth and the other gear has 10 teeth. If the bigger gear turns around 5 times, how many times will the smaller gear turn?
10 times will the smaller gear turn.
What is the ratio?
The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Since the smaller gear has 10 teeth and the bigger gear 20, the smaller gear will turn twice for every rotation of the larger gear (20/10=2).
Therefore, if the larger gear rotates five times, the smaller gear will rotate two times five times, or ten times. The smaller gear will thus rotate 10 times.
So, if the bigger gear turns around 5 times, the smaller gear will turn around 5 x 2 = 10 times.
Therefore, the smaller gear will turn 10 times.
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Can someone help me put these in order please!
The order of steps of constructing an inscribed circle of a triangle:
Construct one of the angle bisectors of the triangle. Make sure that it intersects the side opposite of the angle.Construct another angle bisector of the triangle for a different angle. Make sure that it intersects the side opposite of the angle.Identify the point of intersection of the two angle bisectors. This is the incenter and is also the center of the inscribed circle.Construct a circle that has a radius of the length from the incenter to one of the points where an angle bisector intersects a side of the triangle.How to construct the circle ?Commence the process by sketching a line that cuts one angle of the triangle in two and intersects the opposing side at some point. Through this action, a pair of miniature triangles with congruent figures materialize.
Subsequently, draft an additional bisector for another angle of the triangle. The second dividing line needs to meet the side opposite to the situated angle at a specific location.
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I keep coming up with 75. The answer is 85.5. How do you get it?picture below of problem.
10A) A large company is trying to determine the mean number of bags of dog food sold per day in
its stores. The dot plot shows the mean number of bags sold per day from 40 samples of 25
stores (rounded to the nearest 10 bags).
Means of Samples
0
50
100
150
Bags of Dog Food Sold per Day
How many bags of dog food sold per day is an appropriate estimate of the population mean?
Round to the nearest tenth.
10B) Find and interpret the variability in the distribution.
To find the variability in the distribution of the means, we need to calculate a measure of spread, such as the standard deviation. We can use the dot plot to estimate the standard deviation of the distribution.
From the dot plot, we see that the range of the means is from 0 to 150 bags of dog food sold per day. The midpoint of this range is 75, which we can use as an estimate of the population median. We can estimate the standard deviation by calculating the distance between the median and the quartiles.
From the dot plot, we can see that the lower quartile (Q1) is around 60, and the upper quartile (Q3) is around 110. Therefore, the interquartile range (IQR) is:
IQR = Q3 - Q1 = 110 - 60 = 50
We can use the IQR to estimate the standard deviation by assuming that the distribution is approximately normal and using the empirical rule, which states that:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.
Since the IQR is about half of the range, we can estimate the standard deviation as:
SD ≈ IQR / 1.35 ≈ 50 / 1.35 ≈ 37
Therefore, an appropriate estimate of the standard deviation of the distribution of means is 37, rounded to the nearest whole number.
Interpretation: The variability in the distribution of means is relatively large, with a standard deviation of approximately 37 bags of dog food sold per day. This means that the mean number of bags sold per day can vary by as much as 37 bags from one sample to another.
A group of students is collecting 16 oz and 28 oz jars of peanut butter to donate to a food bank. At the end of the collection period, they donated 1,876 oz of peanut butter and a total of 82 jars of peanut butter to gre food bank.
a. Write a system of equations that represents the constraints in this situation. Be sure to specify the variables that you use.
b. How many 16 oz jars and how many 28 oz jars of peanut butter were donated to the food bank? Explain or show how you know.
35 16 oz jars and 47 28 oz jars of peanut butter were donated to the food bank by solving equation
Let x be the number of 16 oz jars of peanut butter collected, and y be the number of 28 oz jars of peanut butter collected.
The system of equations that represents the constraints in this situation is:
x + y = 82 (total number of jars collected)
16x + 28y = 1876 (total amount of peanut butter collected in ounces)
b. To solve for the number of 16 oz jars and 28 oz jars of peanut butter donated to the food bank
we need to solve the system of equations from part (a). One way to do this is to use elimination:
Multiplying the first equation by 16, we get:
16x + 16y = 1312
Subtracting this equation from the second equation, we get:
12y = 564
Dividing both sides by 12, we get:
y = 47
Substituting this value of y into the first equation, we get:
x + 47 = 82
Subtracting 47 from both sides, we get:
x = 35
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4) Create a check register using graph paper and enter the following transactions.
a. Your balance on 10/01 is $1,863.90.
b.
On 10/3, you write check 621 for $71.10 to the Telephone Company.
c. On 10/7, you write check 622 for $500.00 to Banner Reality for rent.
d.
On 10/8, you write check 623 for $51.12 to Electric Company for utility bill.
e.
On 10/10, you write check 624 for $25.00 to Cathy Santoro for piano lesson.
On 10/15, you deposit your paycheck of $650.00
f.
g.
h.
i.
j.
On 10/16, you write check 625 for $200.00 to Don's Day Camp.
On 10/18, you write check 626 for $90.00 to Ed's Sporting Goods.
On 10/21, you write check 627 for $49.00 to Maple Place Garage.
On 11/15, you deposit your paycheck of $400.00.
A table representing the transactions based on the question prompt is given below:
The Check Register TableDate Transaction Type Check No. Description Debit (-) Credit (+) Balance
10/01 Starting Balance - - - - $1,863.90
10/03 Check 621 Telephone Company $71.10 - $1,792.80
10/07 Check 622 Banner Reality (Rent) $500.00 - $1,292.80
10/08 Check 623 Electric Company $51.12 - $1,241.68
10/10 Check 624 Cathy Santoro (Piano) $25.00 - $1,216.68
10/15 Deposit - Paycheck - $650.00 $1,866.68
10/16 Check 625 Don's Day Camp $200.00 - $1,666.68
10/18 Check 626 Ed's Sporting Goods $90.00 - $1,576.68
10/21 Check 627 Maple Place Garage $49.00 - $1,527.68
11/15 Deposit - Paycheck - $400.00 $1,927.68
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Convert 7oz to ____ L.
helppppppppppppppppppppp!PLEASE THE ONLY THNG S THS !!!AM BEGGNG YOU SOMEBODY!!PLEASE
The cost of one hour of television each day is $1.
We have,
The average electricity bill reduced to $130 to $40.
Number of days in month= 30 days
So, the cost of one hour of television is
= (130- 40) /30
= 90 /30
= $30
Thus, the cost of one hour of television is $ 30.
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Type the correct answer in the box. Round off your answer to the nearest integer.
Two planes, A and B, start from the same place and move in different directions, making an angle of 50° between them. The speed of plane A is
200 miles per hour, and the speed of plane B is 300 miles per hour.
The two planes are
miles apart after one hour.
I need help with this to find x and y value pls explain me with reasons.
The x and y values in the triangle are:
x = 58°
y = 26°
How to find x and y values in the triangle?Trigonometry deals with the relationship between the ratios of the sides of a triangle with its angles.
To find the x and y values in the triangle, check the attached image for labeling.
In the image:
Triangle ABC is isosceles. Thus,
t = 61° (base angles of isosceles triangles are equal)
x + t + 61 = 180 (sum of angles in a triangle is 180°)
x + 61 + 61 = 180
x = 180 - 61 - 61
x = 58°
x + v = 180 (sum of angles on a straight line is 180°)
58 + v = 180
v = 180 - 58
v = 122°
In triangle ACD:
32 + v + y = 180 (sum of angles in a triangle is 180°)
32 + 122 + y = 180
y = 180 - 32 - 122
y = 26°
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Which of the following images shows only a line segment highlighted in red? (3 points)
Figure A has four line segments connected to form a square, with the circle in the upper left corner colored red. Figure B has four line segments connected to form a square, the line segment on the right and the bottom line segment connect at the vertex and are colored red. Figure C has four line segments connected to form a square, with the bottom line segment colored red. Figure D has four line segments connected to form a square, with the top line segment and the bottom line segment colored red.
a
Figure A
b
Figure B
c
Figure C
d
Figure D
Figure C shows only a line segment highlighted in red.
Figure C has four line segments connected to form a square, with the bottom line segment colored red.
The other three line segments in the figure are not colored, and only the bottom line segment is highlighted in red.
This means that only a line segment is shown in red, which is what the question is asking for.
Hence, figure C shows only a line segment highlighted in red.
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The current mean weekly wage in a certain industry is 2,117. if the mean weekly wage increases by 4.75% what is the new mean average
The new mean annual wage is; $ 43,149.82.
Given that the initial mean weekly wage is $ 2.117.
The growth rate is 4.75%.
We need to find a new annual wage.
Consider the equation, A be the new annual wage.
Here R is the growth rate and P is the initial mean weekly wage and T is the number of weeks in a year.
The number of weeks in a year = 52 weeks.
Substitute P= 2,117, R =4.75% = 0.0475and T =52 in the equation.
A = 2.117 x 52(1 + 0.0475)
A = 43,149.82
The new mean annual wage is; $ 43,149.82.
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Evaluate the following expression:
\left( \frac{16}{9} \right)^{2/3} \cdot \left( \frac{4}{3} \right)^{4/3} \cdot \left( \frac{9}{16} \right)^{2/3} \cdot \left( \frac{3}{4} \right)^{4/3}
We raise the fraction to the power of 4/3.
To evaluate the expression:
\left( \frac{16}{9} \right)^{2/3} \cdot \left( \frac{4}{3} \right)^{4/3} \cdot \left( \frac{9}{16} \right)^{2/3} \cdot \left( \frac{3}{4} \right)^{4/3},
we can simplify each term within the parentheses before multiplying them together.
Let's simplify each term step by step:
\left( \frac{16}{9} \right)^{2/3}:
To simplify this term, we raise the fraction to the power of 2/3.
\left( \frac{16}{9} \right)^{2/3} = \left( \left( \frac{2^4}{3^2} \right)^{1/3} \right)^2 = \left( \frac{2^{4 \cdot 1}}{3^{2 \cdot 1}} \right)^2 = \left( \frac{2^4}{3^2} \right)^2 = \left( \frac{16}{9} \right)^2 = \frac{16^2}{9^2} = \frac{256}{81}
\left( \frac{4}{3} \right)^{4/3}:
Similarly, we raise the fraction to the power of 4/3.
\left( \frac{4}{3} \right)^{4/3} = \left( \left( \frac{2^2}{3^1} \right)^{1/3} \right)^4 = \left( \frac{2^{2 \cdot 1}}{3^{1 \cdot 1}} \right)^4 = \left( \frac{2^2}{3^1} \right)^4 = \left( \frac{4}{3} \right)^4 = \frac{4^4}{3^4} = \frac{256}{81}
\left( \frac{9}{16} \right)^{2/3}:
We raise the fraction to the power of 2/3.
\left( \frac{9}{16} \right)^{2/3} = \left( \left( \frac{3^2}{2^4} \right)^{1/3} \right)^2 = \left( \frac{3^{2 \cdot 1}}{2^{4 \cdot 1}} \right)^2 = \left( \frac{3^2}{2^4} \right)^2 = \left( \frac{9}{16} \right)^2 = \frac{9^2}{16^2} = \frac{81}{256}
\left( \frac{3}{4} \right)^{4/3}:
We raise the fraction to the power of 4/3.
\left( \frac{3}{4} \right)^{4/3} = \left( \left( \frac{3^1}{2^2} \right)^{1/3} \right)^4 = \left( \frac{3^{1 \cdot 1}}{2^{2 \cdot 1}} \right)^4 = \left( \frac{3^1}{2^2} \right)^4 = \left( \frac{3}{4} \right)^4 = \frac{3^4}{4^4} = \frac{81}{256
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Need help please and thank you
Hey!
For any graphing calculator problems I would recommend using desmos if your teacher allows it or getting a graphing calculator such as a ti-nspire :)
This way, it will be able to graph and get the answers quicker!
The answers to this question is (37.5,15) and (0,60). To find your answers when you graph always look for where the lines intersect. If the lines do not intersect then it is not one of your answer choices. (examples are below).
A school district sends an online survey to all parents of students in the district asking for feedback on props educational changes on recent tax cuts
The approach employed in this specific instance is a non-probability sampling technique labeled as convenience sampling.
How is this sampling method used?It involves selecting the participants based on convenience or, in other words, selecting those who are readily available to take part in the study. Hence the school district has decided to dispatch the survey to all parents whose children have access to the online questionnaire.
The selected sample principally arises from considerations of the ease with which it can be attained, thus making convenience rather than randomness the dominant factor informing the selection process.
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A school district sends an online survey to all parents of students in the district asking for feedback on props educational changes on recent tax cuts
What is the sampling method used here
What is the area of this figure?
Answer:
142ft^2
Step-by-step explanation:
I hope this picture helps, but if you have any questions about the steps let me know
Find a polynomial function f(x) of degree 3 with zeros, 2, -3 , 5 and f(3)=6
A polynomial function f(x) of degree 3 with given zeros, 2, -3 , 5 and condition f(3)=6 is given by f(x) = -1/2 (x-2)(x+3)(x-5).
Degree of the polynomial function is equal to 3.
Zero's of the polynomial function is equal to 2, -3 , 5 .
And f(3) = 6
If 2, -3, and 5 are zeros of f(x), then we can write function as,
f(x) = a(x-2)(x+3)(x-5)
where a is some constant.
To determine the value of a, we can use the fact that f(3) = 6.
Substituting x = 3 into the equation above, we get,
f(3) = a(3-2)(3+3)(3-5)
= -12a
Here we have,
f(3) = 6, so we can set these two expressions equal to each other and solve for a,
⇒ -12a = 6
⇒ a = -1/2
Now we can substitute this value of a back into the equation for f(x) that we found earlier,
⇒ f(x) = -1/2 (x-2)(x+3)(x-5)
Therefore, a polynomial function f(x) of degree 3 with zeros 2, -3, 5, and f(3) = 6 is equal to f(x) = -1/2 (x-2)(x+3)(x-5).
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A.solves routine and non-routine problems involving perceentage using appropriate strategies and tools.M5NS-IIIIb-40
Observe the solution to the given problem below.
christmas season is coming and ana is so excited to do her shopping in her list is a pair of shoes that she will wear for their christmas party.what made her more excited was when she saw that her dream pair of shoes is on sale.
from P 4 295, it is now sold with 20%
The sale price of the shoe is given as follows:
P3,436.
How to obtain the sale price of the shoe?The sale price of the shoe is obtained applying the proportions in the context of the problem.
The initial price is of:
P 4,295.
The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:
0.8 x 4295 = P3,436.
Missing InformationThe problem asks for the selling price of the shoe.
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If there is a polynomial of a higher degree than a quadratic, it might have more than two solutions. For example, a cubic polynomial could have up to three solutions.
The polynomial equation 20z3−11z2−3z=0 is factorable. Factor the polynomial completely and set each of the factored terms equal to zero, just like you would with a quadratic equation. What are the solutions to the given polynomial equation?
The preceding polynomial equation has three solutions: z = 0, z = 3/4, and z = -1/5.
First, we can factor out a common factor of z:
z(20z² - 11z - 3) = 0
Now we need to factor the quadratic expression in the parentheses.
We can use the quadratic formula or factor by grouping to do this. Factoring by grouping yields:
z(20z² - 11z - 3) = 0
z(4z - 3)(5z + 1) = 0
Setting each of the factored terms equal to zero, we have:
z = 0, 3/4, -1/5
Therefore, the solutions to the given polynomial equation are z = 0, z = 3/4, and z = -1/5.
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What is the value of y in the formula shown when x = 4/5?
y = 4/x
+ √x + 0.2 - 5x
y =
(please look at photo)
Answer:
y = 2
Step-by-step explanation:
substitute x = [tex]\frac{4}{5}[/tex] ( = 0.8) into the formula
y = [tex]\frac{4}{0.8}[/tex] + [tex]\sqrt{0.8+0.2}[/tex] - 5(0.8)
= 5 + [tex]\sqrt{1}[/tex] - 4
= 5 + 1 - 4
= 6 - 4
= 2
How do I solve this?
Answer: 1/5
Step-by-step explanation:
In this case, you multiple the exponents together because you are raising a power to a power:
25^(-3/2 * 1/3)
25^(-3/6)
25^(-1/2)
Next, when the power is negative, we can get rid of it by changing the whole number to its reciprocal (divide the number by one):
1/(25^(1/2))
Now, when an exponent is a fraction, the numerator is what the base is raised to and the denominator is what the base is rooted to:
1/(sqrt(25))
Now, simplify:
1/5
(2a³) (3a4) simplify no negative exponents
6a7
Step-by-step explanation:
To simplify the expression (2a³) (3a4), you can use the laws of exponents. First, you can multiply the coefficients 2 and 3 to get 6. Then, you can add the exponents of 'a' which gives you a total of 3+4=7. Therefore, the simplified expression is 6a7. It does not have any negative exponents, and it represents the product of two expressions with the same base 'a' and coefficient multiplication.
Answer: 6a7
Step-by-step explanation: Got this right b4.
what radian measure is equivalent to 300
The equivalent radian to 300 degree is 5π/3.
The given angle measures 300 degree.
We know that, formula used to convert degrees is Radians = Degrees × π / 180
Here, Radians = 300×π/180
= 30 ×π/18
= 10π/6
= 5π/3
Therefore, the equivalent radian to 300 degree is 5π/3.
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Solve 19 × 6 using distributive law.
The solution to the given expression by using distributive law is 114
What is distributive law?The distributive property posits that an expression that is provided in the form of A (B + C) can be further expressed as A × (B + C) = AB + AC. This distributive law is also useful for subtraction and is expressed as, A (B - C) = AB - AC. This implies that operand A is distributed between the other two operands.
From the given information, we are to expand 19 × 6 using the distributive law. The first step would be to expand 19 into two integers.
Let the two integers be 10 and 9.
So, we can have can express this by using the addition distributive law: A(B+ C)
Mathematically, we have:
= 6(10 + 9)
= 6(19)
= 114
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HURRY DUE TONIGHT
Danielle was completing her science project and mixed saline solutions A and B. Brand A was a six gallon 18% saline solution and she ended up with an 18 gallon 8% saline solution mixture. Find the percent of saline solution in brand B.
A. 21%
B. 3%
The percentage of saline solution in brand B is 3%.
Let x be Percentage of saline solution in brand B
We know that the overall volume of saline solution in the combination is 18% of 6 gallons plus x% of (18 - 6) gallons since Danielle blended brands A and B to make a total of 18 gallons of 8% saline solution.
Then the equation is given as,
0.18(6) + 0.01x(18 - 6) = 0.08(18)
Simplifying and solving for x, we get:
1.08 + 0.12x = 1.44
0.12x = 0.36
x = 3
Therefore, the percentage of saline solution in brand B is 3%.
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Find the x value and explain with reasons for both pls
Applying the triangle sum theorem, the value of x in the image given is:
x = 33°; x = 45°
How to Find the Value of x in the Triangles?Recall that according to the triangle sum theorem, all three interior angles of a triangle is equal to 180 degrees.
a. x + 21 + (180 - 54) = 180 [triangle sum theorem]
x + 147 = 180
x = 180 - 147
x = 33°
b. (180 - 102) + x + 57 = 180 [triangle sum theorem]
x + 135 = 180
x = 180 - 135
x = 45°
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4. Chelsea determined that the value of x in the triangle at the right was 5.
a. Find the value of each angle by substituting 5 for x.
b. Was Chelsea's solution, x = 5, correct? How do you know?
15x
x
11x
(8x+5)
Z
a.) The value of each angle when 5 is substituted for X would be ;
Y = 55°
Y = 55°W = 75°
Y = 55°W = 75°Z = 45°
b). Chelsea is wrong in her calculation because the total internal angle of a triangle should be 180° and not 175°.
How to calculate the value of the various angles through substitution?For angle Y;
11x = 11(5) = 55°
For angle W;
15x = 15(5) = 75°
For angle Z;
(8x+5) = 8(5) +5
= 45°
The total angles = 55+75+45 = 175°
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Which set of ordered pairs represents a function?
O {(-5, -9), (-7,-9), (-5, -7), (-8,6)}
O {(-1,6), (0, -3), (5, -9), (-1,3)}
O {(1, 2), (-6, 2), (3,9), (5,3)}
O {(-3,9), (2, 7), (2, -4), (1,5)}
The set of ordered pairs which represents a function among the given answer choices is; {(1, 2), (-6, 2), (3,9), (5,3)}.
Which of.the answer choices represents a function?By definition, a function is a special kind of relation in which case, each input value is assigned not more than one output value.
On this note, by evaluation of the given sets of ordered pairs; the set {(1, 2), (-6, 2), (3,9), (5,3)} represents the relation which is a function.
Ultimately, the answer choice which represents a set of ordered pairs that represents a function is; {(1, 2), (-6, 2), (3,9), (5,3)}.
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