Collecting the like terms in the expression 5z - 7 - 13z + 35 gives -8z + 28
How to collect like terms on the expressionFrom the question, we have the following parameters that can be used in our computation:
5z - 7 - 13z + 35
Consider an expression given as
Ax + Bx
Where A and B are constants and x is a variable
The terms Ax and Bx are like terms
using the above as a guide, we have the following:
5z - 7 - 13z + 35 = 5z - 13z - 7 + 35
Evaluate the like terms
5z - 7 - 13z + 35 = -8z + 28
Hence, collecting the like terms gives -8z + 28
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What is the remainder when the following polynomial division is performed? Place the answer in the proper location of the gird. Do not include parentheses in your answer.
The remainder of the polynomial division [tex]\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)}[/tex] is 2y²
How to determine the remainder of the polynomial divisionFrom the question, we have the following parameters that can be used in our computation:
[tex]\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)}[/tex]
When the numerator is expanded, we have
[tex]\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = \frac{(y - 1)(y^3 + 1) + 2y^2}{y^3 + 1}[/tex]
Split the expanded expression
[tex]\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = \frac{(y - 1)(y^3 + 1)}{y^3 + 1} + \frac{2y^2}{y^3 + 1}[/tex]
Evaluate
[tex]\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = y - 1 + \frac{2y^2}{y^3 + 1}[/tex]
From the above, we have
Quotient = y - 1
Remainder = 2y²
Hence, the remainder of the polynomial division is 2y²
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(PLEASE ANSWER ASAP)
Answer:
alternate interior angles are congruent
) 65 people were asked on the activities they engage in during their free time. The results showed that 23 visit national parks, 26 engage in cycling while 22 engage in swimming. Furthermore 9 engage in swimming and visit national parks, 9 engage in swimming only while 11 visit national parks only. How many engage in
i. Swimming and cycling
Answer:
Step-by-step explanation:
i am working on the assumption that nobody does all three of them
i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.
the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.
so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4
Mathematicias pls help me ples
This problem is relatively simple. Before we begin, it might be beneficial to imagine the graph as a vertical number line. Imagining it this way makes it easy to count the units between them and gives you the answer: [tex]$\boxed{4}$[/tex].
Here's a slightly more advanced way to think about it:
The example question tells us to subtract the distance between the two points. The formula for this is [tex]\sqrt{\big{(}(x_{2}-x_{1})+(y_{2}-y_{1})\big{)}^2[/tex], but for this question, let's say that it is [tex]\sqrt{(y_{2}-y_{1})^2[/tex], or, to simplify it even more, [tex]$|y_{2}-y_{1}|$[/tex]. Now that we know the formula, we can substitute our y-values into the last formula and solve. Let's say that Point C is our first point and Point D is our second.
[tex]\big{|}(-8)-(-4)\big{|} = \big{|}-8+4\big{|} = \big{|}-4\big{|} = \boxed{4}[/tex] , so [tex]$4\text{ units}$[/tex] is our answer.
Disclaimer: Neither of the last two formulas I provided is the actual formula, just a version of the Distance Formula that might be easier to understand. The first formula is the actual thing, but you will encounter this in math later in life, probably around 8th or 9th grade.
A lawnmower was discounted 32%. The lawnmower sold for $117.81 including sales tax of 5% of the sale price. What was the original price of the mower?
Step-by-step explanation:
We can begin by using the fact that the selling price was 117.81, including a sales tax of 5%. Let x be the original price of the lawnmower.
After the discount of 32%, the selling price is:
0.68x + 0.05(0.68x) = 117.81
Simplifying and solving for x, we get:
0.68x + 0.034x = 117.81
0.714x = 117.81
x = 165
Therefore, the original price of the lawnmower was $165.
how to find x values
Answer:
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find
A cube has a volume of 216 cubic inches. What is the length of each edge of the cube? A. 9 in. B. 6 in. C. 4 in. D. 3 in.
The length of each edge of the cube = 6 inches, Thus option B is correct.
The volume of a cube = 216 cubic inches,
length of each edge of a cube is an inch
To find the value of a:
The formula for the volume of a cube is [tex]a^{3}[/tex]
The volume of cubic = [tex]a^{3}[/tex]
V = [tex]a^{3}[/tex]
substitute the volume value given in the equation in the above formula
216 = [tex]a^{3}[/tex]
[tex]a = \sqrt[3]{216}[/tex]
[tex]a[/tex] = 6
a = 6inches
Therefore, the length of each edge of the cube is 6 inches.
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ACTIVITY 1 1.1 Resources required: ruler, protractor, compass and coloured pencils Step 1: Draw a horizontal line segment, OM, of any length, the longer the better. Step 1 Solution
The solution to the problem at hand i.e. to draw a horizontal line segment, OM, of any length, the longer the better using ruler, protractor, compass and coloured pencils
are as follows:
Step 1: Take a ruler and align it with a sheet of paper and draw a line. This line can be of any length, although longer lines are preferred.
Step 2: The line is now OM; we must now label its endpoints. Label the leftmost point O, and the rightmost point M.
Step 3: The coloured pencils are used to add decorations to the line. To add decorations, use coloured pencils to make patterns and stripes along the length of the line. This is entirely optional and based on personal preference.
Step 4: To ensure that the line is perfectly horizontal, the protractor should be used. Place the protractor on the line and make sure the zero-degree angle is at O. The line will be horizontal if it is parallel to the baseline of the paper.
Step 5: Using a compass, measure the length of OM to ensure that it is of the desired length.
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What is the sign of -xy? A:Positive B:Negative or C:Zero
The sign of -xy cannot be determined without knowing the signs of x and y. It can be positive, negative, or zero.
The signs of x and y influence the sign of -xy. A positive result is produced when multiplying two numbers with the same sign (both positive or both negative), while a negative result is produced when multiplying two numbers with opposite signs (one positive and the other negative). Their product is 0 when either one or both of the values are zero.
Therefore, depending on the signs of x and y, the sign of -xy can be positive, negative, or zero.
-xy is negative if x and y are both positive.
-xy is positive if x and y are both negative.
Regardless of the sign of the other number, if either x or y is zero, then -xy is also zero.
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The figure below is a square. Find the length of side x in simplest radical form with
rational denominator.
Answer: [tex]x=2\sqrt{5}[/tex]
Step-by-step explanation:
Detailed explanation is attached below.
What is the meaning of "inductive set"?
In mathematics, an inductive set is a collection of elements that satisfies certain properties based on the principle of mathematical induction.
What is an inductive setIt is a fundamental concept in set theory and mathematical reasoning.
The principle of mathematical induction states that if we have a property or statement that holds for a base case (usually the smallest element or a specific starting point) and if we can prove that whenever the property holds for a particular element, it also holds for the next element, then the property holds for all elements in the set.
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If A={o,b,s,e,r,v,a,n,t,l,y} and U={a,b,c,d,e,f,g,h,I,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z} find [A’]
Answer:
[A'] = {c,d,f,g,h,i,j,k,m,n,p,q,u,w,x,z}
Step-by-step explanation:
[A'] is read as the set of A complement, which is all the elements from the universal set that are not contained in set A.
Therefore, [A'] = {c,d,f,g,h,i,j,k,m,n,p,q,u,w,x,z}
Which of the following shows a 90° counterclockwise rotation of the blue figure
help pleaseee bestanswer will get brainly
The central angle of the given circle is seen as: ∠GQH
How to identify the central angle?A central angle of a circle is defined as an angle that exists between two radii with the vertex at the center. The central angle of an arc is also defined as the central angle subtended by the arc. The measure of an arc is the measure of its central angle.
We are given the arc name as Arc GEH.
From the definition above, it is very clear that the central angle will be ∠GQH because it includes the two radii with the vertex at the center.
Thus, we conclude that the correct central angle from the given arc is stated as ∠GQH
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In a health club, research shows that on average, patrons spend an average of 42.5 minutes
on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally
distributed variable. Find the probability that randomly selected individual would spent
between 30 and 40 minutes on the treadmill.
0,30
0.70
0.40
Less than 1%
Answer:
0.30
Step-by-step explanation:
To find the probability that a randomly selected individual would spend between 30 and 40 minutes on the treadmill, we need to calculate the z-scores corresponding to these values and then use the z-table or a statistical calculator to find the probability.
First, we calculate the z-scores using the formula:
z = (x - μ) / σ
where x is the value (in this case, 30 and 40), μ is the mean (42.5), and σ is the standard deviation (4.8).
For x = 30:
z = (30 - 42.5) / 4.8 ≈ -2.604
For x = 40:
z = (40 - 42.5) / 4.8 ≈ -0.521
Next, we look up the probabilities associated with these z-scores in the z-table or use a statistical calculator.
From the z-table or calculator, the probability corresponding to z = -2.604 is approximately 0.0047, and the probability corresponding to z = -0.521 is approximately 0.3015.
To find the probability between 30 and 40 minutes, we subtract the probability associated with z = -2.604 from the probability associated with z = -0.521:
P(30 ≤ x ≤ 40) = P(z = -0.521) - P(z = -2.604)
≈ 0.3015 - 0.0047
≈ 0.2968
Therefore, the probability that a randomly selected individual would spend between 30 and 40 minutes on the treadmill is approximately 0.2968, which is equivalent to 29.68%. Rounding up we will get 0.30.
Hope this helps!
Peggy designed a pond for her backyard. She'll surround
a square patio area with a round pond. Her design and
the scale she'll use to build the design are both shown
below.
It will cost $6 per square foot to dig out the pond portion
of the yard and $1.75 per square foot to build the patio
area.
Approximately how much will she spend constructing the
pond and patio in her backyard?
Scale
1 cm = 5 ft.
A $551.80
B $1,459
C
$2.575
2 cm
2 cm
Patio
4 cm
Pond
***||| theres another answer which is D. 7,111” but it got cutt off lol|||***
Answer:Peggy will spend approximately $363.52 constructing the pond and patio in her backyard. The correct answer is not provided among the options given (A, B, C).
Step-by-step explanation:
To calculate the cost of constructing the pond and patio in Peggy's backyard, we need to determine the areas of the pond and patio and then multiply them by their respective costs per square foot.
From the given scale, we can convert the dimensions of the pond and patio from centimeters to feet. According to the scale, 1 cm represents 5 ft.
Patio dimensions:
Width: 2 cm (2 cm * 5 ft/cm = 10 ft)
Length: 2 cm (2 cm * 5 ft/cm = 10 ft)
Area of patio = Width * Length = 10 ft * 10 ft = 100 ft²
Pond dimensions:
Width: 4 cm (4 cm * 5 ft/cm = 20 ft)
Length: 4 cm (4 cm * 5 ft/cm = 20 ft)
Area of pond = π * (Width/2)² = π * (20 ft/2)² = π * 10 ft² ≈ 31.42 ft²
Cost calculation:
Cost of pond = Area of pond * Cost per square foot = 31.42 ft² * $6/ft² = $188.52
Cost of patio = Area of patio * Cost per square foot = 100 ft² * $1.75/ft² = $175.00
Total cost = Cost of pond + Cost of patio = $188.52 + $175.00 = $363.52
Suppose a normal distribution has a mean of 98 and a standard deviation of 6. What is P ( x <| 104 )
The probability of the data less than or equal to 104 is 84%.
What is the probability of the data less than or equal to 104?The probability of the data less than or equal to 104 is calculated by applying normal distribution formula.
In a standard normal distribution curve, we have the following;
One standard deviation below the mean = M - S.D = 34%
One standard deviation above the mean = M + S.D = 34%
The number of data that would be at 104 is calculated as;
M + S.D = 98 + 6
M + S.D = 104
So we can see that 104 lie at one standard deviation above the mean.
mean = 50%
one standard deviation above the mean = 34%
The total probability = 50% + 34% = 84%
P ( x <| 104 ) = 84%
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Given f(x) = log2 (x+2), complete the table of values for the function -f(x) - 3. Show your work.
Answer:
-6
Step-by-step explanation:
If we convert the first function to the second form we get f(x) = -log2 (x+2) - 3. If we replace x with 6 we get ( -log2 8 ) -3. -log2 8 is equal to -3. -3 - 3 = -6.
George and Manuel had a roofing business George as owner of the materials received $3 for every $2 manual received on a job that paid $750 what amount did each receive
Manuel received $187.50, and George received $562.50 for the job.
Let's break down the information provided:
The job paid a total of $750.
George received $3 for every $2 that Manuel received.
To determine the amounts George and Manuel received, we can set up a ratio based on their earnings.
Let's assume Manuel's earnings as the base amount:
George's earnings : Manuel's earnings = $3 : $2
We can set up the following equation to solve for Manuel's earnings:
(Manuel's earnings / Manuel's earnings) = ($2 / $2)
Since the ratio is equivalent, we can say:
George's earnings / Manuel's earnings = $3 / $2
To find the amount each person received, we'll assign a variable to Manuel's earnings. Let's call it "x."
Therefore, George's earnings can be represented as "3x."
According to the given information, their total earnings should sum up to $750:
x + 3x = $750
Combining like terms, we have:
4x = $750
To solve for x, we divide both sides by 4:
x = $750 / 4
x = $187.50
Now, we can determine the amounts each person received:
Manuel's earnings = x = $187.50
George's earnings = 3x = 3 * $187.50 = $562.50
Therefore, Manuel received $187.50, and George received $562.50 for the job.
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For the athletic banquet one adult ticket cost is $15.00 and one student ticket cost $10.00 One hundred forty were sold for a total of $1600
is it possible to have 131 quests in a particular arrangement?
Answer:
yes
Step-by-step explanation:
by what percent will a fraction change if its numerator is decreased by 60% and its denominator is decreased by 20%
These shapes are similar.
Find X.
5
5
30
24
30
Answer: 4
Step-by-step explanation:
This figure is a rectangular prism.
Select ALL figures that are NOT formed by a horizontal
slice parallel to the base.
A
B
C
D
square
right triangle
isosceles trapezoid
rectangle
“This figure is a rectangular prism” it says at the top btw”
if u do this ty
The horizontal slice of a rectangular prism will always be a rectangle. Therefore, the correct answers are options A, B and C.
A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.
The horizontal cross section of a rectangular prism will always be a rectangle.
Therefore, the correct answers are options A, B and C.
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The area of the triangle is 360 square millimeters
41 mm on both sides
The height is 40
What is the triangles base, b?
As per the given triangle, the base of the triangle, b, is 360 millimeters.
We may use the formula for the area of a triangle to determine the triangle's base, or b, given its 360 square millimetres in area, 41 mm for each side, and 40 millimetres in height.
The formula for calculating a triangle's area is:
Area = (base * height) / 2
Given that,
Area = 360 square millimetres
Height = 40 mm
Sides = 41 mm
So, 360 = (b * 40) / 2
720 = b * 2
b = 720 / 2
b = 360
Thus, the base of the triangle is 360 mm.
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Fill in the table using this function rule y= - 2x + 3
Step-by-step explanation:
you just have to put that value in place of x in the function.
don't be so lazy you a hole do it yourself
a) What fraction of an hour is 40 minutes, in its simplest b) I sleep 8 hours a night. What fraction of a day is this? c) How many hours is of a day? How many hours is 1 5 pond of her n
a) The value of fraction is,
⇒ 2 / 3
b) The value of fraction is,
⇒ 1 / 3
c) There are 24 hours in a day.
Now, We can simplify all the fraction as,
a) To find fraction of an hour is 40 minutes,
Since, 1 hour = 60 minutes
Hence,
⇒ 40 / 60
⇒ 4 / 6
⇒ 2 / 3
b) Since, 1 day = 24 hours
Hence, we get;
⇒ 8 / 24
⇒ 1 / 3
c) We know that,
⇒ 1 day = 24 hours
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Cuanto mide el largo de un rectángulo cuyo perímetro es 16cm y su área 12 cm al cuadrado ?
5. A conical shaped pile of sand at the beach has a base circumference of 16.5 feet
and stands 10.4 feet high. The Department of Public Works is going to remove
75% of the sand. How much sand will be left in the pile after they remove 75% of
the sand?
Answer: 18.78 cubic feet
Step-by-step explanation:
The detailed analysis is attached below.
Eye Color of Males Surveyed
Green
Blue
5
16
Brown
27
Eye Color of Females Surveyed
Blue
Brown
19
18
Green
3
What percent of students in the survey are either female or have green eyes? Round your answer to the nearest tenth.
About % are either female or have green eyes.
What percent of students in the survey are males who do not have green eyes? Round your answer to the nearest tenth.
About % are males who do not have green eyes.
Find the sum of these two percents.
The sum of these two percents is %.
The sum of the percentage of students who are either female or have green eyes and the percentage of males who do not have green eyes is approximately 99.7%.
How to determine the sum of these two percents.The sum of these two percents is %.Percentage of Females: (1918 / (1918 + 516 + 27)) * 100 = (1918 / 2461) * 100 ≈ 78.0%
Percentage of Students with Green Eyes: ((516 + 3) / (1918 + 516 + 27)) * 100 = (519 / 2461) * 100 ≈ 21.1%
Percentage of Students who are either Female or have Green Eyes: 78.0% + 21.1% ≈ 99.1%
Therefore, approximately 99.1% of students in the survey are either female or have green eyes.
Percentage of Males with Green Eyes: (516 / (516 + 3)) * 100 = (516 / 519) * 100 ≈ 99.4%
Percentage of Males who do not have Green Eyes: 100% - 99.4% ≈ 0.6%
Therefore, approximately 0.6% of students in the survey are males who do not have green eyes.
To find the sum of these two percentages:
Sum of Percentages: 99.1% + 0.6% ≈ 99.7%
Therefore, the sum of the percentage of students who are either female or have green eyes and the percentage of males who do not have green eyes is approximately 99.7%.
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