The possible heights of the parallelogram are 2/3 and 3
So, the correct option is A and C
The given expression:
area of a parallelogram, A = 12 square unit
a side of the parallelogram, = 18 units
another side of the parallelogram = 6 units
let,
the height of the parallelogram, h
The area of a parallelogram is given as;
Area = base (b) x height (h)
height (h) = Area/base(b)
From the given sides, the possible heights of the parallelogram are calculated as follows;
if the base, b = 18 units
height(h) = 12/18
= 2/3
Also, if the base, b = 6 units
height(h) = 12/6
= 2
Therefore, the possible heights of the parallelogram are 2/3 and 2
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You receive an allowance on the first of every month starting on January 1st. Each month, your allowance increases by $2.50. When you sum up all the allowance you received that year in December, it totals $225. Model the amount of allowance you received each month.
Equation?
Continuous or Discrete?
Answer:
Equation is [tex]a_n = 2.50n + 2.50[/tex]
This is discrete
=======================================================
Explanation:
There are n = 12 months in a year.
[tex]a_1[/tex] = first term = x
d = common difference = 2.50, which is the amount the allowance is increasing month to month.
[tex]S_n = \text{Sum of the first n terms of an arithmetic sequence}\\\\S_n = (n/2)*(2a_1 + d(n-1))\\\\S_{12} = (12/2)*(2\text{x} + 2.50(12-1))\\\\S_{12} = 6(2\text{x} + 27.5)\\\\S_{12} = 12\text{x} + 165\\\\[/tex]
The sum of the first n = 12 terms of the arithmetic sequence is 12x+165, where x is the first term (i.e. the allowance on January 1st).
We're told that this total is $225. We'll set the value of [tex]S_{12}[/tex] equal to 225 and solve for x.
[tex]S_{12} = 225\\\\12\text{x} + 165 = 225\\\\12\text{x} = 225 - 165\\\\12\text{x} = 60\\\\\text{x} = 60/12\\\\\text{x} = 5[/tex]
Therefore, you got $5 on January 1st. Then 5+2.50 = 7.50 dollars on February 1st. Then 7.50+2.50 = 10 dollars on March 1st. And so on, until reaching December. All of those dollar amounts then should add to $225 to help confirm the answer.
This equation is discrete because the terms are finite from n = 1 to n = 12. We can't have a midpoint of say between months 3 and 4. It doesn't make sense to have month 3.5 for instance. There's only a set amount of payments.
--------
Now that we know [tex]a_1 = 5[/tex] is the first term, we can then determine the value of any allowance value for any given value of n.
[tex]a_n = \text{nth term of arithmetic sequence}\\\\a_n = a_1 + d(n-1)\\\\a_n = 5 + 2.50(n-1)\\\\a_n = 5 + 2.50n-2.50\\\\a_n = 2.50n + 2.50\\\\[/tex]
Let's see what the allowance would be for month n = 2
[tex]a_n = 2.50n + 2.50\\\\a_{2} = 2.50(2) + 2.50\\\\a_{2} = 5 + 2.50\\\\a_{2} = 7.50\\\\[/tex]
The allowance for month n = 2 (aka February) is $7.50, which was mentioned earlier in the previous section. I'll let you confirm the other values of n.
Keep in mind that n is a positive whole number in the set {1,2,3,...,10,11,12}. It might help to make a table of values.
A concession stand serves hot dogs and
hamburgers at a ratio of 3 to 2. Based on this
ratio, how many hamburgers will be served if
there are a total of 60 hot dogs served? Use a
tape diagram to model your thinking.
Using ratios we know that 40 hamburgers will be served.
What are ratios?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.So, a number of hamburgers that will be served are:
The ratio of hotdogs and hamburgers = 3:2The total number of hotdogs served is 60.So, the number of hamburgers will be:
3/60 = 2/x3x = 60×23x = 120x = 120/3x = 40Therefore, using ratios we know that 40 hamburgers will be served.
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Correct question:
A concession stand serves hot dogs and hamburgers at a ratio of 3 to 2. Based on this ratio, how many hamburgers will be served if there are a total of 60 hot dogs served?
13
The table shows the ratio of teachers to children needed for two activities.
Climbing
Walking
teachers: children
1 : 4
1 :9
(a) There are 7 teachers to take children climbing.
What is the greatest number of children that can go climbing?
Answer:
28
Step-by-step explanation:
You require a teacher : children ratio of at least 1 : 4 for the activity of climbing, and you want to know the greatest number of children that can go climbing with 7 teachers.
SetupWe can describe this problem by the inequality ...
teachers/children ≥ 1/4
7/children ≥ 1/4 . . . . . for 7 teachers
Solutionmultiplying by (4·children) gives ...
28 ≥ children
At most, 28 children can go climbing.
Express using exponents and simplify any numerical coefficients: 2 · 2 · y · y · y · y
Answer:
4 x y
Step-by-step explanation:
y x y x y x y = y
2 x 2 = 4
4 x y
A dressmaker sells a shirt for $75. If she makes a 25% profit, how much did it cost her to make the shirt?
Answer: $56.25
Step-by-step explanation:
x = cost to make the shirt
x + 75(0.25) = 75
x = 75 - 18.25 = 56.25
To set up a wireless network for internet access at home, you buy a network
router for $75.00. The fee for internet service is $18.00 per month.
a. Write an expression for the amount of money you spend in n months.
b. How much money will you spend in 12 months? Show your work.
a.) Expression for the amount of money is 75+18n
b.) money spend in 12 months is $291
From the question, we have
Buy a network router for $75.00. The fee for internet service is $18.00 per month.
a.) Expression for the amount of money (y) is,
y = 75+18n
b.) money spend in 12 months = 75+18*12
= $291
Addition:
The phrase "the addition" refers to the combining of two or more integers. Three is written as three plus three since the plus sign (+) signifies the sum of two integers. The frequency with which the plus symbol (+) is used is likewise under your control. for example, 3 + 3 + 3 + 3. The teaching of addition in math to children is crucial. In primary school, students learn fundamental addition sums, such as one-digit facts, math addition sums, and double-digit arithmetic addition sums. One of the most fundamental and exciting Math concepts for primary school children is sums in addition. Because math is a fascinating subject, children begin learning basic mathematical concepts like adding numbers in their early years.
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a hammer get 300miles on 20 gallons of gas. How many miles can it cover on 50 gallons of gas
Answer:
750 miles
Step-by-step explanation:
20 gallons -------------- 300 miles
1 gallon ---------------- 300/20 = 15 miles
50 gallons -------------- 15x50 = 750 miles
Regional erosion occurs at a rate of 2 m per 1,000 years. How much regional erosion will occur over 1,000,000 years? responses 20 m 20 m 200 m 200 m 2,000 m 2,000 m 100,000 m.
The erosion occurs at a rate of 2/1000 m/years. Over 1,000,000 years, the erosion will be 2,000 meters.
Rate is a ratio between one quantity to another quantity. Rate is also a measure of how fast a quantity changes when another quantity changes. For instance, velocity is a rate to measure the change of distance per amount of travelled time.
Suppose we have two quantities: x and y, with rate of change in y per change in x is denoted by dy/dx, then
y = dy/dx · x
In the given problem:
y = length of erosion
t = time
dy/dt = 2 meters / 1000year = 2/1000 meters/year
Then,
y = dy/dt · t
= 2/1000 · 1,000,000 = 2,000 meters
Hence, over 1,000,000 years, the regional erosion = 2,000 meters
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Question 5 (1 point)
What is the best description for the lines represented by these equations?
y = 4x + 3
y=-4x-2
a.Parallel
b.Perpendicular
c.Neither
Answer:
-2x + 15.
Step-by-step explanation Perpendicular lines have slopes that are opposite reciprocals of each other. Therefore, the slope of the line is -2. When we solve for the y-intercept, the result is 15.
Is the following statement a good definition? A cat is an animal that is a mammal
yes or no?
Answer:
yes
Step-by-step explanation:
A cat is a domestic species of small carnivorous mammal. It is the only domesticated species in the family Felidae and is often referred to as the domestic cat to distinguish it from the wild members of the family. A cat can either be a house cat, a farm cat or a feral cat; the latter ranges freely and avoids human contact.
So, it will be considered as a yes.
Given the polynomial f(x)= 2x^3-x^24x4
, what i the mallet poitive integer a uch that the intermediate value theorem guarantee a zero exit between 0 and a ?
The smallest positive integer a such that the intermediate value theorem guarantee a zero exist between 0 and 1
given that
polynomial f(x) = 2[tex]x^{3}[/tex] - [tex]x^{2}[/tex]- 4x+4
first derivation of f(x)
f'(x) = 6[tex]x^{2}[/tex] - 2x - 4
= 6[tex]x^{2}[/tex] - 6x +4x -4
= 6x(x-1) + 4(x-1)
= (6x+4)(x-1)
x = -0.6,1
second derivation of f(x)
f''(x) = 12x-2
now substitute x values in f''(x)
x=1
f"(x) = 12(1) - 2 = 12-2= 10
x= -0.61
f"(x) = 12(-0.61) -2 = -7.32-2= -9.32
a=1
the intermediate value theorem guarantee a zero exist between 0 and 1
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can someone please help me?
Using the volume formula, the height of the cylinder is [tex]h = \frac{v}{\pi r^{2} }[/tex]
How to solve for height in a cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.
In other words, a cylinder is a geometric solid with two circular bases joined by a curved surface.
The volume of a cylinder can be represented as follows:
The formula to calculate volume of a cylinder is given by the product of base area and its height
v = πr²hwhere
h = height of the cylinderr = radius of the cylinderTherefore, the question asked us to solve for height, h.
Hence, let's make height the subject of the formula.
v = πr²h
divide both sides by πr²
[tex]\frac{v}{\pi r^{2} }=\frac{\pi r^{2} h}{\pi r^{2} }[/tex]
Therefore,
[tex]h = \frac{v}{\pi r^{2} }[/tex]
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A fast-food restaurant offers delivery service anywhere within a 6-miles radius. What area does the restaurant delivery service cover? Round your answer to the nearest square mile.
The restaurant delivery service cover the area 113.04 miles².
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
A fast-food restaurant offers delivery service anywhere within a 6-miles radius.
Now,
The area cover by delivery service = πr²
Here, r = 6 miles
Thus, The area cover by delivery service = πr²
= 3.14 x 6²
= 3.14 x 36
= 113.04 miles²
Therefore, The restaurant delivery service cover the area 113.04 miles².
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what is the answer to 365 x 240?
Answer:87,600
Step-by-step explanation:
What is the equation in slope intercept form of the line that passes through the y-intercept (0, 1) and has a slope of 4?
Responses
y = 4x - 1
y = 4x - 1
y = 4x - 11
y = 4x - 11
y = 4x + 11
y = 4x + 11
y = 4x + 1
The equation in slope intercept form of the line that passes through the y-intercept (0, 1) and has a slope of 4 is y = 4x + 1
The line is passing through the y intercept = (0, 1)
Here at x = 0, the values of y = 1
Then the y intercept of the line is 1
The slope of the line = 4
The slope of the line is the change in y coordinate with respect to the change in x coordinates of the function
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
x is the x coordinate
y is the y coordinate
Then the equation in the slope intercept form
y =4x + 1
Hence, the equation in slope intercept form of the line that passes through the y-intercept (0, 1) and has a slope of 4 is y = 4x + 1
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A sequence of patterns is made from circular tiles and square tiles
Here are the first three patterns in the sequence.
ooo
a b
000
pattern number 1 pattern number 2
pattern number 3
a) How many square tiles are needed to make pattern number 7?
b) How many circular tiles are needed to make pattern number 20?
c) When the pattern number is odd, the total number of tiles (square
and circular) needed to make the pattern
A will always be even B will always be odd C could be even or odd
(2)
(2)
(2)
a) 49 square tiles are needed to make pattern number 7
b) 84 circular tiles are needed to make pattern number 20
c) When the pattern number is odd, the total number of tiles (square
and circular) needed to make the pattern is B) always odd
What is meant by sequence?A sequence in mathematics is an enumerated collection of objects in which repetitions are permitted and order is important. It, like a set, has members (also called elements, or terms). The length of the sequence is defined as the number of elements (which could be infinite). Unlike a set, the same elements can appear multiple times in a sequence at different positions, and the order does matter. Formally, a sequence can be defined as a function from natural numbers (the sequence's positions) to the elements at each position. The concept of a sequence can be extended to include an indexed family, which is defined as a function from an arbitrary index set.
a) Squares tiles needed for 7 pattern =n²
n²=7²
n²=49
b) Circular tiles for 20th pattern=4(n+1)
=4(20+1)
=4(21)
=84
c) Total tiles(square and circle)
=n²+4(n+1)
for n=odd (let n=1,3,5)
n=1; 1+4(1+1)=9
n=2; 9+4(3+1)=25
n=5; 25+4(5+1)=49
Therefore, It is always odd
So, the answer is option B
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love = what? what will happen to the rest couples
Answer: love=an intense feeling of deep affection
Step-by-step explanation:
Encuentra todos los ceros X³ +9x²+26x+24 si (x+3) es un factor
The simplified value of the expression (x³ + 9x²+ 26x + 24), when divided by (x + 3), is: the quotient will be x^2 + 6x + 8 and the remainder will be 0. (x + 3) will be a factor of (x³ + 9x²+ 26x + 24).
Let us solve the given algebraic expression by the long division method:
We are given the expression:
(x³ + 9x²+ 26x + 24) and (x + 3)
We need to perform the division of the given algebraic expression:
x + 3 ) x^3 + 9x^2 + 26x + 24 ( x^2 + 6x + 8
x^3 + 3x^2
- -
6x^2 + 26x + 24
6x^2 + 18x
- -
8x + 24
8x + 24
- -
0
So,
quotient = x^2 + 6x + 8
remainder = 0
As the remainder is 0.
So, (x + 3) will be a factor of (x³ + 9x²+ 26x + 24)
Thus, the simplified value of the expression (x³ + 9x²+ 26x + 24), when divided by (x + 3), is: the quotient will be x^2 + 6x + 8 and the remainder will be 0. (x + 3) will be a factor of (x³ + 9x²+ 26x + 24).
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a factory makes trash bags using plastic pellets. th plastic pellets are placed in barrels which are then poured into a machine. when the machine is operating the change to a barrel of pellets is 3 kg per minute. Each full barrel contains 18 kg of plastic pellets. are there enough pellets in a full barrel for the machine to make bags for 5 minutes.
Yes, there is enough weight of plastic pellets in a full barrel for the machine to make trash bags for 5 minutes.
It is given that the factory makes trash bags using plastic pellets. The plastic pellets are placed in barrels. The barrels containing the plastic pellets are then poured into a machine. When the machine is operating, the change from a barrel of pellets to the trash bags is 3 kg per minute. Each full barrel contains 18 kg of plastic pellets.
We need to check if there are enough pellets in a full barrel for the machine to make trash bags for 5 minutes. Let the time for which the machine can make the bags from a single barrel of plastic pellets be denoted by the variable "t". The time taken by the machine to fully convert a barrel full of plastic pellets into trash bags is the ratio of the total weight of plastic pellets in the barrel to the rate of conversion of the plastic pellets into trash bags.
t = 18/3
t = 6
Hence, the machine can convert a barrel of plastic pellets into trash bags in a time duration of 6 minutes. So, there are enough pellets in a full barrel for the machine to make bags for 5 minutes.
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the volume of a rectangular prism is given by 33x3+71x2+54x+24. the height of the prism is given by 3x+4. find an expression for the area of the base of the prism.
The expression for the rectangular prism's base area is 11x² + 7x + 5.
Given;
The volume of rectangular prism = 33x³ + 43x² + 29x + 10
The height of the prism = 3x + 2
We know that, the area of the prism = length * breadth
where as, volume = length * breadth * height
So, area = volume / height
Using synthetic division, dividing volume by height, we get;
3x+2 ) 33x³ + 43x² + 29x + 10 ( 11x² + 7x + 5
33x3 + 22x2
---------------------------------
21x² + 29x
21x² + 14x
----------------------------------
15x + 10
15x + 10
----------------------------------
x
Quotient is 11x² + 7x + 5 which is equal to expression for the area of the base of the rectangular prism.
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kent spent 5/6 hour washing dishes on Monday as shown on the number line . kent washed dishes for the same amount of time on Tuesday and Wednesday. much time did kent spend washing dishes during those 3 days
Answer:150 minutes easy?
Step-by-step explanation:
a) Factorise x^2+ 5x + 6
Step-by-step explanation:
[tex] {x}^{2} + 5x + 6[/tex]
[tex] {x}^{2} + 6x - x + 6[/tex]
[tex]x(x + 6) - 1(x + 6)[/tex]
[tex](x - 1)(x + 6)[/tex]
3. Choose the correct answer.
Which theorem or postulate could be used to prove the congruence of the triangles?
|x-3| = |9-2x| solve the following question
Answer:
x = 4 or x = 6
Step-by-step explanation:
to solve the inequality
solve both
x - 3 = 9 - 2x OR x - 3 = - (9 - 2x)
x - 3 = 9 - 2x ( add 2x to both sides )
3x - 3 = 9 ( add 3 to both sides )
3x = 12 ( divide both sides by 3 )
x = 4
OR
x - 3 = - (9 - 2x)
x - 3 = - 9 + 2x ( subtract 2x from both sides )
- x - 3 = - 9 ( add 3 to both sides )
- x = - 6 ( multiply both sides by - 1 )
x = 6
Gary is buying a $1,250 computer on an installment plan. He makes a down payment of $150. He has to make monthly payments of 48.25 for 2 1/2 years. What is the total finance charge?
Answer:
Step-by-step explanation:
Down payment = $150
Monthly Payment = $48.5
Buyer price = $1250
Number of months = 30 (2 1/2 years)
The total amount of monthly payments = Monthly payments × Number of months
= 48.5 × 30
= 1447.50
The total cost = Total amount of monthly payments + Down payments
= 1447.50 + 150
= 1597.50
Finance charge = Total cost - Buyer price
= 1597.50 - 1250
= 347.50
0
10
5
13
4. (04.02 MC)
What is the remainder when (3x4 + 2x³ + x² + 2x − 19) ÷ (x + 2)? (6 points)
Answer:
5
Step-by-step explanation:
Since we have given that
Let f(x) = 1 + x + x^2. Use the Mean value Theorem to show that there is a real number c,0 < c < 2, such that f(2) - f (0) = f'(c) (2 - 0). Find all such c. Show your work in the space provided.
The value o f c based on The Mean Value Theorem is 1
The Mean Value Theorem stated that if f(x) is a continuous on [a,b] and differentiable on (a,b) then there is a c such that:
f'(c) = [tex]\frac{f(b)-f(a)}{b-a}[/tex] ... (i)
Based on the question, we got equations:
f(x) = 1 + x + x² ... (ii)
By using derivative, we get:
f'(x) = 1 + 2x ... (iii)
From the question, we get:
f(a) = f(0)
f(b) = f(2)
Then we need to find the value of both f(0) and f(2):
f(0) = 1 + (0) + (0)²
f(0) = 1 ... (iv)
f(2) = 1 + (2) + (2)²
f(2) = 7 ... (v)
We also need to find the equation for f'(c) based on equation (iii):
f'(x) = 1 + 2x
f'(c) = 1 + 2c ... (vi)
We will input equations (iv) and (v) into equation (i) to find another equation of f'(c):
f'(c) = [tex]\frac{f(2)-f(0)}{2-0}[/tex]
f'(c) = [tex]\frac{7-1}{2-0}[/tex]
f'(c) = [tex]\frac{6}{2}[/tex]
f'(c) = 3 ... (vii)
Then we will subtitute the equation (vi) with equation (vii) to find the value of c:
f'(c) = 1 + 2c
3 = 1 + 2c
2c = 2
c = 1... (viii)
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Sally earns $37.00 for 4 hours of babysitting. At this rate, how much more would she eam for 9 hours of babysitting? 6.RP.3 Step 1: Find the Unit rate of how much Sally makes per hour?
Find the Error A student found the slope of one segment on a line to be 4 and the slope of another segment on the same line to be 8/2. He concludes that the slope is different at different points on the line. Correct his thinking.
The slopes are similar in each segment of the line because the ratios, 8/2 and 4/1 are similar.
What is the slope of the triangle?The first step to understanding slope of a line is that; it represents the rate of change in the vertical axis to that in the horizontal axis.
Consequently, it follows that the slope of the first segment can be computed by drawing a triangle with vertical side length of 4 and a horizontal side length of 1.
Hence, the slope of the first segment (from the triangle is) 4 / 1.
Also, for the second segment; a triangle with vertical length; 8 and a horizontal length, 2. Hence, the slope of the segment is; 8 / 2.
Ultimately, since the ratios, 8 / 2 and 4 / 1 are similar, it follows that the two triangles are similar and consequently, the slope is same in each segment of the line.
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On a certain hot summer's day, 559 people used the public swimming pool. The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $1001.25. How many children and how many adults swam at the public pool that day?
The word problem of swimming pool resulted to a simultaneous equation and the solution is
the number of adults in the pool is 242
the number of children in the pool is 317
How to determine the number of adult or children in the swimming poolThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
let the number of adults in the pool be x
let the number of children in the pool be y
559 people used the public swimming pool
559 = x + y
The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $1001.25
1.25y + 2.50x = 1001.25
Hence:
x + y = 559
1.25y + 2.50x = 1001.25
solving the equation gives
y = 317
x = 242
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