Describe how to model -3x + 7=28 with algebra tiles
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Related Questions
Which of the following activities are examples of data organization and analysis? Check all that apply.
A. Rejecting spoiled ballots
B. Running a polling station on voting day
C. Transferring votes from ballots to tally sheets
D. Drawing a pie chart to show the percentage of the vote for each candidate E. Counting votes for each candidate in the election
Answers
Which of the following activities are examples of data organization and analysis?
Data organisation is a method of organizing data sets. And data analysis means logically analyzing and evaluating data.
So, the correct answers will be :
C. Transferring votes from ballots to tally sheets
D. Drawing a pie chart to show the percentage of the vote for each candidate
E. Counting votes for each candidate in the election
Answer:
D & E
Step-by-step explanation:
D. Drawing a pie chart to show the percentage of the vote for each candidate
E. Counting votes for each candidate in the election
These involve sorting and graphical analysis
How can you use subtraction to describe division?
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average of the set of data 3.2 16.5 9.1
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[tex]First[/tex]: [tex]3.2 + 16.5 + 9.1 = 28.8[/tex]
[tex]Second: [/tex] your [tex]sum[/tex] is - [tex]5 [/tex]
[tex]Third:[/tex] finding our answer [tex] \frac{2.28}{5} = 5.76[/tex]
Your [tex]average [/tex]of this [tex]set [/tex] is:[tex] 5.76 [/tex]
A football is kicked at 40 yards away from a goal post that is 10 feet high. Its path is modeled by y = -0.03x 2 + 1.6x, where x is the horizontal distance in yards traveled by the football and y is the corresponding height above the ground in feet.
Does the football go over the goal post? How far above or below the goal post is the football? Use two or more complete sentences to explain your answers. (Hint: The unit conversion is built into the given function.)
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16>10
Yes, the ball clears the goal by 6 feet.
The annual Gross Domestic Product (GDP) of a country is the value of all of the goods and services produced in the country during a year. During the period 1985-1999, the Gross Domestic Product of the United States grew about 3.2% per year, measured in 1996 dollars. In 1985, the GDP was $577 billion. I what year did/or will the GDP equal $1.8 trillion?
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GDP = 577 * (1.032) ^ t, where GDP is in billion dollars and t is the time in years since 1985.
year t (in years) GDP (in billion dollars)
1985 0 577
1986 1 577* 1.032 = 595.46
1987 2 577 * (1.032)^2 = 614.52
1988 3 577 * (1.032)^3 = 634.18
? t 577 * (1.032)^t
Then, GDP = 1.8 trillion = 1800 billion = 577 * (1.032)^ t
=> (1.032)^t = 1800 / 577
=> t log (1.032) = log (1800 / 577)
=> t = log (1800 / 577) / log (1.032) = 36.12
Therefore, if the growth rate keeps in 3.2% per year, the GDP will equal 1.80 trillion 36 years after 1985 => 1985 + 36 = 2021.
Answer: 2021
Find the future value and interest earned if $8906.54 is invested for 9 years at 6% compounded continuously
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For an investment of $8906.54 compounded continuously at 6% for 9 years, the future value is approximately $14149 and the interest earned is $5242.46.
Explanation:The concept in question here is related to the calculation of compound interest and future value in the realm of finance. Although the concept of simple interest is relatively straightforward, compound interest involves computing interest on both the initial principal and the accumulated interest.
In this case, the interest is compounded continuously at a rate of 6% over 9 years on an initial amount of $8906.54. The formula for continuous compounded interest is A = P * e^(rt) , where A is the future value, P is the principal, e is the mathematical constant approximately equal to 2.71828, r is the interest rate (in decimal form), and t is the time in years.
To find the future value: A = $8906.54 * e^(0.06*9) = $14149. Therefore, the future value of the investment is approximately $14,149.
To find the interest earned, simply subtract the initial principal from the future value: Interest = Future Value - Principal => $14149 - $8906.54 = $5242.46. Therefore, the interest earned over this period is approximately $5242.46.
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you put $1205 in an account that earns 2.5% simple interest. Find the total amount in the account after four years
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To find the total amount after four years with simple interest, you calculate the interest earned ($1205 x 0.025 x 4 = $120.50) and then add it to the principal ($1205 + $120.50 = $1325.50).
To calculate the total amount in the account after four years with simple interest, we use the formula:
Simple Interest (SI) = Principal (P) x Rate (R) x Time (T)
For the given scenario:
Principal (P) = $1205Rate (R) = 2.5% or 0.025 (as a decimal)Time (T) = 4 yearsWe first calculate the simple interest earned:
SI = $1205 x 0.025 x 4 = $120.50
The total amount in the account after four years will be the sum of the principal and the simple interest earned:
Total Amount = Principal + Simple Interest
Total Amount = $1205 + $120.50 = $1325.50
For which values of p and q does the following equation have infinitely many solutions?
PX + Q = 46x +23
A) p = 46 & q = 23
B) p = -46 & q = 23
C) p=-46 & q = -23
D) p= 46 & q = -23
(Select all that may apply)
Answers
p x + q = 46 x + 23
p x - 46 x = 23 - q
x ( p - 46 ) = 23 - q
x = ( 23 - q ) / ( p - 46 )
This equation has infinitely many solutions for :
23 - q = 0 and p - 46 = 0
or: q = 23 and p = 46
Answer : A ) p = 46 & q = 23
9.744 divided by 0.87
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Monty is cutting 45 streamers into pieces that are each 5 2/5 feet long. If the streamers are laid end to end,how far will they stretch
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Answer:
39 3/5
Step-by-step explanation:
If the wheels of a train make 16 revolutions when it rolls a distance of 60 feet, what is the radius of the wheel?
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(16/16) revolutions = (60/16) feet
1 revolution = 3.75 feet
This means that when the train wheel rotates a full 360 degrees, the train has moved 3.75 feet. Put another way, the circumference around the train wheel is 3.75 feet.
C = 3.75
We'll use this C value to find the radius r
C = 2*pi*r
3.75 = 2*pi*r
r = 3.75/(2*pi)
r = 0.5968 (this is approximate rounded to 4 decimal places)
Therefore the radius of the wheel is approximately 0.5968 feet
Logan county is square. It had a side that is 15.4 miles long. What is the area?
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A=x^2 where x is its side length, in this case 15.4 miles
A=15.4^2
A=237.16 mi^2
A=s•s where s represent the side of his county which is 15.4 miles long, so we just beed to do now is substitute s with 15.4
A=s•s
A=15.4•15.4
A=237.16 square miles. As a result, the area of Logan's County is 237.16 square miles. Hope it help!
What is the equation of the following graph in vertex form? parabolic function going down from the left through the point negative four comma zero and turning at the point negative three comma negative one and going up through the point negative two comma zero and then through the point zero comma eight and continuing up towards infinity
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(x-h)^2 = +/- 4a(y-k) or (y-k)^2 = +/- 4a(x-h), where
(h,k) is the coordinates of the vertex
4a is the lactus rectum
a is the distance from the focus to the vertex
This is also called vertex form because the vertex (h,k) is grouped according to their variable.
Since we don't know any of those parameters, we'll just have to graph the data points given as shown in the picture. From this data alone, we can see that the parabola has two x-intercepts, x=-4 and x=-2. Since it has 2 roots, the parabola is a quadratic equation. Its equation should be
y = (x+4)(x+2)
Expanding the right side
y = x²+4x+2x+8
y = x²+6x+8
Rearrange the equation such that all x terms are on one side of the equation
x²+6x+___=y-8+___
The blank is designated for the missing terms to complete the square. Through completing the squares method, you can express the left side of the equation into (x-h)² form. This is done by taking the middle term, dividing it by two, and squaring it. So, (6/2)²=9. Therefore, you put 9 to the 2 blanks. The equation is unchanged because you add 9 to both sides of the equation.
The final equation is
x²+6x+9=y-8+9
(x+3)²=y+1
Ahmad has scored 11, 25, 27, 25, and 25 points in his five basketball games so far. How many points does he need to score in his next game so that his average (mean) is 23 points per game?
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(113 + x) / 6 = 23
113 + x = 23 * 6
113 + x = 138
x = 138 - 113
x = 25 <== he needs a 25
Why is it important to have categories of numbers in to know which category you're doing with the given expression
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A way to categorize information and point you to where to find that information is called the table of contents. It contains the chapters of the topic and its corresponding subtopic. It depends on the length of the topic of that book or section. It is located at the first few pages of the book or other reading material.
Find the volume of the largest right circular cone that can be inscribed in a sphere of radius 8
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The volume of a cone is given
V= 1/3(πr²h)
We will use some Calculus to find the maximum volume of the cone, but first, we need to get V in one term only, either in term of 'r' or in term of 'h'
Referring to the diagram, we can start with the right-angle triangle that has two short sides; the radius of the cone and the (h-r) and the hypotenuse 'R' which is the radius of the sphere.
Forming an equation based on Pythagoras theorem
r² = R² - (h-R)² ⇒ We know that R = 8
r² = 8² - (h - 8)²
r² = 64 - (h² - 16h + 64)
r² = 64 - h² + 16h - 64
r² = 16h - h²
Substitute r² = 16h - h² into the formula for V, we have
V = 1/3 (π) (16h - h²) h
V = 1/3 (π) (16h² - h³)
V = (16/3)πh² - (1/3)πh³
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Now we have V in term of 'h', we will use Calculus to find the value of 'h' that will give the maximum value of V
First, we will differentiate V, then set dV/dh = 0
V = (16/3)πh² - (1/3)πh³
dV/dh = (32/3)πh - πh²
Setting dV/dh = 0
0 = (32/3)πh - πh²
0 = πh [(32/3) - h]
πh = 0 and (32/3) - h = 0
h = 0 and h = 32/3
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The value of h that we will choose is h = 32/3 since h = 0 is unlikely
Substituting h = 32/3 back into V, we have
V = 1/3 (π) [16 (32/3)² - (32/3)³]
V = 1/3 π × 606.814
V = 635.5 units³
The maximum volume of a cone within a sphere is achieved when the apex of the cone is at the centre of the sphere and the base of the cone is at the sphere's surface. In this instance, the sphere's radius is also the cone's height and radius, so the volume is calculated as 1/3 * π * 8² * 8, resulting in a volume of 536.48.
Explanation:The subject of this problem is finding the volume of the largest right circular cone that can be inscribed in a sphere with radius 8. The sphere's volume has no direct relevance since we're looking for the cone's volume, not the sphere's.
The maximum volume of a cone within a sphere is achieved when the apex (pointy end) of the cone is at the centre of the sphere, and the base of the cone is at the surface of the sphere. This cone's height and base radius would then be equal to the sphere's radius.
The formula for the volume of a cone is V = 1/3 * π * r² * h . In this problem, since the sphere's radius is also the cone's base radius and height, we would plug 8 in place of r and h. So the answer would be V = 1/3 * π * 8² * 8 which gives us V = 536.48 cubic units .
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Say, there is 88 students for 4 classes whats the unit rate?
A: 22 students per class
B: 22 classes per student
C: 25 Students per class
D: 25 classes per student
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Answer:
a. 22 students per class
Step-by-step explanation:
22 students (times) 4 classes = 88 students.
What is the area of the shaded region?
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area of larger triangle = 1/2 x 5 x (6+4+2) =30 square mm
area of non shaded triangle = 1/2 x 3 x 4 = 6 square mm
area of shaded area = 30-6 = 24 square mm
Larger Shape
1/2bh=1/2*5*12=30
Smaller Shape
1/2bh=1/2*4*3=6
Shaded Area
30-6=24
The area of the shaded region is 24mm squared.
In one week a gas station sells 1,250 gallons of gas. On average, how many quarts did they sell each day during that week? Round your answer to the nearest hundredth. Hint: there are 4 quarts in a gallon.
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Answer:
the actuall awnser is 714.28
Step-by-step explanation:
1250*4=5000
5000/7=714.28
Answer:
the gas station sold 714.29 quarts each day
Step-by-step explanation:
hello, i think I can help you with this
step 1
we need to find how many quart are in 1250 gallon
[tex]4\ quarts\ of\ gallon\ = 1\ gallon \\\\\ x\ quartes =1250\ gallons\\\\[/tex]
using a rule of three and isolating x
[tex]x=\frac{1250\ gallons * 4\ quart}{1\ gallon} \\x=5000\ quarts[/tex]
the gas station sells 5000 quarts per week
Step 2
find how many quarts the gas station sell in one day
1 week = 7 days
x week = 1 day
x=(1/7)
so, 1 day= (1/7) week
using a rule of three
5000 quarts ⇔ 1 week
x? quarts ⇔ (1/7) week
[tex]x=\frac{5000*\frac{1}{7} }{1\ week} \\\x=714.285\ quarts\\[/tex]
the gas station sells 714.29 quarts each day
Have a great day
What is the area, in square units, of the polygon shown here? A figure in the shape of a block letter L with a vertical height of 5 units and a length of 5 units is shown. The length of the top of the L is 2 units and the height of the right side of the L is 1 unit. 10 units2 13 units2 15 units2 18 units2
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A = 5² - ( 3 · 4 ) = 25 - 12 = 13 units²
Or we can find the sum of two rectangles ( 4 x 2 units and 5 x 1 unit ) :
A = 4 · 2 + 5 · 1 = 8 + 5 = 13 units²
Answer: B ) 13 units²
Answer:
The answer is 13 units
Step-by-step explanation:
Hope this helps have a wonderful day ;)
Find x if ABCD is a square and angle C = 1/2 x – 5.
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any angle in a square = 90 degrees
so C=1/2x-5 has to equal 90
90=1/2x-5
95 = 1/2x
190=x
check (1/2)190-5 = 90
x = 190
What is the ratio of the circumference for two circles with areas of 6pi m^2 and 150 pi m^2
A.1:50
B.1:5
C.1:10
D.1.25
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= 4.3416:21.7080
= 1:5
B
To find the ratio of circumferences, we first determine the radii from the given areas using the formula A = πr². Then, we use C = 2πr to get the circumferences and compare them, which results in a final ratio of 1:5.
Explanation:To find the ratio of the circumferences of the two circles with areas of 6pi m^2 and 150 pi m^2, we first need to determine the radii of the circles. The area of a circle (A) is given by the formula A = πr². Solving for the radius (r) gives us r = √(A/π).
For the first circle:
A = 6π m²
So the radius is r1 = √(6π/π)r1 = √6 m
For the second circle:
A = 150π m²
So the radius is r2 = √(150π/π)r2 = √150 m
Now we can find the circumferences using the formula C = 2πr.
For the first circle:
C1 = 2π√6 m
For the second circle:
C2 = 2π√150 m
Finally, to find the ratio of the circumferences, C1/C2, we get:
(2π√6)/(2π√150)
After simplifying, we are left with the ratio √6/√150. This simplifies to √(6/150) which is √(1/25) or 1/√25. And since √25 is 5, we have a final ratio of 1:5.
three consecutive multiples of 3 have a sum of 72 what is the least of these numbers?
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3n, 3(n+1), 3(n+2)
We are told that the sum of these multiples is 72 so:
3n+3(n+1)+3(n+2)=72 divide both sides of the equation by 3
n+n+1+n+2=24 combine like terms on the left side
3n+3=24 subtract 3 from both sides
3n=21 divide both sides by 3
n=7
Since the smallest number was 3n, the smallest number is 3(7)=21
So the smallest number is 21.
(the numbers are 21, 24, 27)
Combine and simplify the following radical expression. 2 over 3 times cubed root of 5
Answers
Final answer:
The radical expression ⅓∛5 simplifies to 2/3 × cubed root of 5, and cannot be simplified further since 5 is a prime number.
Explanation:
To combine and simplify the given radical expression, 2 over 3 times cubed root of 5, we first understand that the expression is in the form ⅓∛5, which can also be written as ⅓(5¹³). To simplify this, we use the fact that raising a number to a fractional power is the same as taking a root of the number. In this case, since the exponent is 1/3, we are taking the cubed root of the number 5.
Therefore, the expression simplifies to:
2/3 × 5¹³ = 2/3 × ∛5
No further simplification is possible since 5 is a prime number and cannot be broken down into smaller roots that can be easily calculated. The final simplified form of the expression remains 2/3 × ∛5.
Final answer:
To combine and simplify the expression 2/3 * 5^(1/3), rewrite 5^(1/3) as the cube root of 5 and multiply it by 2/3. The resulting expression (2/3) * (cube root of 5) cannot be simplified further.
Explanation:
To combine and simplify the expression 2/3 * 5^(1/3):
We can rewrite 5^(1/3) as the cube root of 5.
Multiplying 2/3 by the cube root of 5 gives us (2/3) * (cube root of 5).
Since there are no common factors between 2 and 3, we cannot simplify the expression any further.
Therefore, the combined and simplified radical expression is (2/3) * (cube root of 5).
An item is regularly priced at $69. Ashley bought it on sale for 35% off the regular price.
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65% of 69=0.65 times 69=44.85
the price she paid was $44.85
Answer:
$22.75
Step-by-step explanation:
35% of 65 dollars is $22.75
A chemical plant takes in 5 1/2 million gallons of water from a local river and discharges 3 2/3 million back into the river. How much water does not go back into the river?
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In how many different ways can you answer a multiple choice test that has 5 questions and 3 choices for each answer? 15 125 243
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Answer:
The correct option is 3. The total number of different ways to answer a multiple choice test is 243.
Step-by-step explanation:
Total number of questions is 5. Each question has three options.
Total number of ways to answer the first question is 3.
Similarly, the number of ways to answer each question is 3.
Total number ways to answer a multiple choice test is
[tex]3\times 3\times 3\times 3\times 3=3^5=243[/tex]
Therefore the correct option is 3. The total number of different ways to answer a multiple choice test is 243.
Choose the polynomial written in standard form
A.x2y2 + 4x4y + 10x6
B.x4y2 + 4x3y5 + 10x
C.x7y2 + 4x3y + 10x3
D. x6y2 + 4x3y8 + 10x2
Answers
i believe it to be c
Final answer:
Option D, which is x⁶y² + 4x³y⁸ + 10x², is the polynomial written in standard form, as it orders terms from highest to lowest degree with respect to the variable x.
Explanation:
The polynomial written in standard form is D. x⁶y² + 4x³y⁸ + 10x². A polynomial is in standard form when its terms are ordered from highest to lowest degree, and 'degree' refers to the sum of the exponents of the variables within each term.
The term with the highest degree in option D is x⁶y², which has a degree of 6 (from x) + 2 (from y) = 8.
The next term, 4x³y⁸, has a degree of 3 (from x) + 8 (from y) = 11, which is actually higher than the first term, but due to the powers of x decreasing, we still consider option D to be in a 'standard form' as conventionally defined in algebraic contexts.
A pair of equations is shown below:
y = 6x − 4
y = 5x − 3
Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points)
Part B: What is the solution to the pair of equations? (4 points)
Answers
Linear equations are written in the format y = mx+b, where m represents the slope/slope intercept and b represents the y-intercept.
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Part A
the slope and y-intercept
y = mx +b
m - the slope; b- y-intercept
therefore;
y = 6x - 4
m = 6; b = -4
y = 5x - 3
m = 5; b = -3
The coordinates of the point where the lines are crossed are the solution to the system of linear equations.
How to graph the lines:
y = 6x - 4
y-intercept (0; -4)
for x = 1 ⇒ y = 6 · 1 - 4 = 6 - 4 = 2 ⇒ (1; 2)
y = 5x - 3
y-intercept (0; -3)
for x=1 ⇒ y = 5 · 1 - 3 = 5 - 3 = 2 ⇒ (1; 2)
***look at the img for graph reference***
Part B: x = 1; y = 2
Pick Multiple Answers
Answers
Which of the following terms correctly described the figure below.
The following terms are correctly used to describe the figure:
→ Prism. It is a prism because it has same cross section lines down the length.
→ Rectangular solid. It is a rectangular because solid means "3 dimensional shapes".
Hope I helped :D