Answer: D. 2w + 2(2w+3) = 96
Step-by-step explanation:
Perimeter = 2l + 2w
l = 2w + 3
Plug l into the perimeter equation
Perimeter = 2w + 2(2w+3)
Perimeter = 96
96 = 2w + 2(2w+3)
If you want to simplify, w = 22.5
What is the area formula for parallelograms?
Similar to how a rectangle's area is calculated, a parallelogram's area is calculated as base times height.
Explain about the area formula for parallelograms?The four sides of a parallelogram, a geometric shape made up of two pairs of parallel lines, are parallel. The opposite sides and angles of a parallelogram have equal lengths and measures.
By multiplying the base and altitude of a parallelogram, the area of the shape can be determined. A parallelogram's base and altitude are always parallel to one another. A parallelogram's area can be calculated using the following equation: Area of parallelogram = base height square units.
You can use the following formula to determine any parallelogram's area:
Area = base x height
It should be mentioned that a parallelogram requires a perpendicular base and height.
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A construction crew is building a circular playground.
The playground is surrounded by a fence that is 47. 1
feet long. About how much area will the playground
cover? Use 3. 14 for r. Round to the nearest tenth.
Help pls!
Rounding to the nearest tenth, the area of the playground is 176.7 square feet.
As per the data given in the question,
We have,
The shape of the playground = circular
So, for finding the area of a circle, we can use the formula of finding the area of a circle:
So, the value of the area will be: A = πr^2,
where A is the area and r is the radius.
Since the fence is 47.1 feet long,
we can assume that it is the circumference of the circle and divide it by 2π to find the radius:
47.1 feet / 2π
= 47.1 / (2 * 3.14)
= 7.5 feet
So the radius is 7.5 feet and the area of the playground is:
A = π * 7.5^2
A= 3.14 * 56.25
= 176.71 square feet
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A 6-ft observer casts a 4-ft shadow at the same time a nearby chimney casts a 238-foot shadow. How tall is the chimney?
The height of the chimney is 357 feet according to mentioned dimensions of the chimney and observer.
The ratio of base and height according to angled of elevation will be -
tan theta = perpendicular ÷ base. The same will be for chimney. Hence, equating the ratio of both to find the height of chimney.
The formula will be -
Perpendicular ÷ base of observer = perpendicular ÷ base of chimney
6/4 = height/238
Rewriting the equation according to height of chimney
Height = (6 × 238)/4
Performing multiplication on Right Hand Side of the equation
Height = 1428/4
Performing division on Right Hand Side of the equation
Height = 357
Thus, chimney is 357 feet tall.
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Redraw the triangle with sides that are 1/3 as long as the sides of the original 15 m 9 m Original 12 m a Calculate the perimeters of BOTH triangles. Perimeter (P = s + s + s) of original Perimeter of new A b. Calculate the areas of BOTH triangles. Area (A= 1 2 b^ * h) of original Area of new A . What is the relationship between the perimeters of the triangles?
The new triangle has sides of 3m, 4m, and 5m as the attached picture below.
The perimeter of the original triangle is 36 and the new triangle is 12. The area of the original triangle is 54 and the new one is 6The new triangle's perimeter is a third of the original's perimeter, which represents the ratio of both trianglesThe new triangle has sides of 1/3 of the original. Then:
1/3 x 15 m = 5m
1/3 x 9 m = 3 m
1/3 x 12 m = 4 m
The new triangle is as the attached picture below
The perimeter of the original triangle is:
P original = 15 + 9 + 12
P original = 36 m
The perimeter of the new triangle is:
P new = 5 + 3 + 4
P new = 12 m
The area of the original triangle is:
Area original = 1/2 x 12 x 9
Area original = 54 m
The area of the new triangle is:
Area new = 1/2 x 4 x 3
Area new = 6
The relationship between both triangles' perimeter is:
P original : P new = 36 : 12
= 3 : 1 --> ratio of both triangles
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what’s the answer to this question i’ve been trying my hardest and i still haven’t go it can somebody please help
a) Dilation 1 has a scale factor of 3 units.
b) Dilation 2 has a scale factor of 4 units.
c) Dilation 3 has a scale factor of 0 units.
What is a scale factor?
A scale factor is a number used to multiply the dimensions of a shape to enlarge or reduce its size. In geometry, the scale factor is used to create similar figures by preserving their shape while changing their size. If a figure is scaled up by a scale factor of 'k', its dimensions are increased by a factor of 'k'. If a figure is scaled down, its dimensions are reduced by a factor of 'k'.
For the triangle, the scale factor would be 3 units.
For the square, the scale factor would be 4 units.
For the line, the scale factor would be 0 units.
Hence,
a) Dilation 1 has a scale factor of 3 units.
b) Dilation 2 has a scale factor of 4 units.
c) Dilation 3 has a scale factor of 0 units.
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Help please!!
Use the first and last data points to find the slop intercept equation of the trend line.
The slope-intercept equation of the line that best fits the data, with a slope of 5.3333 and a y-intercept of 9.6666.
What is the slope?
The slope of a line represents the change in the dependent variable (y) for a unit change in the independent variable (x). In this case, the slope of the line of best fit represents the average change in the test grade for a one hour increase in studying. To find the slope, you can use the formula:
m = (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n)
To find the slope-intercept equation of the trend line using the first and last data points, we'll first find the slope (m) of the line. The slope can be found using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where x₁ and y₁ are the values for the first data point, and x₂ and y₂ are the values for the last data point. In this case, the first data point is (1, 15) and the last data point is (7, 47):
m = (47 - 15) / (7 - 1) = 32 / 6 = 5.3333
Next, we'll use the slope and the first data point to find the y-intercept (b) using the formula:
b = y₁ - m * x₁
b = 15 - 5.3333 * 1 = 15 - 5.3333 = 9.6666
Finally, we'll use the slope and y-intercept to write the slope-intercept equation of the line:
y = mx + b
y = 5.3333x + 9.6666
Hence, the slope-intercept equation of the line that best fits the data, with a slope of 5.3333 and a y-intercept of 9.6666.
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Answer:
[tex]y=\dfrac{16}{3}x+\dfrac{29}{3}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
The first and last data points of the given table are:
(1, 15)(7, 47)Substitute the data points into the slope formula to find the slope of the trend line:
[tex]\text{Slope}\;(m)=\dfrac{47-15}{7-1}=\dfrac{32}{6}=\dfrac{16}{3}[/tex]
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Substitute the found slope and the first data point into the slope-intercept formula and solve for b:
[tex]\implies 15=\dfrac{16}{3}(1)+b[/tex]
[tex]\implies 15=\dfrac{16}{3}+b[/tex]
[tex]\implies b=15-\dfrac{16}{3}[/tex]
[tex]\implies b=\dfrac{45}{3}-\dfrac{16}{3}[/tex]
[tex]\implies b=\dfrac{45-16}{3}[/tex]
[tex]\implies b=\dfrac{29}{3}[/tex]
Therefore, the equation of the trend line in slope-intercept form is:
[tex]y=\dfrac{16}{3}x+\dfrac{29}{3}[/tex]
How many inches is 5 3 height?
Height is 63 inches, or 5 3 inches.
Explain about the inches?A measurement of distance or length in US units. A foot is 12 inches long and a yard is 36 inches long. 2.54 cm are exactly one inch.
A measurement of 1 inch is about equivalent to 2.54 cm. Add 2.54 cm to the provided inch number to convert it to centimetre values. 0.393701 inches are equal to 1 centimetre.
The smallest length you can measure with a ruler is 1/16 inch since each inch is divided into 16 lines, each of which is 1/16 inch long.
If you don't have a measuring device around, use the top of your thumb or another item that is roughly the same length to estimate measurements in inches. A foot is made up of 12 inches.
= (5 x 12) + 3.
= 60 +3
= 63
You now have 63 inches altogether.
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Why are there 52 weeks in a year and not 48 weeks given that there are only 4 weeks per month (4 x 12 = 48)?
A month does not have four weeks, nor does a year have 52 weeks.
The ISO week-numbering year, however, has 52 or 53 weeks.
That translates to 364 or 371 days rather than the typical 365 or 366 days.
Are there 4 weeks in every month?Since every month has at least 28 days, every month has 4 full weeks.
There are extra days in some months.
1 week = 7 days.
For the months of January, March, May, July, August, October, and December, a month has 4 weeks and 3 days.
A month in April, June, September, and November has 4 weeks and 2 days.
February in a leap year has 4 weeks and 1 day in a month.
There are around 29 days more than a calendar year.
Which means 4 weeks plus some days.
From 12 month: 4 × 12 = 48 weeks.
Form 29 extra days: 4 weeks and 1 days.
Total weeks: 52 weeks in a year.
Total days: 52 × 7 + 1 = 365 days in a year.
In a leap year, the month of February has 4 weeks and 1 day.
366 days make up a leap year.
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scatterplot is the best visualization for showing which of the following (choose one or more)? group of answer choices indirect or negative relationship between two ratio variables the relationship between two interval/ratio variables correlation frequency of two nominal variables
Scatterplots are best for showing the relationship between two interval/ratio variables and indirect or negative relationship between two ratio variables.
Scatterplots are best for showing:
⇒the relationship between two interval/ratio variables
⇒indirect or negative relationship between two ratio variables
Scatterplots display points on a coordinate plane, with one variable plotted on the x-axis and the other variable plotted on the y-axis. This allows us to see the pattern of relationship between the two variables. If there is a positive or negative relationship, we can see if the points tend to increase or decrease as we move from left to right or from bottom to top. If the relationship is indirect, we can see if the points tend to curve in one direction or another.
Scatterplots are not the best visualisation for showing: correlation
frequency of two nominal variables
For showing correlation, a line of best fit (regression line) can be added to a scatterplot, but other visualizations such as a correlation matrix or a heat map are more commonly used.
For showing frequency of two nominal variables, a two-way table or a mosaic plot are better suited, as they can display the count or proportion of cases for each combination of the two nominal variables.
Therefore, Scatterplots are best for showing the relationship between two interval/ratio variables and indirect or negative relationship between two ratio variables.
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Scatterplots are best for showing the relationship between two interval/ratio variables and indirect or negative relationship between two ratio variables.
Scatterplots are best for showing:
⇒the relationship between two interval/ratio variables
⇒indirect or negative relationship between two ratio variables
Scatterplots display points on a coordinate plane, with one variable plotted on the x-axis and the other variable plotted on the y-axis. This allows us to see the pattern of relationship between the two variables. If there is a positive or negative relationship, we can see if the points tend to increase or decrease as we move from left to right or from bottom to top. If the relationship is indirect, we can see if the points tend to curve in one direction or another.
Scatterplots are not the best visualization for showing: correlation
frequency of two nominal variables
For showing correlation, a line of best fit (regression line) can be added to a scatterplot, but other visualizations such as a correlation matrix or a heat map are more commonly used.
For showing frequency of two nominal variables, a two-way table or a mosaic plot are better suited, as they can display the count or proportion of cases for each combination of the two nominal variables.
Therefore, Scatterplots are best for showing the relationship between two interval/ratio variables and indirect or negative relationship between two ratio variables.
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Goran buys candy that costs $8 per pound. He will spend at least $56 on candy. What are the possible numbers of pounds he will buy?
Use P for the number of pounds Goran will buy.
Write your answer as an inequality solved for p.
The inequality is written as 8p ≤ 56. Then the number of pounds of candy will be 7 pounds.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Goran buys candy that costs $8 per pound. He will spend at least $56 on candy.
Let 'p' be the number of pounds of the candy. Then the inequality is given as,
8p ≤ 56
p ≤ 56 / 8
p ≤ 7
The inequality is written as 8p ≤ 56. Then the number of pounds of candy will be 7 pounds.
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Jane has $14000 in a savings account that earns 2.5% annually. How much interest will she have earned after 9 months?
Answer:
Below
Step-by-step explanation:
Interest for a WHOLE 12 months would be 14 000 * .025 = 350
but Jane had the account for 9 out of 12 months
9/12 * 350 = 262.50 dollars
Which equation represents a tangent function with a domain of all real numbers such that x is not equal to pi over 2 plus pi times n comma where n is an integer?.
y = tan(x) - (π/2 + πn)
This equation represents a tangent function with a domain of all real numbers, except for multiples of pi/2 plus pi.
The equation y = tan(x) - (π/2 + πn) represents a tangent function with a domain of all real numbers except for multiples of pi/2 plus pi. This equation is useful for finding the tangent value of any given x-value, as long as it is not equal to a multiple of pi/2 plus pi. The equation works by subtracting the multiple of pi/2 plus pi from the x-value, and then finding the tangent of the new value. This allows the tangent of the x-value to be found, regardless of whether or not it is equal to a multiple of pi/2 plus pi.
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find 6.50) The difference between annual compound interest on a ca sum of money for two years at 20% p.a. and semi- compound interest on the same sum of money at the same of interest and for the same period of time is Rs. 482 Calculate the sum (Ans: Rs. 20000
The sum of compound interest on a sum of money is (principal ) Rs 2000.
How is compound interest determined?CI = P*(1+R/100) is the formula for compound interest, which is computed by multiplying the starting principle amount by one and annual interest rate multiplied by the number of compound periods minus one (T)
CI = A – P
Periodic compounding formula is another name for this formula. In this case, A stands for the updated principle amount or the entire sum of money after the compounding period. P stands for the first or original quantity.
now we have :-
time (annual)=2
time (semi-annual)=4
rate (annual)= 20
rate (semi-annual=10
difference compound interest = 482
CI(semi-annual)-CI(annual) =482
P*(1+10/100)^(4) - P*(1+20/100)^(2)=482
P{ (14641/10000) - (36/25)}= 482
P(241/10000)=482
P=(482*10000)/241
P= 20000.
So, sum of money is (principal ) Rs 2000.
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Sandra, Davion, Taylor, and James each purchased a medium soda from the concession
stand at a soccer game. At the end of the game, Sandra drank of her soda, Davion drank
82% of his, Taylor drank 0.85 of hers, and James drank of his. Who drank the most soda
from their cup?
James and Sandra drank the most soda from their cup.
Why are they the persons that drank most?The information that was given gave specific amount that each person drank from their soda, but James and Sandra were not given a specific amount, so one can only assume they drank the most since their own percentage of drink is not disclose.
Percentage is a way to express a number as a fraction of 100. It's often denoted using the symbol "%". For example, 50% means 50 per 100, or one half
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Pls Help will give brainlyest (15 pts)
Answer:
r ≥2, r<0
Step-by-step explanation:
1st blank:
1. Multiply both sides by 2
2. Simplify. 7r-20≥ -6
2nd blank:
1. multiply both sides by 2 to get (2(r+14))/2 < 7*2.
2. Simplify. You should get r+14 <14
3. Subtract 14 from both sides to isolate r.
4. Answer is r<0
Able, Baker, and Charlie are the only three stocks in an index. The stocks sell for $37, $312, and $94, respectively. If Able undergoes a 3-for-4 reverse stock split, what is the new divisor?
In order to calculate the new divisor for a 3-for-4 reverse stock split, we must first calculate the new share price for Able. Since 3/4 of the shares are being replaced with just 1/4 of the old shares, the new price for Able will be $111 (3 x $37 = $111).
The divisor is used to calculate the new index value by dividing the sum of the new share prices by the divisor. Therefore, the new divisor will be 1.33 ($111 + $312 + $94 = $517 / 1.33 = $389.28). This is because the new share prices will total $517 and when you divide that by the divisor, the index value will be $389.28.
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solve the initial value problem. ′=−2,(0)=−4 (express numbers in exact form. use symbolic notation and fractions where needed.)
According to the concept of fraction the value of the quantity at any time t is -4.
A fraction is a mathematical representation of division of two numbers. In this case, we will be using fractions to solve an initial value problem.
The initial value problem is ′=−2,(0)=−4.
This means that the rate of change of the quantity is -2 and its starting value at time 0 is -4.
To solve this problem, we need to find the value of the quantity at some other time.
Here the first step is to find the general solution to the differential equation ′=−2.
This can be done by integrating both sides, which gives us
=> −2.
Integrating, we get
=> −2 + C, where C is an arbitrary constant.
Next, we use the initial value to find the value of C.
We know that when t=0, the value of the quantity is -4, so we can substitute these values into the general solution to get
=> -4 = -2 + C.
Solving for C, we get C = -2.
Finally, we substitute C into the general solution to get
=> -2 -2 = -4.
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Part 1 of 2
Use the GCF and the Distributive Property to find the sum.
30+42
Write each number as a product using the GCF as a factor, and apply the Distributive Property.
30+ 42 =
(Use the operation symbols in the math palette as needed. Do not simplify.)
The expression when evaluated is 72 and the expression is 6 * (5 + 7)
How to evaluate the expression using the propertyThe greatest common factor (GCF) of 30 and 42 is 6. We can write each number as a product of 6 and another factor:
30 = 6 * 5
42 = 6 * 7
Now we can use the distributive property to find the sum:
30 + 42 = 6 * 5 + 6 * 7
= 6 * (5 + 7)
= 6 * 12
= 72
So, the sum of 30 and 42 is 72.
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PLEASE HELPPPPPLLLLPPP
In the given diagram, 4 = 45°, 5= 135°, and 10 11.
Part A: Solve for the values of the remaining angles. Show all of your work.
Part B: Use complete sentences to describe the angle relationship between the following angle pairs:
<4 and <1
<7 and <5
<9 and <10.
PLEASE HELP
Answer:
Step-by-step explanation:
Part A:
To find the value of the remaining angles, we can use the fact that the sum of the angles in a triangle is 180°.
First, let's find the value of <1. We have:
<4 + <1 + <2 = 180°
4 + <1 + (180° - 5 - 4) = 180°
4 + <1 + 171° = 180°
<1 = 5°
Next, let's find the value of <7. We have:
<7 + <5 + <6 = 180°
<7 + 135° + (180° - 10 - 5) = 180°
<7 + 135° + 165° = 180°
<7 = 0°
Finally, let's find the value of <9. We have:
<9 + <10 + <11 = 180°
<9 + 11° + (180° - 10 - 11) = 180°
<9 + 11° + 159° = 180°
<9 = 0°
Part B:
The angle <4 is supplementary to angle <1, meaning they add up to 180°.
The angle <7 is congruent to angle <5, meaning they have the same measure.
The angle <9 is congruent to angle <10, meaning they have the same measure.
A peron purchaed 10 egg for ₹4 and old 8 egg for ₹4. The profit or lo in the bargain will be
The person incurred a loss of: ₹8 in the bargain.
The person purchased 10 eggs for ₹4 each, so the total cost of the eggs is:
10 * 4 = ₹40.This is the money they spent on buying the eggs.
They then sold 8 eggs for ₹4 each,
so the revenue from the sale is:
8 * 4 = ₹32.This is the money they received from selling the eggs.
To calculate the profit or loss in the transaction, we subtract the cost from the revenue:
₹32 - ₹40 = -₹8.A negative result indicates a loss. So, in this case, the person incurred a loss of ₹8 in the bargain. This means they received less money from selling the eggs than what they spent on buying them.
Complete Question:
"A person purchased 10 eggs for ₹4 and sold 8 eggs for ₹4. The profit or loss in the bargain will be?"
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At the beginning of spring, Shaniece planted a small sunflower in her
backyard. When it was first planted, the sunflower was 25 inches tall. The
sunflower then began to grow at a rate of 0.5 inches per week. How tall would
the sunflower be after 10 weeks? How tall would the sunflower be after w
weeks?
Please help fast!!!!
The sunflower be after w weeks would be 25 + 0.5 * w inches tall.
What do you mean by algebraic expression?Let's say James and Natalie were playing with matchsticks when they had the idea to create number patterns with them. James made the number 4 with four matchsticks. In order to create a pattern with two 4s, Natalie added three extra matchsticks. They understood that they could keep adding three matchsticks each round to make an additional "four" by doing so. They deduced from this that, generally speaking, in order to create a pattern with n number of 4s, you need 4+ 3(n-1) sticks. We refer to 4+ 3(n-1) as an algebraic expression in this case.
To calculate the height of the sunflower after 10 weeks, we can use the formula:
height = starting height + growth rate * time elapsed
where the starting height is 25 inches, the growth rate is 0.5 inches per week, and the time elapsed is 10 weeks.
So the height after 10 weeks would be:
height = 25 + 0.5 * 10 = 25 + 5 = 30 inches
Therefore, the sunflower would be 30 inches tall after 10 weeks.
To calculate the height after w weeks, we can use the same formula:
height = 25 + 0.5 * w
So the height after w weeks would be:
height = 25 + 0.5 * w inches
This gives you the height of the sunflower in inches after w weeks of growth.
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which type of chart makes this most apparent
A bar chart is the best type of chart to visualize the comparison of values over a period of time. It is easy to read and makes it easier to compare and contrast each value. The bars make it easy to see the changes in values over time.
A bar chart would make this most apparent.
A bar chart is the best type of chart to visually represent the comparison of values over a period of time. It is simple to read, and makes it easier to compare and contrast each value.
A bar chart is the best type of chart to visualize the comparison of values over a period of time. It is easy to read and makes it easier to compare and contrast each value. The bars make it easy to see the changes in values over time.
A bar chart is the best type of chart to visually represent the comparison of values over a period of time. It is simple to read, and makes it easier to compare and contrast each value.
A bar chart is the best type of chart to visualize the comparison of values over a period of time. It is easy to read and makes it easier to compare and contrast each value. The bars make it easy to see the changes in values over time.
the complete question is :
Which type of chart makes it most apparent that one group has a significantly higher value than the other?
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Solve for x: 3 < x + 3 < 6
A. 6 < x < 9
B. 6 > x > 9
C. 0 < x < 3
D. 0 > x > 3
Answer:
C
Step-by-step explanation:
create two inequalities:
3 < x + 3 and x + 3 < 6
0 < x and x < 3
Proposed solutions for which any denominator equals ____ are excluded from the solution set of a rational equation.
Answer:
0
Step-by-step explanation:
I believe it's 0, because if the denominator is equal to 0, our answer would be undefined
use the chain rule of differentiation to find the derivative with respect to t of g(t)=cos(ωt) .
the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get: ∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2- 2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0
a. The region D in the x-y plane is illustrated in the figure below.
b. ∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0
a. The region D in the x-y plane is the area bounded by the two parabolas y= 2x2 and y= 1 x2. This can be seen in the sketch below.
b. To evaluate the integral ∫∫ df(x,y)dxdy, we need to evaluate the integral of the function f(x,y) = x2y over the region D. We can do this by setting up the integral as follows:
∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy
Next, we can evaluate the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get:
∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0
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Ethan is 1.85 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 28.45 meters. He stands 24.3 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
The height of the tree that casts a shadow is 28.45 meters will be 12.68 meters.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
Ethan is 1.85 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 28.45 meters. He stands 24.3 meters away from the tree.
Then the height of the tree is given as,
h / 1.85 = 28.45 / (28.45 - 24.3)
h / 1.85 = 28.45 / 4.15
h = 1.85 x 28.45 / 4.15
h = 12.68 meters
The height of the tree that casts a shadow is 28.45 meters will be 12.68 meters.
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the equation for line r can be written as y= 1 2 x 8. line s, which is perpendicular to line r, includes the point (2, – 7). what is the equation of line s?
If the line "r" written as y = 1/2x + 8. is perpendicular to Line "s" which includes the point (2,-7) , then the equation of line"s" is y = -2x -3 .
The Equation of Line perpendicular to another line can be found by interchanging the x and y variables and negating the slope sign .
The equation of line r is : y = 1/2x + 8, and the slope of line r is 1/2.
The slope of a line perpendicular to line r will be the negative reciprocal of 1/2 that is -2.
So the equation of line s, which is perpendicular to line r and passes through the point (2, -7), can be written as follows:
⇒ y -(-7) = -2(x - 2)
Expanding and simplifying, we get:
⇒ y + 7 = -2x + 4 ⇒ y = -2x -3
Therefore , the equation of line s is ⇒ y = -2x -3 .
The given question is incomplete , the complete question is
The equation for line r can be written as y = 1/2x + 8. Line "s" which is perpendicular to line r, includes the point (2,-7). What is the equation of line s ?
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What is the volume of the following rectangular prism? Volume ==equals units^3 3 cubed
Answer:
To find volume of rectangular prism you must find the length, width, and height!
Step-by-step explanation:
Volume = (Width) (height) (length)
Volume= Width x height x Length
you must multiple the length, width, and height together to get VOLUME:)
HOPE THIS HELPS :)
The dog shelter serves 120 pounds of food per day. If
each dog eats 1 %4 pounds of food how many dogs are
in the shelter?
a. 26 dogs
b. 66 dogs
69 dogs
d. 96 dogs
C.
Answer:
The answer should be 20 days.
Step-by-step explanation:
The way that I solved it: 1/4 times 5.
Simplify the following expressions.
1. 11(5) - 11(4) =
2. 8(-3 + 2) =
3. 6(9) - 4(6) =
4. 7(4) - 2(0) =
5. 15(3) - 2(12) =
6. 9(5 + 3) =
7. 12(2) - 7(2) =
8. 8(3) =
9. (6)(6) =
10. 11(9) =
11. 8(5) - 2(7) =
12. 5(n) =
13. 5y(2) =
14. 13(x + 2) =
15. 16(5x - 8) =
16. 23y( 2 + 4) =
The simplification are as follows:
11(5) - 11(4) = 55 - 44 = 118(-3 + 2) = 8(-1) = -86(9) - 4(6) = 54 - 24 = 307(4) - 2(0) = 28 - 0 = 2815(3) - 2(12) = 45 - 24 = 219(5 + 3) = 9(8) = 7212(2) - 7(2) = 24 - 14 = 108(3) = 24(6)(6) = 3611(9) = 998(5) - 2(7) = 40 - 14 = 265(n) = 5n (Note: n is a variable)5y(2) = 10y13(x + 2) = 13x + 2616(5x - 8) = 80x - 12823y(2 + 4) = 23y(6) = 138y.What is simplification in mathematics?Simplification in mathematics refers to the process of making an expression, equation, or mathematical problem easier to understand, solve, or manipulate by reducing its complexity. This can be achieved by combining like terms, cancelling out common factors, reducing fractions, or using the properties of arithmetic operations.
The goal of simplification is to transform a complex expression into a simpler form that can be more easily understood or used in further mathematical analysis.
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