Answer: The slope of the ramp is defined as the rise over the run, where the rise is the height of the step (2 feet) and the run is the horizontal distance from the bottom of the ramp to the step (7.0 feet). However, since the ramp is not straight but inclined, we need to use the length of the ramp (7.3 feet) to calculate the actual horizontal distance it covers.
Therefore, the run of the ramp is the square root of the difference between the length of the ramp squared and the height of the step squared:
run = sqrt(7.3^2 - 2^2) = sqrt(52.29 - 4) = sqrt(48.29) ≈ 6.95 feet
Now we can calculate the slope of the ramp:
slope = rise / run = 2 / 6.95 = 0.2885 ≈ 2/7
Therefore, the slope of the ramp is approximately 2/7.
I need help solving this quadratic equation. 3y(-2y+x)-5y(-7x+y)
The solutions to the quadratic equation 3y(-2y+x)-5y(-7x+y) are y = -16x + 32x√2 and y = -16x - 32x√2
To solve the quadratic equation 3y(-2y+x)-5y(-7x+y), we first need to simplify it by distributing the terms inside the parentheses:
3y(-2y+x) = -6y² + 3xy
-5y(-7x+y) = 35xy - 5y²
Next, we can substitute these expressions back into the original equation and simplify it further:
3y(-2y+x)-5y(-7x+y) = (-6y² + 3xy) - (35xy - 5y²) = -6y² + 3xy - 35xy + 5y² = -y² - 32xy
Now, we have simplified the quadratic equation to the standard form of ax² + bx + c = 0, where a = -1, b = -32x, and c = 0. To solve for y, we can use the quadratic formula:
y = (-b ± √(b² - 4ac)) / 2a
Plugging in the values for a, b, and c, we get:
y = (-(-32x) ± √((-32x)² - 4(-1)(0))) / 2(-1) = (32x ± √(1024x²)) / (-2)
Simplifying further, we get:
y = -16x ± 32x√2
In conclusion, we can simplify the given quadratic equation by distributing the terms inside the parentheses, and then rearrange it to the standard form ax² + bx + c = 0. We can then use the quadratic formula to solve for y, and simplify the solutions.
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The graph of a linear function is given below. What is the zero or the function
Answer: -2
Step-by-step explanation:
You can see it clearly passes through an origin consisting of -2
Answer:
Step-by-step explanation:
A -5
A marine biologist measured one dish that was 1 1/4 of a foot and a second fish that was 3/4 of a foot long. How much longer was the first fish
Answer:
1/3 foot longer
Step-by-step explanation:
2/3-1/3=1/3
A three dimensional figure is formed by a rectangular prism and an isosceles triangular prism as shown in the diagram below
Use the information given in the image to find the surface area of the composite figure
The surface area of the composite figure is 4364 sq. m.
What is a composite figure?A composite figure that consists of more than one shape. Thereby it is formed by joining two or more shapes.
In the given composite figure, we have;
i. area of one triangular surface = 1/2 x base x height
= 1/2 x 25x13
= 162.5
area of one of its triangular surfaces is 162.5 sq. m.
ii. area of rectangular surface 1 = length x width
= 27 x 18
= 486 sq. m.
iii. area of rectangular surface 2 = length x width
= 27 x 23
= 621 sq. m.
iv. area of rectangular surface 3 = length x width
= 25 x 23
= 575 sq. m.
v. area of its base = length x width
= 27 x 25
= 675 sq. m.
surface area of the composite figure = (2*162.5) + (2*486) + (2*621) + (2*575) + 675
= 4364
The surface area of the composite figure is 4364 sq. m.
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Determine if the question is a Statistical Question
Answer:
no not satisacl
Step-by-step explanation:
which expression shows the distance between the points -2.8, 1.6
The expression shows the distance between the points -2.8, 1.6 is |x-y| units
When two numbers are pointed on the number line and they are x and y, then the expression to represent the difference between those two numbers is |x-y|
Let x = -2.8 and y = 1.6
Therefore, the distance between those two points is given by;
|x-y|
= |-2.8-1.6|
= |-4.4|
= 4.4 units.
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Tripp is training for a half marathon. He runs 3
miles his first week of training. Each week after, he runs
2 more miles than he did the week before. Which equation represents the total number of miles,
, he runs after
weeks?
Equation that represents the total number of miles he runs after weeks is n * (n + 2).
The equation that represents the total number of miles Tripp runs after "n" weeks can be written as:
Total miles = 3 + 5 + 7 + ... + (2n + 1)
We can see that the first week Tripp runs 3 miles, and every week after that, he adds 2 more miles to the previous week's total. So, for the second week, he runs 3 + 2 = 5 miles, and for the third week, he runs 5 + 2 = 7 miles, and so on.
To simplify the equation, we can use the formula for the sum of an arithmetic series:
S = (n/2) * (a + l)
where S is the sum of the series, n is the number of terms in the series, a is the first term, and l is the last term.
In this case, the first term is 3, and the last term is (2n + 1), since Tripp is adding 2 miles each week. So, we have:
Total miles = (n/2) * (3 + 2n + 1)
Simplifying this equation, we get:
Total miles = (n/2) * (2n + 4)
Total miles = n * (n + 2)
Therefore, the equation that represents the total number of miles Tripp runs after "n" weeks is:
Total miles = n * (n + 2)
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Choose the expression that is equivalent to 5^-10/(5^4)(5^0)
The expression that is equivalent to [tex]5^{-10}/(5^4)(5^0)[/tex] is [tex]5^{-14[/tex].
We can simplify the expression using the rules of exponents, which state that when we divide two powers with the same base,
we can subtract their exponents, and when we multiply two powers with the same base, we can add their exponents.
Also, any number raised to the power of zero is equal to 1.
Using these rules, we have:
[tex]5^{-10} / (5^4)(5^0) \\= 5^{-10} / (5^4) \\= 5^{-10-4}\\ = 5^{-14[/tex]
Therefore, the expression that is equivalent to [tex]5^{-10}/(5^4)(5^0)[/tex] is [tex]5^{-14[/tex].
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Can you help please i need to answer real quick please
Answer:
Step-by-step explanation:
D 48 cubic ft
draw a number line from -5 to +5
Answer:
here
Step-by-step explanation:
Answer:
Explanation:
-5 -4 -3 -2 -1 0 1 2 3 4 5
Find the value of x and y variable in the following parallelogram
Answer:
y + 5 = 3y - 1
2y = 6, so y = 3
4x - 2 = x + 10
3x = 12, so x = 4
Correct answer gets brainliest!!
Answer:
c and d
Step-by-step explanation:
it is a 2d object
so it can only be measured in 2 directions (up and side) it has no depth as it is 2 dimensional. and it is round and cannot have a point.
Answer:
D. It is a two-dimensional object.
The statement D is true about the figure above. The figure is a circle, which is a two-dimensional object.
Statement A is not true. A point is a location in space, but a circle is a shape that takes up space and has a defined area.
Statement B is not true either. A circle has only one measurement, which is its radius or diameter. The radius is the distance from the center of the circle to any point on its circumference, while the diameter is the distance across the circle through its center.
Statement C is also not true. A circle cannot "grow" into a three-dimensional object because it is a two-dimensional object that exists in a flat plane. However, multiple circles can be stacked on top of each other to form a cylinder, which is a three-dimensional object.
Translate this sentence into an equation.
Answer:v-14=42
Step-by-step explanation: Since Vidya’s age is v and when it is decreased by 14, v-14=42
Try These questions out and I’ll give you brainliest
Detailed expressions of distributive property are simplified below.
How to determine distributive property?Using the distributive property, simplify each expression as follows:
-2t(-9+9t) = 18t - 18t²
-9n(-8n-7) = 72n + 63n = 63n - 72n = -9n
-3b (6b+6) = -18b - 18
-7r(8+ 3r) = -56r - 21r²
3m(-2+3m) = -6m + 9m²
7w(-8 +3w) = -56w + 21w²
2w(-w-4) = -2w² - 8w
69(-4+8q) = -276 + 552q
-8v (-2-5v) = 16v + 40v²
-8a(7a + 2) = -56a - 16a²
5g(g-1) = 5g² - 5g
y(-9 + 6y) = -9y + 6y²
6b (8+7b) = 48b + 42b²
3r(-4r-8) = -12r² - 24r
3d(-5+8d) = -15d + 24d²
-7r(4-6r) = -28r + 42r²
-8j(7-6j) = -56j + 48j²
-3j (9+9j) = -27j - 27j²
2m(4-4m) = 8m - 8m²
8c(-5c+9) = -40c + 72c²
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I’ll give brainliest Write an inequality that represents this situation below.
Your suitcase for vacation will fit at most 11 outfits you already have 5 packed
Answer: 6 ≤ x ≤ 11
Step-by-step explanation:
Let x be the number of additional outfits that can be packed in the suitcase.
The suitcase will fit at most 11 outfits, which means that x cannot be greater than 11 outfits.
On the other hand, 5 outfits have already been packed, so the number of additional outfits that can be packed is at least 6.
Therefore, the inequality that represents this situation is 6 ≤ x ≤ 11.
In triangle FGH, m∠F=59°
and m∠H=77
Complete the equation to determine m∠G
Answer: 44 degrees
Step-by-step explanation: 59+77+x=180
x=44
Boris needs $8058 for a future project. He can invest $6000 now at an annual rate of 7%, compounded quarterly. Assuming that no withdrawals are made, how long will it take for him to have enough money for his project?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
It will take Boris approximately 4.02 years to have enough money for his project if he invests $6000 now at an annual rate of 7%, compounded quarterly.
The formula for compound interest is:
[tex]A = P(1 + \dfrac{r}{n})^{(nt)}[/tex]
where A is the future value of the investment, P is the principal amount invested, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, Boris has invested $6000 at an annual interest rate of 7%, compounded quarterly. Therefore, we have:
P = 6000
r = 0.07 (since 7% is the annual interest rate)
n = 4 (since the interest is compounded quarterly)
A = 8058
We can solve for t by rearranging the formula:
[tex]t =\dfrac{ ln(\dfrac{A}{P})} { n ln(1 + \dfrac{r}{n})}[/tex]
Substituting the values we have:
[tex]t = \dfrac{ln(\dfrac{8058}{6000}) }{ [4 ln(1 + \dfrac{0.07}{4})]}[/tex]
t ≈ 4.02 years
Therefore, it will take Boris approximately 4.02 years to have enough money for his project if he invests $6000 now at an annual rate of 7%, compounded quarterly.
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solve the expression
(x2-9)
Answer:
This equals (2x-9), you cannot simplify it more because it's a variable and number. They have to both be numbers without variables or both variables to simplify.
Step-by-step explanation:
? This makes no sensibility.....
which of the following functions represent the graph g(x) above
The function represented by the graph given is equivalent to -
g(x) = (x - 4)².
The function plotted represents a quadratic equation. A quadratic equation has a degree of 2. The given function is shifted to the left by 4 units. This means that the following transformation will take place on the x - coordinate of each and every point lying on the graph -
f(x, y) → f(x - 4, y)
So, we can write the function as -
g(x) = (x - 4)²
So, the function represented by the graph given is equivalent to -
g(x) = (x - 4)²
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HELPS PLEASE!! THE PCTURE :)
By solving it as a sequence, it will take 9 years for the club to plant 54 flowers in the courtyard.
How many years will it take for 54 flowers to grow in the courtyard?The number of years will it take for 54 flowers to grow in the courtyard is determined by solving the planting method as a sequence.
The nth term of the sequence Z is given by:
Z = a1 + (n-1)d
where Z = 54
a1 = 6
n = ?
d = d
Solving for n:
54 = 6 + (n - 1) * 6
48 = (n - 1) * 6
8 = n - 1
n = 8 + 1
n = 9
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Composite shape area
Answer:
The area of composite shapes is the area that is covered by any composite shape. The composite shape is a shape in which some polygons are put together to form a required shape. These shapes or figures can be made up of a combination of triangles, squares, quadrilaterals, etc.
explanation:
By the following steps mentioned below, we can calculate the area of the composite shapes.
Step 1: Break the compound shape into basic shapes.
Step 2: Find the area of each and every basic shape.
Step 3: Add all the areas of basic shapes together.
Step 4: Represent the answer in square units.
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The right cylinder shown below has a height of 9 meters. A cone is contained within the cylinder.
X
The cone and cylinder share a base. The vertex, X, of the cone is located in the same plane as the bottom of the cylinder and the volume of the cone is about 57 cubic
meters.
What is the radius of the cylinder (rounded to the nearest tenth, if needed)?
meters
Answer:
to the nearest tenth)?
First, we need to find the volume of the cylinder. Since we have the height and are trying to find the radius, we can use the formula for the volume of a cylinder:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
We don't know the volume of the cylinder, but we can use the volume of the cone and the fact that the cone and cylinder share a base to find the radius. The volume of a cone is given by:
V = (1/3)πr^2h
where V is the volume, r is the radius, and h is the height.
We know that the height of the cone is 9 meters and its volume is 57 cubic meters, so we can set up an equation:
57 = (1/3)πr^2(9)
Simplifying, we get:
19 = πr^2
Dividing both sides by π and taking the square root, we get:
r ≈ 2.2
Therefore, the radius of the cylinder is about 2.2 meters (rounded to the nearest tenth).
9. Emily's employer offers a pension plan that
calculates the annual pension as the prod-
uct of the final average salary, the number
of years of service, and a 2% multiplier. Her
employer uses a graded 5-year vesting for-
mula as shown. After 4 years, Emily leaves
her job. Her average salary was $65,000. 29
How much pension will she receive?
Emily will get a $1,040 annual pension payout from her former employer's pension plan.
How to Solve the Problem?Emily is not fully vested in the pension plan because she left her work after four years. She is vested in 20% of the pension plan under the graded 5-year vesting schedule.
We can use the following formula to compute Emily's annual pension:
Annual pension = (final average income) x (service years) x (2% multiplier)
Emily's final average income in this scenario was $65,000, and she worked for 4 years. As a result, her annual pension would be:
Annual pension = ($65,000) multiplied by (4 years) multiplied by 2%
Pension = $5,200 per year
Emily, on the other hand, is only vested in 20% of her pension plan because she quit her work before the entire 5-year vesting term. As a result, her real pension payment will be:
Annual pension = ($65,000) multiplied by (4 years) multiplied by 2%
Pension = $5,200 per year
Emily, on the other hand, is only vested in 20% of her pension plan because she quit her work before the entire 5-year vesting term. As a result, her real pension payment will be:
(vested percentage) x (annual pension) equals pension payment
(20% of $5,200) equals pension payout
$1,040 in pension payments
As a result, Emily will get a $1,040 annual pension payout from her former employer's pension plan.
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Deion was the lucky journalist assigned to cover the Best Beard Competition. He recorded the contestants' beard colors in his notepad. Deion also noted if the contestants were signed up for the mustache competition later in the day. Dark beard Light beard Only in the beard competition 4 3 Also in the mustache competition 3 2 What is the probability that a randomly selected contestant is only in the beard competition and has a light beard?
HELP HELP ASAPPPPPPP
The measures of angles and classification for the triangles are:
(20). m∠A = 33, m∠B = 66, m∠C = 81. Acute triangle
(21) m∠R = 20, m∠S = 140, m∠T = 20. Isosceles triangle
(22). m∠W = 75, m∠Y = 15, m∠Z = 90. Right triangle.
How to evaluate for angle measures of each trianglesThe sum of the interior angles of a triangle is equal to 180°, thus;
(20). x + 2x + 2x + 15 = 180°
x = 165/5
x = 33°
m∠A = 33
m∠B = 2(33) = 66
m∠C = [2(33) + 15] = 81
This is an acute triangle, as all its angles are less than 90°.
(21). x + 7x + x = 180°
9x = 180
x = 20
m∠R = 20
m∠S = 7(20) = 140
m∠T = 20.
This is an Isosceles triangle, because it have two equal base angles.
(22). x - 15 + 2x - 165 + 90 = 180°
3x - 90 = 180°
x = 270/3
x = 90.
m∠W = (90 - 15) = 75
m∠Y = [2(90) - 165] = 15
m∠Z = 90.
This is a Right triangle because it as one of its angle equal to 90°.
Therefore, the measures of angles and classification for the triangles are:
(20). m∠A = 33, m∠B = 66, m∠C = 81. Acute triangle
(21) m∠R = 20, m∠S = 140, m∠T = 20. Isosceles triangle
(22). m∠W = 75, m∠Y = 15, m∠Z = 90. Right triangle.
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Karen was cutting out some fabric for a friend. She cut a piece that was 6 cm wide and had an area of 36cm how long was the piece? I’m confused
The length of piece of fabric is 6 cm.
Since, Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Given that, Karen was cutting out some fabric for a friend. She cut a piece that was 6 centimeters wide and had an area of 36 square cm.
Here, area of rectangular shaped fabric is Area =Length × Width
36=Length × 6
Length =6 cm
Therefore, the length of piece of fabric is 6 cm.
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P= $1000, r = 3%, t = 2 years
The Simple Interest (SI) for a principal amount of $1000, a rate of interest of 3%, and a time period of 2 years is $60.
Using the formula for Simple Interest (SI):
SI = (P x r x t) / 100
where P is the principal amount, r is the rate of interest, and t is the time period in years.
Substituting the given values:
SI = (1000 x 3 x 2) / 100
SI = 60
Therefore, the Simple Interest (SI) for a principal amount of $1000, a rate of interest of 3%, and a time period of 2 years is $60.
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answer
pls ans pls ans pls ans
The value of k is given as follows:
k = 10.
How to obtain the value of k?The quadratic function in the context of this problem is defined as follows:
y = 3x² - 8x + 2k + 1.
The coefficients are given as follows:
a = 3, b = -8 and c = 2k + 1.
The product of the roots of quadratic function is given as follows:
c/a.
For this problem, the product is of 7, hence the value of k is obtained as follows:
(2k + 1)/3 = 7
2k + 1 = 21
2k = 20
k = 10.
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Find the surface area of the cylinder. Round your answer to the nearest tenth.
cm²
12 cm
-6 cm
Answer:
the surface area of the cylinder is about 452.2 square centimeters.
Step-by-step explanation:
To find the surface area of a cylinder, you need to use the formula: A=2πr2+2πrh where A is the surface area, r is the radius of the circular base, and h is the height of the cylinder In this case, you are given the diameter of the base as 12 cm, so you need to divide it by 2 to get the radius: r=212=6 cm
You are also given the height of the cylinder as 6 cm.
Plugging these values into the formula, you get: A=2π(6)2+2π(6)(6)
Simplifying, you get: A=72π+72π
Adding, you get: A=144π cm2
Using a calculator, you can approximate π as 3.14 and get: A≈452.16 cm2
Rounding to the nearest tenth, you get: A≈452.2 cm2
On Feb 15, if EIF costs $40/share...
How many new shares did your contribution buy?
How many total shares do you now own?
How much have you spent so far on your whole portfolio?
What is the average cost you’ve paid per share?
What is the current value of your whole portfolio?
How did you benefit from the share price dropping?
What is a downside of the share price dropping?
The new shares which the contribution buy is:
= $200 / $40/share
= 5 new shares.
How many total shares do you now own?There are 5 shares bought on Feb 15. Therefore, the total shares owned = 5.
How much have you spent so far on your whole portfolio?An amount of $200 is spent on Feb 15. So, the total spent will be $200.
What is the average cost you’ve paid per share?Average cost per share = Total spent / Total shares owned
Average cost per share = $200 / 5 shares
Average cost per share = $40/share
What is the current value of your whole portfolio?Current value of portfolio = Total shares owned × Current share price
Current value of portfolio = 5 shares × $40/share
Current value of portfolio = $200
How did you benefit from the share price dropping?I benefited from the share price dropping because the subsequent monthly contributions could buy more shares for the same amount of money.
What is a downside of the share price dropping?However, the downside of the share price dropping is that the current value of the portfolio decreases which potentially leads to lower returns when selling the shares in the future.
Missing words "To minimize risk, you’ve decided to invest your IRA money in a low cost index fund called Einstein’s Index Fund 500 (EIF). You’ve decided you can afford to invest $200 per month, and your account is set to automatically buy $200 worth of shares on or near the 15th of every month."
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