Find the slope of a ramp with a height-to-distance ratio of 1 to 12 feet.
The slope of a ramp with a height-to-distance ratio of 1 to 12 feet is 4.76 degrees.
What is the slope of a line?The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The tangent relation or the height-to-distance ratio helps to determine the slope of the line.
It is given that the height-to-distance ratio of a slope is given as 1 to 12 feet.
So,
[tex]\tan \alpha = 1/12\\\alpha= \tan^{-1}1/12\\\alpha= 4.76^\circ[/tex]
So, the slope of the ramp is about 4.76 degrees.
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2. (05.03 MC)In the figure below, AABC 2 ADEF. Point C is the point of intersection between AG and BF, while point E is the point of intersection between DG and BFДАBFProve AABC AGEC. (10 points)
Prove that Tringle ABC is congruent to tringle GEC
Once again, you're trying to get out of the classroom. The distance to the door from your desk is d meters. Your first step is 1/6 that distance. Each successive step is 1/6 the previous distance. How far have you traveled? Express each result using exponetial notation for 8 steps, 12 steps, 20 steps, and n steps.
Given:
The distance to the door from your desk is d meters.
Your first step is 1/6 that distance =
[tex]\frac{1}{6}d[/tex]Each successive step is 1/6 the previous distance.
so, the second step =
[tex]\frac{1}{6}\cdot\frac{1}{6}d=(\frac{1}{6})^2d[/tex]The third step =
[tex]\frac{1}{6}\cdot(\frac{1}{6})^2d=(\frac{1}{6})^3d[/tex]And so on,
So, for the step number n, the formula will be :
[tex]=(\frac{1}{6})^n\cdot d[/tex]So, for 8 steps
You will have traveled =
[tex]=(\frac{1}{6})^8\cdot d[/tex]For 12 steps =
[tex]=(\frac{1}{6})^{12}\cdot d[/tex]For 20 steps =
[tex]=(\frac{1}{6})^{20}\cdot d[/tex]For n steps =
[tex]=(\frac{1}{6})^n\cdot d[/tex]
At the craft store, Elena bought a bag of purple and blue marbles. She received 19 purple marbles and 6 blue marbles. What percentage of the marbles were purple? were purple?
She received 19 purple and 6 blue marbles, so the total number of marbles is 19 + 6 = 25
Percentage of purple marbles = 100 * 19/25 = 1900/25 = 76%
Percentage of blue marbles = 100 * 6/25 = 600/25 = 24%
Answer:
Percentage of purple marbles = 76%
Percentage of blue marbles = 24%
A shipping center keeps track of the number of customers in each store at Lunch times the data shows the number of customers in the 15 different stores in the shopping center last su day.
A histogram is a representation that organizes a group of data points into specified ranges.
For the given data:
4, 18 , 20, 17, 16, 23, 19, 14, 8, 8, 6, 12, 20, 14, 18
To solve the equation x/5= 30 you will ...O divide both side by 5. The solution is x=6O multiply both sides by 5. the solution is x=150O Add 5 to both sides. The solution is x=35O Subtract 5 from both sides. The solution is x=25
You have the equation:
[tex]\frac{x}{5}=30[/tex]To solve this equation you have to clear the variable x. You can clear the variable x, as follow:
You multiply both sides of the equation by 5.
[tex](5)\frac{x}{5}=30(5)[/tex]Then the solution is:
[tex]x=150[/tex]What is the equation, in slope-intercept form, of the line that passes throughthe point (8, -6) and is perpendicular to y = 4x+7?
From the problem, we are given a point (8, -6) and an equation y = 4x + 7
The equation we are to obtain is perpendicular to y = 4x + 7
In Mathematical terms, it means the slope of the given equation and the one we are to find follow the relation:
[tex]\begin{gathered} m_1\text{ = }\frac{-1}{m_2_{}_{}} \\ \text{where m}_{1\text{ }}\text{represents the slope of the first equation and }m_2\text{ represents the slope of the second equation} \end{gathered}[/tex]slope of the given equation = 4
[tex]\text{Slope of the required equation = }\frac{-1}{4}\text{ = -0.25}[/tex]The required equation passes through a point (8,-6)
The formula for obtaining the equation with a given slope that passes through a point is given as :
[tex]\text{ (y - y}_1)=m(x-x_1)[/tex]By substituting;
[tex]\begin{gathered} (y\text{ - (-6)) = -0.25(x - 8)} \\ y\text{ + 6 = -0.25x + 2} \\ y\text{ = -0.25x -4} \end{gathered}[/tex]The equation in slope-intercept form is y = -0.25x - 4
[First Person To Answer Will Get 5 Stars And Brainlyest] Help Please.
Distance is the total movement of an object without any regard to direction. Total distance jogged by Linsey is 420 yards.
What is distance?
Distance is the total movement of an object without any regard to direction
Given data
vertex 1 is at ( -4, - 1)
vertex 2 is at ( - 4, 5)
vertex 3 is at (2,5)
vertex 4 is at ( 2, -1 )
Lindseys jogs along the edge of the park in order from vertex 1 to the vertex 2 , vertex 2 to vertex 3 and vertex 3 to vertex 4 and then back to vertex 1. One unit in the coordinate grid is 20 yards.
Let us calculate distance vertex 1 and vertex 2of (-4,-1) and (-4,5)
x₁=-4,x₂=-4, y₂=5, y₁=-1
Distance=√(x₂-x₁)²+(y₂-y₁)²
Substitute the values x₁=-4,x₂=-4, y₂=5, y₁=-1 in distance formula
=√(-4+4)²+(5-(-1))²
=√6²
=6
Since 1 one unit on the coordinate gride equal 20 yd.
so 6×20=120 yards.
Now for four vertices we get 4×120=480 yards.
So total distance jogged by Linsey is 420 yards.
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Mason was creating a sundae masterpiece by adding the following chips to his ice cream. He added 1/3 cup of dark chocolate chips, 1/4 cup of milk chocolate chips, 3/4 cup of peanut butter chips, and 1/2 cup of butterscotch chips. At the last minute, he removed all of the milk chocolate chips to save to eat later. Determine how many chips he put on his sundae. Express your answer as a fraction.
Mason added 19/12 cups of chips to his sundae.
How many chips he put on his sundae?We know that Mason has a sundae and he put:
1/3 cup of dark chocolate chips.1/4 cup of milk chocolate chips (latter are removed)3/4 cup of peanut butter chips 1/2 cup of butterscotch chipsTo get the total number of chips, we just need to add these fractions (except the one for the milk chocolate chips, as these are removed).
Then we will get:
Total = 1/3 + 3/4 + 1/2 = 4/12 + 9/12 + 6/12 = 19/12
Where we used the common denominator 12 to add the fractions.
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Help me! i need this answer now i am so dead. if i get it worng please help pls
Answer:
x = 4.8
Step-by-step explanation:
Area = Length times width
12 = 2.5x Divide both sides by 2.5
4.8 = x
Which expression is equivalent to 7a-8-12a +4?A.-gaB.31aC. -5a - 4D.19a + 12
Step 1
Rearrange the expression to bring like terms together.
[tex]\begin{gathered} 7a-8-12a+4 \\ 7a-12a\text{ -8+4} \end{gathered}[/tex]Step 2
Simplify to get the final answer
[tex]-5a-4[/tex]Hence the right answer is option C
Jumping makes a frog so tired, each successive jump is 1/3 the distance of the previous hump. If a frog jumps 24 cm on its first jump, how far will the frog travel after four jumps?
Answer:
35 5/9 cm total
Step-by-step explanation:
24 + 8 + 8/3 + 8 / 9 = 35 5/9 cm
Question 23 Differentiate. f(x) = (5x - 5)(6x + 1) O f'(x) = 60x - 25 O f'(x) = 30x - 25 O f'(x) = 60x - 35 f'(x) = 60x - 12.5
We have to differentiate f(x).
We can do this as:
[tex]\begin{gathered} f(x)=(5x-5)(6x+1)=30x^2-30x+5x-5=30x^2-25x-5 \\ f\text{'}(x)=30\cdot(2x)-25\cdot(1)-0 \\ f\text{'}(x)=60x-25 \end{gathered}[/tex]The answer is f'(x)=60x-25.
Function ggg can be thought of as a translated (shifted) version of f(x)=x^2f(x)=x
2
f, left parenthesis, x, right parenthesis, equals, x, squared.
A parabola labeled f has a vertex at the point 0, 0. A parabola labeled g has a vertex at the point negative 4, negative 5.
Write the equation for g(x)g(x
The equation for g(x) is g(x) = x²-3
When x=0, f(x)= 0 and so has a vertex at (0,0)
Given that g(x) is a shifter version of f(x) and has a vertex at (0,-3), g(x) must be shifted down the y axis such that g(x)= x2+c when x=0 and g(x)= -3 -3=0+c c=-3 when x=3.
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Given that (9,-8) is on the graph of f(x), findthe corresponding point for the functionf(x - 2).Enter the correct answer.0000 CDONEClear allDOO
(7,-8)
1) Considering that f(x-2) is a transformation of f(x). Precisely, a horizontal translation to the right.
2) So, we can write out the following:
[tex]\begin{gathered} f(x)=x \\ f(9)=-8 \\ \\ f(x-2)=x \\ f(9-2)=-8 \\ f(7)=-8 \end{gathered}[/tex]Note that a horizontal translation just "pushes to the right". So there was no vertical shift.
3) Hence, the answer is (7,-8)
ARCHAEOLOGY A farm lane in Ohio crosses two long, straight earthen mounds that may have been built about 2000 years ago. The mounds are about 200 feet apart, and both form a 63° angle with the lane, as shown. Are the mounds parallel? How do you know?
Yes. Because Mound 1 and Mound 2 form a pair of corresponding angles with that red transversal line (lane). Corresponding angles are congruent and parallel to each other.
1) Since both mounds share the same measure of the angle, then we can say that those mounds are yes, parallel to the lane since they both corresponding angles, and corresponding angles are parallel and congruent to each other.
2) So the answer is :
Yes. Because each mound 1 and Mound 2 form a pair of corresponding angles with that red transversal line. Corresponding angles are congruent and parallel to each other.
a=1.9 in, A=46.5°, C=90°Solve the right triangle. Round side lengths one decimal place.
SOLUTION
Given the following
[tex]a=1.9in,A=46.5^0,C=90^0[/tex]Consider the image below
To solve the right triangle, we need to find the following:
[tex]b=\text{?,c}=\text{?and B=?}[/tex]To find B, we use the sum of angles in a triangle
hence
[tex]\begin{gathered} A^0+B^0+C^0=180^0^{} \\ \text{where A=46.5}^0,C=90^0 \end{gathered}[/tex]Substituting into the equation we have,
[tex]\begin{gathered} 46.5^0+B+90^0=180^0 \\ 136.5+B=180^0 \end{gathered}[/tex]Subtract 136.5 from both sides
[tex]\begin{gathered} 136.5+B-136.5^0=180^0-136.5^0 \\ \text{Then} \\ B=180^0-136.5 \\ B=43.5^0 \end{gathered}[/tex]hence
B = 43.5°
To find b, we use the trigonometry ratio for tangent
From the triangle above
[tex]\begin{gathered} \tan A=\frac{a}{b} \\ \text{Where A=46.5in, a=1.9in, b=?} \end{gathered}[/tex]Substituting into the equation
[tex]\begin{gathered} \tan 46.5=\frac{1.9}{b} \\ \text{Then } \\ b=\frac{1.9}{\tan46.5} \\ \text{Where tan46.5=1.0538} \end{gathered}[/tex]Then
[tex]b=1.8030[/tex]hence
b = 1.8in to 1 decima place
To find c, we also apply trigonometry ratio for sine of an angle
[tex]\begin{gathered} \text{sinA}=\frac{opposite}{\text{hypotenuse}} \\ \text{Where } \\ A=46.5^0,\text{ opposite =1.9in},\text{ hypotenuse =c} \end{gathered}[/tex]Substituting the values into the equation we have,
[tex]\begin{gathered} \sin 46.5=\frac{1.9}{c} \\ Multiply\text{ both sides by c, we have } \\ c\times\sin 46.5=\frac{1.9}{c}\times c \\ \text{Then } \\ c\times\sin 46.5=1.9 \end{gathered}[/tex]Divide both sides by 1.9, we have
[tex]\begin{gathered} c=\frac{1.9}{\sin 46.5}=\frac{1.9}{0.7254} \\ \text{Then} \\ c=2.6193 \end{gathered}[/tex]hence
c = 2.6 in
Therefore, to solve the right triangle, we have
Answer; B = 43.5°, b = 1.8in, c = 2.6 in
What’s the correct answer answer asap for brainlist
Answer: C
Step-by-step explanation: A is definitely not correct. not b. not d
The money was distributing un equally. Because of the great depression, the lower classes made less money
The average age of 6men is 35years and the average age of 4 of them is 32years. Find the age of the remaining 2 men if one is 3years older than the other
The age for two men is 39.5 and 42.5.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific variables in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables.
Given:
Average of 6 men = 35
Average of 4 men = 32
So, Total age of 6 men
=6x35
=210 years
and, Total age of 4 men
=32 x 4
=128 years
Then, the remaining age for 2 people
= 210 - 128
=82 years
Let the age for two be x and y
then , x+ y=82
and x-y=3
On solving
2x =85
x=42.5 years
and y=39.5 years
Hence, the age for two men is 39.5 and 42.5.
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-9(x-4)=81 i know what im doing im jsur stuck
Solution:
The equation in the question is given below as
[tex]-9(x-4)=81[/tex]Step 1:
Expand the brackets in the qu
Many delivery trucks feature a "How Am I Driving?” sticker on the rear bumper, along with a phone number. This sticker allows drivers to report erratic driving by the truck driver or offer a compliment if they like. A dispatcher at the trucking station accepts calls and records information from those who call the phone number. The dispatcher reports that in the past month, 218 calls were received. Of those calls, 178 reported negative driving behaviors by the truck drivers. How might this data-collection method produce bias in obtaining an estimate of all drivers who are satisfied with the company’s truck drivers?
This sample may lead to nonresponse bias because many drivers may not call the phone number.
This sample may lead to undercoverage bias because some drivers will be more likely to be included in the sample.
The sample may lead to response bias because some who call the phone number may not provide a truthful opinion.
This sample may lead to voluntary response bias because drivers can choose to call the phone number and register an opinion.
The way in which this data-collection method produce bias in obtaining an estimate of all drivers who are satisfied with the company’s truck drivers is that: D. This sample may lead to voluntary response bias because drivers can choose to call the phone number and register an opinion.
What is sampling bias?A sampling bias can be defined as a type of bias in which members of an intended population are selected in such a way that some members have a higher or lower sampling probability (chances) than the other members.
This ultimately implies that, a sampling bias would occur when members of an intended population are selected incorrectly and as such resulting in a sample that is not representative of the entire population.
Generally speaking, a voluntary response sample is a data-collection technique (method) that is always biased because it only include individuals who choose to volunteer, unlike a simple random sample.
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A 5-gallon radiator is full and contains a 40% solution of antifreeze. how much needs to be drained out and replaced with pure antifreeze to obtain a 70% solution?
Solution:
Let x be the number of antifreeze solution. Thus;
[tex](0.4)x+1(5-x)=0.7x[/tex]We would solve for x;
[tex]\begin{gathered} 0.4x+5-x=0.7x \\ \\ 5=x-0.4x+0.7x \\ \\ 5=1.3x \\ \\ x=\frac{5}{1.3} \\ \\ x=3.85 \end{gathered}[/tex]Hence, the amount needs to be drained out is;
[tex]\begin{gathered} 5-x=5-3.85 \\ \\ =1.15 \end{gathered}[/tex]Answer: 1.15 gallon
The graphs below have the same shape. What is the equation of the blue graph? Gox= ?
Here, we want to deduce the equation of the blue graph
From what we have, we can see that the image of the f(x) was moved 2 units to the right and 1 unit upwards
What this mean is that, we have 1 added to the y value and 2 added to the x value
So, the equation of the blue graph is
[tex]G(x)=(x+2)^2+1[/tex]1. Solve for xWxk=for x
Answer:
x=W/k
Explanation:
Given the equation
[tex]W=xk[/tex]To solve for x, we divide both sides of the equation by k.
[tex]\begin{gathered} \frac{W}{k}=\frac{xk}{k} \\ x=\frac{W}{k} \end{gathered}[/tex]Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex. (7,2) (-4,0) (-6, -7)
ANSWER:
STEP-BY-STEP EXPLANATION:
[tex]undefined[/tex]Find the distance between the two points in simplest radical form.
(6,9) (9,6)
Answer:
3√2
Step-by-step explanation:
[tex] \sqrt{ {(6 - 9)}^{2} + {(9 - 6)}^{2} } [/tex]
[tex] \sqrt{ {( - 3)}^{2} + {3}^{2} } [/tex]
[tex] \sqrt{9 + 9} = \sqrt{2 \times 9} = \sqrt{2} \sqrt{9} = 3 \sqrt{2} [/tex]
The circle graph shows how the annual budget for a company is divided by department. Use this graph to answer the questions below.(a) Which department gets approximately one-fourth of theannual budget?Select OneSupportEngineeringMediaEditorialResearch(b) Approximately what percentage of the budget goes toEngineering and Support combined?20% O 40%60%80%SalesХ5?
Observe the given graph carefully.
In a circle graph, the circle is divided into different sectors, each characterized by its central angle.
The complete circle measures 360 degrees. So the complete distribution (100% data) corresponds to 360 degrees.
In the given problem, we are concerned with the budget,
[tex]360^{\circ}=100\text{ percent budget}[/tex](a)
Consider the following,
[tex]\begin{gathered} \text{ Total budget}=360^{\circ} \\ \frac{1}{4}\times\text{ Total budget}=\frac{1}{4}\times360^{\circ}=90^{\circ} \end{gathered}[/tex]So, one-fourth of the budget will correspond to the department which covers the 90-degree sector of the circle graph.
As observed from the graph, the most suitable department under this criteria is the Engineering Department.
Thus, Engineering Department gets approximately one-fourth of the annual budget.
(b)
Consider that the departments Engineering and support combiningly cover a little more than one-third of the area of complete circle.
Consider the following,
[tex]\begin{gathered} 360^{\circ}=100\text{ percent} \\ 120^{\circ}=\frac{120}{360}\times100=33.33\text{ percent} \end{gathered}[/tex]Note that the area covered by the department is a little more than one-third, so the corresponding percentage value must also be a little more than 33.33%.
From the available options, 40% is the value available next to 33.33%, so this should be the most suitable choice.
Thus, it can be concluded that approximately 40% of the annual budget goes to the departments Engineering and Support combined.
Therefore, option (b) is the correct choice.
If f (x) = 4x2 + 3x − 5, then the quantity f of the quantity x plus h end quantity minus f of x end quantity all over h is equal to which of the following? a 4 times the quantity x plus h end quantity squared plus 3 times the quantity x plus h end quantity minus 5 minus 4 times x squared plus 3 times x minus 5 all over h b 4 times the quantity x squared plus 2 times x times h plus h squared end quantity plus 3 times the quantity x plus h end quantity minus 5 minus the quantity 4 times x squared plus 3 times x minus 5 end quantity all over h c the quantity 4 times x plus 4 times h end quantity squared plus the quantity 3 times x plus 3 times h end quantity minus 5 minus the quantity 4 times x squared plus 3 times x minus 5 end quantity all over h d 4 times the quantity x plus h end quantity squared plus 3 times x minus 5 minus 4 times x squared minus 3 times x plus 5 all over h
The difference quotient of the function f(x) = 4x² + 3x - 5 is [f(x + h) - f(x)]/h = 8x + 4h + 3
How to evaluate the difference quotient?The function is given as
f(x) = 4x² + 3x - 5
Start by calculating the function f(x + h)
So, we have the following
f(x + h) = 4(x + h)² + 3(x + h) - 5
Expand
f(x + h) = 4(x² + 2xh + h²) + 3(x + h) - 5
Open the brackets
f(x + h) = 4x² + 8xh + 4h² + 3x + 3h - 5
The difference quotient is then calculated as
[f(x + h) - f(x)]/h
This gives
[f(x + h) - f(x)]/h = (4x² + 8xh + 4h² + 3x + 3h - 5 - 4x² - 3x + 5)/h
Evaluate the like terms
[f(x + h) - f(x)]/h = (8xh + 4h² + 3h)/h
Evaluate the quotients
[f(x + h) - f(x)]/h = 8x + 4h + 3
Hence, the value of [f(x + h) - f(x)]/h is 8x + 4h + 3
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Complete question
If f(x) = 4x² + 3x - 5, then [f(x + h) - f(x)]/h is equal to which of the following?
4x-3
x=2
4(2)-3
The ____ property is used here.
According to the commutative property, the numbers we use can be moved around or swapped around without changing the solution. For addition and multiplication, the principle is true, but not for division or subtraction.
4x-3
Is x=2
4(2)-3
This uses the ___ attribute?
Answer:
(5,-5) commutative property of subtraction property is used.
Example:
It can be commutative if you retain the negative with the 2 and the positive with the 5. Edited: Subtraction is not a commutative operation; for example, 5-2=3 and 2-5=-3. The order of addition or subtraction does not important, though, if you maintain the sign of the integer, as in +5-2=3 and -2+5=3, for example.
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2.2.PS-141You are running a fuel economy study. One of the cars you find is blue. It can travel 39miles on21241 gallons of gasoline. Another car is red. It can travel 22 miles ongallon of gasoline. What is455the unit rate for miles per gallon for each car? Which car could travel the greater distance on 1 gallonof gasoline?CHEThe unit rate for the blue car is mile(s) per gallon.(Simplify your answer. Type an integer, proper fraction, or mixed number.)Enter your answer in the answer box and then click Check Answer.Clear AllICheck Answer2partsremainingReview progressQuestionof 8BackNext →
The blue car has traveled the greater distance on one gallon of gasoline
Explanation:The formula for calculating the unit rate is expressed as shown:
[tex]\text{Rate = }\frac{Distance}{\text{number of gallons}}[/tex]For the blue car
Distance = 39.5miles
Gallons of gasoline = 1.25 gallons
Get the unit rate:
[tex]\begin{gathered} \text{Unit rate = }\frac{39.5}{1.25} \\ \text{Unit rate = 3}1.6\text{ }miles\text{ per gallon} \end{gathered}[/tex]The unit rate of the blue car as a mixed fraction is 31 3/5 miles per gallon
For the red car
Distance traveled = 22.4 miles
Gallons of gasoline = 0.8 gallons of gasoline
Get the unit rate of the red car;
[tex]\begin{gathered} Unit\text{ rate = }\frac{22.4}{0.8} \\ \text{Unit rate = }28\text{miles per gallon} \end{gathered}[/tex]From the unit rates, we can see that the blue car has traveled the greater distance on one gallon of gasoline since its unit rate is greater than that of the red car.