Zhang is constructing a loading ramp (BA) that is 4-feet high (AC). The back of the base (BC) must be 12.8 ft. How long must the entire base (BD) be?
Proportion : __________________
Front of base: __________
Total base: __________
Answers
Answer:
Step-by-step explanation:
This is a geometric means problem where the height (length AC of 4) is the geometric mean between the base BC and the base DC. The proportion is
[tex]\frac{12.8}{4} =\frac{4}{CD}[/tex] . Cross multiply to get
12.8CD = 16 and divide both sides by 12.8 to get that
CD = 1.25
That means that the length of the whole thing, BD, is
12.8 + 1.25 = 14.05
Related Questions
A 2-column table with 7 rows. The first column is labeled x with entries negative 6, negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries 8, 2, 0, negative 2, negative 1, 0, 4.
Which is a possible turning point for the continuous function f(x)?
(–2, 0)
(0, –2)
(2, –1)
(4, 0)
On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 2, 2), (0, 1), (1, 3), (2, negative 4), (4, negative 1).
On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 2, 1), (negative 2, negative 1), (0, negative 2), (0, negative 4), (2, negative 5).
Answers
A possible critical point of the function f(x) is given by: (0,-2)
What are the critical points of a function?The critical points of a function are the values of x for which:
[tex]f^{\prime}(x) = 0[/tex]
At these points, the function can change from decreasing to increasing, or vice-versa.
For the table described, we have that the function is decreasing until (0,-2), then it starts to increase, hence there can be a critical point at (0,-2).
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the area of a rectangle is (16x^2 - 9y^2) square units
Answers
Since both terms are perfect squares, factor using the difference of squares formula,
a
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PLEASE ANSWER QUICKLY
Answers
Answer:
Option (4)
Step-by-step explanation:
See attached image.
can someone please help me
Answers
Based on the knowledge of trigonometric expressions and properties of trigonometric functions, the value of the sine function is equal to - √731 / 30.
How to find the value of a trigonometric functionHerein we must make use of trigonometric expressions and properties of trigonometric functions to find the right value. According to trigonometry, both cosine and sine are negative in the third quadrant. Thus, by using the fundamental trigonometric expression (sin² α + cos² α = 1) and substituting all known terms we find that:
[tex]\sin \theta = -\sqrt{1 - \cos^{2}\theta}[/tex]
[tex]\sin \theta = - \sqrt{1 - \left(-\frac{13}{30} \right)^{2}}[/tex]
sin θ ≈ - √731 / 30
Based on the knowledge of trigonometric expressions and properties of trigonometric functions, the value of the sine function is equal to - √731 / 30.
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Find the midpoint of points A(-9, -3) and B(1, 7) graphically.
Plot the line segment AB
Answers
Answer: (-4,2)
Step-by-step explanation:
To find the midpoint of AB, we have to find the mean of the x coordinates for the x coordinate of the midpoint and the mean of the y coordinates for the y coordinate of the midpoint
So the midpoint is ((-9+1)/2,(-3+7)/2) = (-4,2)
To plot the line AB, just find the points A and B on the graph and draw a straight line from A to B
What is the explicit formula for this sequence?
-9,-3,3,9,15
Answers
Answer: A
Step-by-step explanation:
Normally in choice questions, I would choose to substitute the values into the formulas but I think it is better if I explain to you.
In a sequence, if the numbers increase by d each time and the first number in the sequence is [tex]a_{1}[/tex], then the explicit formula is [tex]a_{1}[/tex] + (n - 1)d when n is the order of the number in the sequence, like n = 1 for the first number, n = 2 for the second number and so on. Using this, we get that the answer to this problem is [tex]a_{n}[/tex] = -9 + (n - 1)6 so the answer is A
Please help em fast I really need help
lf ƒ(x) = 2(x + 1)² and g(x) = 3x- 2 determine f[g(2)]
Answers
Answer:
f(g(2)) = 50
Step-by-step explanation:
evaluate g(2) then substitute the result obtained into f(x)
g(2) = 3(2) - 2 = 6 - 2 = 4 , then
f(4) = 2(4 + 1)² = 2(5)² = 2(25) = 50
Answer:
f[g(2)] = 50
Step-by-step explanation:
Given functions:
[tex]f(x)=2(x+1)^2[/tex]
[tex]g(x)=3x-2[/tex]
We are asked to determine f[g(2)], which is known as a composite function. When solving composite functions, you always work inside out.
Step 1: Find the value of g(2) by substituting 2 for x in function g(x).
[tex]\implies g(2)=3(2)-2[/tex]
[tex]\\\implies g(2)=6-2\Rightarrow g(2)=\boxed{4}[/tex]
Step 2: Substitute the found value into the composite function.
[tex]\\\implies f[g(2)]= 2(4+1)^2[/tex]
[tex]\implies f[g(2)] = 2(5)^2 \Rightarrow 2(25) \Rightarrow \boxed{50}[/tex]
Hence, the value of the composite function f[g(2)] is 50.
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Alan will be traveling out of town for business. during his travel, he is scheduled to have 4 dinners, 5 lunches, and 3 breakfasts. his employer will pay him for these meals at the following rate: $20.20 for dinner, $10.70 for lunch, and $6.93 for dinner. what is the total amount alan will be paid for these meals?
Answers
money paid by employer to Alan is $ 155.09
word problemA word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.
money paid for dinner by employer=$20.20
money paid for lunch by employer =$10.70
money paid for breakfast by employer =$6.93
according to question,
in this problem we will simply multiply quantity of dinners with amount
to get our answer.
so as given in problem Alan scheduled 4 dinners , 5 lunches and 3 breakfast
(4×$20.20)+(5×$10.70)+(3×$6.93)
80.8+53.5+20.79
=$ 155.09
hence money paid by employer to Alan is $ 155.09
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Factorize the expressions 8a⁶ + 5a³ + 1.
Answers
Use a³+b³ +c³ - 3abc
Here a = 2a²
b= -a
And c = 1
Answer:
Step-by-step explanation:
which whole number is equal to the fraction 42/6
Answers
Answer:
7.
Step-by-step explanation:
Think of 42/6 as a division question.
42 ÷ 6.
The answer to this equation is 7.
percentage of 67 of 98
Answers
The percentages of 67 of 98 is 68.36%
Percentages and fractionsFractions are written as a ratio of two integers. According to the question we are to determine the percentage of 67 that is 98.
Fraction of 67 of 98 = 67/98
Percentage = 67/98 * 100
Percentages = 6700/98
Percentages = 68.37%
Hence the percentages of 67 of 98 is 68.36%
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Point Y is the circumcenter of ΔDEF.
Point Y is the circumcenter of triangle D E F. Lines are drawn from the points of the triangles to point Y. Lines are drawn from point Y to the sides of the triangle to form right angles and line segments Y L, Y M, and Y N. The line segments cut the sides of the triangles into 2 equal parts. The length of F Y is 3 x + 7 and the length of Y E is 5 x minus 3.
Find FY.
5
11
17
22
Answers
The length of FY in the triangle that has Y as its circumcenter is: D. 22 units.
What is the Circumcenter of a Triangle?The circumcenter of a triangle is the point where the three perpendicular bisectors of the sides of a triangle intersect.
Based on the definition of the circumcenter, and Y is the circumcenter, therefore:
YE = FY
Plug in the values
5x - 3 = 3x + 7
5x - 3x = 3 + 7
2x = 10
x = 5
FY = 3x + 7 = 3(5) + 7
FY = 22 units.
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Answer:
D
Step-by-step explanation:
PLEASE HELP!!!!
This year, the Nature Club made 3 exhibits per month for its annual fair. This year's fair has twice as many exhibits as last year's. How many exhibits were there in last year's fair?
Answers
Answer: 18
Step-by-step explanation:
There are 12 months in a year. The club made 3 exhibits each month. 3 times 12 is 36. They made twice as many as last year, so divide 36 by 2 and you get 18.
I hope this helps!
Help me please, I'm stuck
Answers
Answer:
Gradient: 5
y-intercept: (0, 15)
Step-by-step explanation:
The gradient is usually just the same as the slope, so if we write the equation in slope-intercept form, y = 5x+15, the coefficient of x value (5) is the slope. The y-intercept is when x equals 0. Plug that in to get y = 15.
Can the sides of a triangle have lengths 2, 4, and 7?
Answers
However, a right triangle cannot have those lengths (because if we inputted the values into the Pythagorean Theorem, it wouldn’t be a true equation).
Hope this helps! (:
Answer:
No, they can't
Step-by-step explanation:
According to the Triangle Inequality Theorem, the largest side cannot be greater than the sum of the other two sides.
2+4= 6<7
As you can see from this Equation NOT any two side are greater than the third making this NOT possibly be a tringle.
2+7=9>4
4+7=11>2
The volume of a box without a lid is given by the formula v = 4x(10-x)^2, where x is a length in inches and v is the volume in cubic inches. what is the volume when x = 5
Answers
The volume of the box without the lid is 500 cubic inches.
What is volume?The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.
Another way to think of volume is as the amount of space a three-dimensional object takes up.
Calculation for the volume of the box-
The volume of a box without a lid is given by the formula v = 4x(10-x)².
Where,
'x' is a length in inches, and
'v' is the volume in cubic inches.
The volume when x = 5 inches.
Substitute the value of 'x' in the formula of volume;
v = 4×5(10-5)²
= 20×5²
v = 500
Therefore, the volume of a box without a lid is 500 cubic inches.
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0.00000007 as a fraction
Answers
Answer:
7/100000000
Step-by-step explanation:
to find this out we can start by saying that 0.7 is 7/10
every 0 in front of 7 after that is adding another 0 to 10
so
0.07 is 7/100
0.00000007 is 7/100000000
A helicopter is 665 feet above the ground. A girl is looking up at the helicopter to form a line. Her line of sight is 5 feet off the ground. The distance between the girl and the helicopter is 280 feet.
A helicopter flies 665 feet above ground. What is the measure of the angle of depression from the helicopter to the girl’s line of sight? Round to the nearest degree.
23°
25°
65°
67°
Answers
The measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
What is a right angle triangle?A right angle triangle has one of its angle as 90 degrees. The sides and angles can be found using trigonometric ratios.
Therefore, angle of depression from the helicopter can be found as follows:
tan x = opposite / adjacent
where
x = angle of depression
Hence,
tan x = 660 / 280
tan x = 2.35714285714
x = tan⁻¹ 2.35714285714
x = 67.1231281953
x = 67°
Therefore, the measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
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Answer:
D = 67
Step-by-step explanation:
need help with the y value
Answers
Answer: 12x
Step-by-step explanation:
The question is asking what equation models the table above. You have to make an equation that when any of the times on the left column are plugged in, the value on the right column are outputted.
For 1, the equation should output 12. For 2, the equation should output 24. For 3, the equation should output 36, and so on.
Here, we see a pattern: for every value we input as the number of seconds, the height is 12 times more than that. Assuming x is the time and y is the height,
[tex]y=12x[/tex]
If we use any x on the left, it's corresponding height will be the y.
Please help and explain how to solve
Answers
Answer:
$ 7.52
Step-by-step explanation:
Find charge per minute
59 - 23 min = 36 minutes cost 16.32 - 10.56 = $ 5.76
or $5.76 / 36 min = 16 cents per min
from 59 to 78 = 19 more minutes x .16/min = $ 3.04
so from 59 to 78 will leave 10.56 - 3.04 = $7.52
Draw a line segment of length 6.4 cm and divide it in to 4 equal parts.
Write the length of each part.
Answers
The length of each part of a the line segment is 1.6 cm if a line segment of length 6.4 cm and divided it in to 4 equal parts
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
The line segment has a length of 6.4 cm. Hence:
Dividing into 4 equal parts = 6.4 / 4 = 1.6 cm
The length of each part of a the line segment is 1.6 cm if a line segment of length 6.4 cm and divided it in to 4 equal parts
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Determine the slope of the line.
Answers
The slope of the line is - 3 / 2 .
How to find slope?The slope of a line is the change in y coordinate with respect to the change in x coordinate.
Therefore, using (0, 6)(4, 0)
Hence,
m = slope = y₂ - y₁ / x₂ - x₁
slope = 0 - 6 / 4 - 0
slope = -6 / 4
slope = - 3 / 2
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increase $32 in the ratio 2:5
decrease 54 litter in the ratio 5:1
Answers
Answer:
Step-by-step explanation:
32 = 2 : 5
32/7 = 4
2 x 4 : 4 x 5
8 : 20
Shawn graphed the points listed below.
(0, 0) (1, -1) (3, 0) (4, 4) (4, 5) (5, 4) (6, -2)
Which pair of points could be used to show that the points Shawn graphed do not represent a function?
A. (4, 4) and (4, 5)
B. (4, 4) and (5, 4)
C. (0, 0) and (3, 0)
D. (1, -1) and (6, -2)
Answers
Answer: A. (4, 4) and (4, 5)
Step-by-step explanation:
The same x value maps onto more than one y value.
One can convert temperature from kelvin into fahrenheit using the formula . what is the temperature in kelvin corresponding to f degrees fahrenheit?
Answers
One can easily convert the temperature using temperature conversion formula given below
K = [tex]\frac{5(F - 32)}{9} + 273.15[/tex]
where F = degrees in Fahrenheit
K = degrees in Kelvin
What is temperature conversion? The measuring units of the temperature recorded in a particular unit can be converted with the aid of a temperature converter. The degree of heat or cold that a solid, liquid, or gas has is expressed by its temperature. A thermometer is used to determine temperature. Although the SI unit for temperature is Kelvin (K), most people measure temperature in Centigrade or Celsius (°C) and Fahrenheit (°F).Know more about temperature conversion https://brainly.com/question/13421795
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Answer this please !
Answers
Answer:
6
Step-by-step explanation:
[tex]\frac{y}{2} =x^{2} -7[/tex]
[tex]\frac{a}{2} =2^{2} -7[/tex]
[tex]\frac{a}{2} =-3[/tex]
[tex]a=-6[/tex]
[tex]\frac{b}{2} =1^{2} -7[/tex]
[tex]\frac{b}{2} =-6[/tex]
[tex]b=-12[/tex]
From the calculations above, we learn that line l and the curve intersect at (2, -6) and (1, -12). Next, we will set up a system of linear equations to solve for the slope and the y-intercept of line l.
[tex]-6=2m+b[/tex]
[tex]-12=m+b[/tex]
[tex]-24=2m+2b[/tex]
[tex]18=-b[/tex]
[tex]b=-18[/tex]
[tex]-12=m-18[/tex]
[tex]m=6[/tex]
Therefore, the slope of line l is 6.
Answer:
slope = 6
Step-by-step explanation:
substitute the given points into the equation of the curve to find a and b
(2, a )
[tex]\frac{a}{2}[/tex] = 2² - 7 = 4 - 7 = - 3 ( multiply both sides by 2 to clear the fraction )
a = - 6
then point (2, a ) = (2, - 6 )
(1, b )
[tex]\frac{b}{2}[/tex] = 1² - 7 = 1 - 7 = - 6 ( multiply both sides by 2 )
b = - 12
then point (1, b ) = (1, - 12 )
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (1, - 12 )
m = [tex]\frac{-12-(-6)}{1-2}[/tex] = [tex]\frac{-12+6}{-1}[/tex] = [tex]\frac{-6}{-1}[/tex] = 6
the price of an all access take it to the fair is $42.99 before tax roland bought the all access ticket for 40% off then he pay 7% sales tax on the discounted price part a how much did roland paid in sale tax? part b what is the total amount that roland paid for the ticket ?
Answers
The total amount that roland paid for the ticket is $27.60
Given that the price of an all-access ticket to the fair is $42.99 before tax. Roland bought the all-access ticket for 40% off.
We need to calculate the total amount paid by the roland
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100
The price after 40% off -
= 42.99*60% = $25.794
Sales tax on 25.794
= 25.794*7% = $1.80558
Total amount Paid for the ticket
= 1.80558 + 25.794 = $27.59958
= $27.60
Hence the total amount paid by roland is $27.60
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If my mother has 5 boys and my father has 4 girls, what is the probability of one being a boy?
Answers
Answer:
5/9
Step-by-step explanation:
4+5=9 and there are 5 boys
the graph below could be the graph of which exponential function?
Answers
The graph above could be a graph of this exponential function: A. F(x) = 3.(1.2)^x.
How to interpret the graph?Mathematically, the standard form of an exponential function is given by:
F(x) = ab^x
Where:
a is the initial value of an exponential function.b is the growth rate.As a general rule, f(x) is an increasing function when b is greater than 1 (b > 1) and f(x) is a decreasing function when b is less than 1 (b < 1)
By critically observing the given graph, we can deduce that the initial value (a) is 3 and it's an increasing function (b > 1).
F(x) = 3.(1.2)^x
Thus, the graph above could be a graph of this exponential function F(x) = 3.(1.2)^x.
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Ed wants to buy a new video game system which costs $250. he has
saved $135. ed charges $9 for each lawn he mows. which equation could
be used to find the number of lawns, x, ed must mow to have more than
the amount he needs to buy the video game system?
Answers
The required equation is 135 + 9x > 250.
The number of lawns Ed must mow is assumed to be x.
The amount Ed charges for each lawn he mows is $9.
Thus, the total amount Ed earns by mowing x lawns = $9x.
The savings which Ed has is $135.
Thus, the total amount Ed will have to spend can be written as the expression, $(135 + 9x).
The cost of the video game is given to be $250.
We are asked to write an equation, that can be used to find the number of lawns Ed mow, that is x so that the amount Ed has will be more than the amount he needs to buy the video game.
This can be shown as the equation:
Total amount Ed has > Cost of the video game,
or, 135 + 9x > 250.
Thus, the required equation is 135 + 9x > 250.
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